Jiantao Jiao

Banghua Zhu, Lun Wang, Qi Pang et al.

We propose Byzantine-robust federated learning protocols with nearly optimal statistical rates. In contrast to prior work, our proposed protocols improve the dimension dependence and achieve a tight statistical rate in terms of all the parameters for strongly convex losses. We benchmark against competing protocols and show the empirical superiority of the proposed protocols. Finally, we remark that our protocols with bucketing can be naturally combined with privacy-guaranteeing procedures to introduce security against a semi-honest server. The code for evaluation is provided in https://github.com/wanglun1996/secure-robust-federated-learning.

Tianhao Wu, Weizhe Yuan, Olga Golovneva et al. · meta-ai

Large Language Models (LLMs) are rapidly surpassing human knowledge in many domains. While improving these models traditionally relies on costly human data, recent self-rewarding mechanisms (Yuan et al., 2024) have shown that LLMs can improve by judging their own responses instead of relying on human labelers. However, existing methods have primarily focused on improving model responses rather than judgment capabilities, resulting in rapid saturation during iterative training. To address this issue, we introduce a novel Meta-Rewarding step to the self-improvement process, where the model judges its own judgements and uses that feedback to refine its judgment skills. Surprisingly, this unsupervised approach improves the model's ability to judge {\em and} follow instructions, as demonstrated by a win rate improvement of Llama-3-8B-Instruct from 22.9% to 39.4% on AlpacaEval 2, and 20.6% to 29.1% on Arena-Hard. These results strongly suggest the potential for self-improving models without human supervision.

Yifei Wang, Tavor Baharav, Yanjun Han et al. · stanford

In the infinite-armed bandit problem, each arm's average reward is sampled from an unknown distribution, and each arm can be sampled further to obtain noisy estimates of the average reward of that arm. Prior work focuses on identifying the best arm, i.e., estimating the maximum of the average reward distribution. We consider a general class of distribution functionals beyond the maximum, and propose unified meta algorithms for both the offline and online settings, achieving optimal sample complexities. We show that online estimation, where the learner can sequentially choose whether to sample a new or existing arm, offers no advantage over the offline setting for estimating the mean functional, but significantly reduces the sample complexity for other functionals such as the median, maximum, and trimmed mean. The matching lower bounds utilize several different Wasserstein distances. For the special case of median estimation, we identify a curious thresholding phenomenon on the indistinguishability between Gaussian convolutions with respect to the noise level, which may be of independent interest.

Ikechukwu Uchendu, Ted Xiao, Yao Lu et al.

Reinforcement learning (RL) provides a theoretical framework for continuously improving an agent's behavior via trial and error. However, efficiently learning policies from scratch can be very difficult, particularly for tasks with exploration challenges. In such settings, it might be desirable to initialize RL with an existing policy, offline data, or demonstrations. However, naively performing such initialization in RL often works poorly, especially for value-based methods. In this paper, we present a meta algorithm that can use offline data, demonstrations, or a pre-existing policy to initialize an RL policy, and is compatible with any RL approach. In particular, we propose Jump-Start Reinforcement Learning (JSRL), an algorithm that employs two policies to solve tasks: a guide-policy, and an exploration-policy. By using the guide-policy to form a curriculum of starting states for the exploration-policy, we are able to efficiently improve performance on a set of simulated robotic tasks. We show via experiments that JSRL is able to significantly outperform existing imitation and reinforcement learning algorithms, particularly in the small-data regime. In addition, we provide an upper bound on the sample complexity of JSRL and show that with the help of a guide-policy, one can improve the sample complexity for non-optimism exploration methods from exponential in horizon to polynomial.

Geng Zhao, Banghua Zhu, Jiantao Jiao et al. · berkeley

We study the problem of online learning in a two-player decentralized cooperative Stackelberg game. In each round, the leader first takes an action, followed by the follower who takes their action after observing the leader's move. The goal of the leader is to learn to minimize the cumulative regret based on the history of interactions. Differing from the traditional formulation of repeated Stackelberg games, we assume the follower is omniscient, with full knowledge of the true reward, and that they always best-respond to the leader's actions. We analyze the sample complexity of regret minimization in this repeated Stackelberg game. We show that depending on the reward structure, the existence of the omniscient follower may change the sample complexity drastically, from constant to exponential, even for linear cooperative Stackelberg games. This poses unique challenges for the learning process of the leader and the subsequent regret analysis.

Banghua Zhu, Ying Sheng, Lianmin Zheng et al.

Large Language Models (LLMs) and other large foundation models have achieved noteworthy success, but their size exacerbates existing resource consumption and latency challenges. In particular, the large-scale deployment of these models is hindered by the significant resource requirements during inference. In this paper, we study two approaches for mitigating these challenges: employing a cache to store previous queries and learning a model multiplexer to choose from an ensemble of models for query processing. Theoretically, we provide an optimal algorithm for jointly optimizing both approaches to reduce the inference cost in both offline and online tabular settings. By combining a caching algorithm, namely Greedy Dual Size with Frequency (GDSF) or Least Expected Cost (LEC), with a model multiplexer, we achieve optimal rates in both offline and online settings. Empirically, simulations show that the combination of our caching and model multiplexing algorithms greatly improves over the baselines, with up to $50\times$ improvement over the baseline when the ratio between the maximum cost and minimum cost is $100$. Experiments on real datasets show a $4.3\times$ improvement in FLOPs over the baseline when the ratio for FLOPs is $10$, and a $1.8\times$ improvement in latency when the ratio for average latency is $1.85$.

Gokul Swamy, Nived Rajaraman, Matthew Peng et al.

Online imitation learning is the problem of how best to mimic expert demonstrations, given access to the environment or an accurate simulator. Prior work has shown that in the infinite sample regime, exact moment matching achieves value equivalence to the expert policy. However, in the finite sample regime, even if one has no optimization error, empirical variance can lead to a performance gap that scales with $H^2 / N$ for behavioral cloning and $H / \sqrt{N}$ for online moment matching, where $H$ is the horizon and $N$ is the size of the expert dataset. We introduce the technique of replay estimation to reduce this empirical variance: by repeatedly executing cached expert actions in a stochastic simulator, we compute a smoother expert visitation distribution estimate to match. In the presence of general function approximation, we prove a meta theorem reducing the performance gap of our approach to the parameter estimation error for offline classification (i.e. learning the expert policy). In the tabular setting or with linear function approximation, our meta theorem shows that the performance gap incurred by our approach achieves the optimal $\widetilde{O} \left( \min({H^{3/2}} / {N}, {H} / {\sqrt{N}} \right)$ dependency, under significantly weaker assumptions compared to prior work. We implement multiple instantiations of our approach on several continuous control tasks and find that we are able to significantly improve policy performance across a variety of dataset sizes.

Banghua Zhu, Jiantao Jiao, Michael I. Jordan

We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). Our analysis shows that when the true reward function is linear, the widely used maximum likelihood estimator (MLE) converges under both the Bradley-Terry-Luce (BTL) model and the Plackett-Luce (PL) model. However, we show that when training a policy based on the learned reward model, MLE fails while a pessimistic MLE provides policies with improved performance under certain coverage assumptions. Additionally, we demonstrate that under the PL model, the true MLE and an alternative MLE that splits the $K$-wise comparison into pairwise comparisons both converge. Moreover, the true MLE is asymptotically more efficient. Our results validate the empirical success of existing RLHF algorithms in InstructGPT and provide new insights for algorithm design. Furthermore, our results unify the problem of RLHF and max-entropy Inverse Reinforcement Learning (IRL), and provide the first sample complexity bound for max-entropy IRL.

Paria Rashidinejad, Hanlin Zhu, Kunhe Yang et al.

Offline reinforcement learning (RL), which refers to decision-making from a previously-collected dataset of interactions, has received significant attention over the past years. Much effort has focused on improving offline RL practicality by addressing the prevalent issue of partial data coverage through various forms of conservative policy learning. While the majority of algorithms do not have finite-sample guarantees, several provable conservative offline RL algorithms are designed and analyzed within the single-policy concentrability framework that handles partial coverage. Yet, in the nonlinear function approximation setting where confidence intervals are difficult to obtain, existing provable algorithms suffer from computational intractability, prohibitively strong assumptions, and suboptimal statistical rates. In this paper, we leverage the marginalized importance sampling (MIS) formulation of RL and present the first set of offline RL algorithms that are statistically optimal and practical under general function approximation and single-policy concentrability, bypassing the need for uncertainty quantification. We identify that the key to successfully solving the sample-based approximation of the MIS problem is ensuring that certain occupancy validity constraints are nearly satisfied. We enforce these constraints by a novel application of the augmented Lagrangian method and prove the following result: with the MIS formulation, augmented Lagrangian is enough for statistically optimal offline RL. In stark contrast to prior algorithms that induce additional conservatism through methods such as behavior regularization, our approach provably eliminates this need and reinterprets regularizers as "enforcers of occupancy validity" than "promoters of conservatism."

Jinning Li, Xinyi Liu, Banghua Zhu et al.

Safe Reinforcement Learning (RL) aims to find a policy that achieves high rewards while satisfying cost constraints. When learning from scratch, safe RL agents tend to be overly conservative, which impedes exploration and restrains the overall performance. In many realistic tasks, e.g. autonomous driving, large-scale expert demonstration data are available. We argue that extracting expert policy from offline data to guide online exploration is a promising solution to mitigate the conserveness issue. Large-capacity models, e.g. decision transformers (DT), have been proven to be competent in offline policy learning. However, data collected in real-world scenarios rarely contain dangerous cases (e.g., collisions), which makes it prohibitive for the policies to learn safety concepts. Besides, these bulk policy networks cannot meet the computation speed requirements at inference time on real-world tasks such as autonomous driving. To this end, we propose Guided Online Distillation (GOLD), an offline-to-online safe RL framework. GOLD distills an offline DT policy into a lightweight policy network through guided online safe RL training, which outperforms both the offline DT policy and online safe RL algorithms. Experiments in both benchmark safe RL tasks and real-world driving tasks based on the Waymo Open Motion Dataset (WOMD) demonstrate that GOLD can successfully distill lightweight policies and solve decision-making problems in challenging safety-critical scenarios.

Banghua Zhu, Stephen Bates, Zhuoran Yang et al.

We study the hidden-action principal-agent problem in an online setting. In each round, the principal posts a contract that specifies the payment to the agent based on each outcome. The agent then makes a strategic choice of action that maximizes her own utility, but the action is not directly observable by the principal. The principal observes the outcome and receives utility from the agent's choice of action. Based on past observations, the principal dynamically adjusts the contracts with the goal of maximizing her utility. We introduce an online learning algorithm and provide an upper bound on its Stackelberg regret. We show that when the contract space is $[0,1]^m$, the Stackelberg regret is upper bounded by $\widetilde O(\sqrt{m} \cdot T^{1-1/(2m+1)})$, and lower bounded by $Ω(T^{1-1/(m+2)})$, where $\widetilde O$ omits logarithmic factors. This result shows that exponential-in-$m$ samples are sufficient and necessary to learn a near-optimal contract, resolving an open problem on the hardness of online contract design. Moreover, when contracts are restricted to some subset $\mathcal{F} \subset [0,1]^m$, we define an intrinsic dimension of $\mathcal{F}$ that depends on the covering number of the spherical code in the space and bound the regret in terms of this intrinsic dimension. When $\mathcal{F}$ is the family of linear contracts, we show that the Stackelberg regret grows exactly as $Θ(T^{2/3})$. The contract design problem is challenging because the utility function is discontinuous. Bounding the discretization error in this setting has been an open problem. In this paper, we identify a limited set of directions in which the utility function is continuous, allowing us to design a new discretization method and bound its error. This approach enables the first upper bound with no restrictions on the contract and action space.

Tianhao Wu, Banghua Zhu, Ruoyu Zhang et al.

Large Language Models (LLMs) can acquire extensive world knowledge through pre-training on large corpora. However, due to exposure to low-quality data, LLMs may exhibit harmful behavior without aligning with human values. The dominant approach for steering LLMs towards beneficial behavior involves Reinforcement Learning with Human Feedback (RLHF), with Proximal Policy Optimization (PPO) serving as the default RL optimizer. Despite its effectiveness, PPO has limitations when optimizing rewards trained from comparison-based loss. Primarily, PPO is not invariant to equivalent reward functions containing identical preference information due to the need to calibrate the reward scale. Additionally, PPO's necessity for token-wise updates introduces complexity in both function approximation and algorithm design compared to trajectory-wise optimization. This paper proposes a new framework, reinforcement learning with relative feedback, and a novel trajectory-wise policy gradient algorithm, Pairwise Proximal Policy Optimization (P3O) that operates directly on comparative rewards. We show theoretically that P3O is invariant to equivalent rewards and avoids the complexity of PPO. Empirical evaluations demonstrate that P3O outperforms PPO in the KL-Reward trade-off and can align with human preferences as well as or better than prior methods. In summary, this work introduces a simpler yet effective approach for aligning LLMs to human preferences through relative feedback.

Banghua Zhu, Hiteshi Sharma, Felipe Vieira Frujeri et al.

Reinforcement learning from human feedback (RLHF) has emerged as a reliable approach to aligning large language models (LLMs) to human preferences. Among the plethora of RLHF techniques, proximal policy optimization (PPO) is of the most widely used methods. Despite its popularity, however, PPO may suffer from mode collapse, instability, and poor sample efficiency. We show that these issues can be alleviated by a novel algorithm that we refer to as Advantage-Induced Policy Alignment (APA), which leverages a squared error loss function based on the estimated advantages. We demonstrate empirically that APA consistently outperforms PPO in language tasks by a large margin, when a separate reward model is employed as the evaluator. In addition, compared with PPO, APA offers a more stable form of control over the deviation from the model's initial policy, ensuring that the model improves its performance without collapsing to deterministic output. In addition to empirical results, we also provide a theoretical justification supporting the design of our loss function.

Shirui Chen, Jiantao Jiao, Lillian J. Ratliff et al.

Masked diffusion language models (MDLMs) offer the potential for parallel token generation, but most open-source MDLMs decode fewer than 5 tokens per model forward pass even with sophisticated sampling strategies, limiting their parallel generation potential. Existing acceleration methods either rely on fixed confidence-based heuristics or use distillation-based approaches that finetune MDLMs on trajectories generated by a base model, which can become off-policy during finetuning and restrict performance to the quality of the base model's samples. We propose \texttt{dUltra}, an on-policy reinforcement learning framework based on Group Relative Policy Optimization (GRPO) that learns unmasking strategies for efficient parallel decoding. dUltra introduces an unmasking planner head that predicts per-token unmasking likelihoods under independent Bernoulli distributions. We jointly optimize the base diffusion LLM and the unmasking order planner using reward signals combining verifiable reward, distillation reward, and the number of unmasking steps. Across mathematical reasoning and code generation tasks, dUltra achieves superior accuracy-efficiency trade-offs compared to state-of-the-art heuristic (Fast-dLLM) and distillation baselines (d3LLM, dParallel), demonstrating that learned unmasking trajectories through on-policy RL enable better exploitation of parallel generation in MDLMs. Code and checkpoints are released at https://github.com/chinsengi/dUltra-os.

Banghua Zhu, Mingyu Ding, Philip Jacobson et al.

Self-training is an important technique for solving semi-supervised learning problems. It leverages unlabeled data by generating pseudo-labels and combining them with a limited labeled dataset for training. The effectiveness of self-training heavily relies on the accuracy of these pseudo-labels. In this paper, we introduce doubly robust self-training, a novel semi-supervised algorithm that provably balances between two extremes. When the pseudo-labels are entirely incorrect, our method reduces to a training process solely using labeled data. Conversely, when the pseudo-labels are completely accurate, our method transforms into a training process utilizing all pseudo-labeled data and labeled data, thus increasing the effective sample size. Through empirical evaluations on both the ImageNet dataset for image classification and the nuScenes autonomous driving dataset for 3D object detection, we demonstrate the superiority of the doubly robust loss over the standard self-training baseline.

Hanlin Zhu, Paria Rashidinejad, Jiantao Jiao

We propose A-Crab (Actor-Critic Regularized by Average Bellman error), a new practical algorithm for offline reinforcement learning (RL) in complex environments with insufficient data coverage. Our algorithm combines the marginalized importance sampling framework with the actor-critic paradigm, where the critic returns evaluations of the actor (policy) that are pessimistic relative to the offline data and have a small average (importance-weighted) Bellman error. Compared to existing methods, our algorithm simultaneously offers a number of advantages: (1) It achieves the optimal statistical rate of $1/\sqrt{N}$ -- where $N$ is the size of offline dataset -- in converging to the best policy covered in the offline dataset, even when combined with general function approximators. (2) It relies on a weaker average notion of policy coverage (compared to the $\ell_\infty$ single-policy concentrability) that exploits the structure of policy visitations. (3) It outperforms the data-collection behavior policy over a wide range of specific hyperparameters. We provide both theoretical analysis and experimental results to validate the effectiveness of our proposed algorithm.

Yixiao Huang, Hanlin Zhu, Zixuan Wang et al.

Chain-of-Thought (CoT) prompting substantially improves the sample efficiency of transformers, reducing the complexity of tasks like parity learning from exponential to polynomial in the input length. However, generating explicit reasoning steps at inference is computationally expensive. Implicit Chain-of-Thought (ICoT) has emerged as a promising empirical remedy that trains models to internalize intermediate steps within their hidden states, but its theoretical foundations remain poorly understood. We give the first theoretical analysis of ICoT, proving that an $L$-layer transformer trained under our proposed Log-ICoT curriculum learns $k$-parity with $\mathsf{poly}(n)$ samples and $L = \log_2 k$ training stages. This matches the sample efficiency of explicit CoT while eliminating its inference overhead, and extends prior one-layer parity guarantees to multi-layer architectures. Compared to standard ICoT, which removes thinking tokens one at a time, Log-ICoT removes them in geometric chunks, reducing the number of stages from linear in $k$ to logarithmic. Experiments on multi-layer transformers confirm the theory and visualize how reasoning is progressively absorbed into deeper layers.

Nived Rajaraman, Yanjun Han, Jiantao Jiao et al.

We consider the sequential decision-making problem where the mean outcome is a non-linear function of the chosen action. Compared with the linear model, two curious phenomena arise in non-linear models: first, in addition to the "learning phase" with a standard parametric rate for estimation or regret, there is an "burn-in period" with a fixed cost determined by the non-linear function; second, achieving the smallest burn-in cost requires new exploration algorithms. For a special family of non-linear functions named ridge functions in the literature, we derive upper and lower bounds on the optimal burn-in cost, and in addition, on the entire learning trajectory during the burn-in period via differential equations. In particular, a two-stage algorithm that first finds a good initial action and then treats the problem as locally linear is statistically optimal. In contrast, several classical algorithms, such as UCB and algorithms relying on regression oracles, are provably suboptimal.

Banghua Zhu, Ziao Wang, Nadim Ghaddar et al.

We consider the problem of computing a function of $n$ variables using noisy queries, where each query is incorrect with some fixed and known probability $p \in (0,1/2)$. Specifically, we consider the computation of the $\mathsf{OR}$ function of $n$ bits (where queries correspond to noisy readings of the bits) and the $\mathsf{MAX}$ function of $n$ real numbers (where queries correspond to noisy pairwise comparisons). We show that an expected number of queries of \[ (1 \pm o(1)) \frac{n\log \frac{1}δ}{D_{\mathsf{KL}}(p \| 1-p)} \] is both sufficient and necessary to compute both functions with a vanishing error probability $δ= o(1)$, where $D_{\mathsf{KL}}(p \| 1-p)$ denotes the Kullback-Leibler divergence between $\mathsf{Bern}(p)$ and $\mathsf{Bern}(1-p)$ distributions. Compared to previous work, our results tighten the dependence on $p$ in both the upper and lower bounds for the two functions.

Banghua Zhu, Ziao Wang, Nadim Ghaddar et al.

We revisit the problem of computing with noisy information considered in Feige et al. 1994, which includes computing the OR function from noisy queries, and computing the MAX, SEARCH and SORT functions from noisy pairwise comparisons. For $K$ given elements, the goal is to correctly recover the desired function with probability at least $1-δ$ when the outcome of each query is flipped with probability $p$. We consider both the adaptive sampling setting where each query can be adaptively designed based on past outcomes, and the non-adaptive sampling setting where the query cannot depend on past outcomes. The prior work provides tight bounds on the worst-case query complexity in terms of the dependence on $K$. However, the upper and lower bounds do not match in terms of the dependence on $δ$ and $p$. We improve the lower bounds for all the four functions under both adaptive and non-adaptive query models. Most of our lower bounds match the upper bounds up to constant factors when either $p$ or $δ$ is bounded away from $0$, while the ratio between the best prior upper and lower bounds goes to infinity when $p\rightarrow 0$ or $p\rightarrow 1/2$. On the other hand, we also provide matching upper and lower bounds for the number of queries in expectation, improving both the upper and lower bounds for the variable-length query model.

Hanlin Zhu, Andrew Cohen, Danqing Wang et al.

Story plots, while short, carry most of the essential information of a full story that may contain tens of thousands of words. We study the problem of automatic generation of story plots, which includes story premise, character descriptions, plot outlines, etc. To generate a single engaging plot, existing plot generators (e.g., DOC (Yang et al., 2022a)) require hundreds to thousands of calls to LLMs (e.g., OpenAI API) in the planning stage of the story plot, which is costly and takes at least several minutes. Moreover, the hard-wired nature of the method makes the pipeline non-differentiable, blocking fast specialization and personalization of the plot generator. In this paper, we propose three models, $\texttt{OpenPlot}$, $\texttt{E2EPlot}$ and $\texttt{RLPlot}$, to address these challenges. $\texttt{OpenPlot}$ replaces expensive OpenAI API calls with LLaMA2 (Touvron et al., 2023) calls via careful prompt designs, which leads to inexpensive generation of high-quality training datasets of story plots. We then train an end-to-end story plot generator, $\texttt{E2EPlot}$, by supervised fine-tuning (SFT) using approximately 13000 story plots generated by $\texttt{OpenPlot}$. $\texttt{E2EPlot}$ generates story plots of comparable quality to $\texttt{OpenPlot}$, and is > 10$\times$ faster (1k tokens in only 30 seconds on average). Finally, we obtain $\texttt{RLPlot}$ that is further fine-tuned with RLHF on several different reward models for different aspects of story quality, which yields 60.0$\%$ winning rate against $\texttt{E2EPlot}$ along the aspect of suspense and surprise.

Junkeun Yi, Damon Mosk-Aoyama, Baihe Huang et al.

Post-training for long-horizon agentic tasks has a tension between compute efficiency and generalization. While supervised fine-tuning (SFT) is compute efficient, it often suffers from out-of-domain (OOD) degradation. Conversely, end-to-end reinforcement learning (E2E RL) preserves OOD capabilities, but incurs high compute costs due to many turns of on-policy rollout. We introduce PivotRL, a novel framework that operates on existing SFT trajectories to combine the compute efficiency of SFT with the OOD accuracy of E2E RL. PivotRL relies on two key mechanisms: first, it executes local, on-policy rollouts and filters for pivots: informative intermediate turns where sampled actions exhibit high variance in outcomes; second, it utilizes rewards for functional-equivalent actions rather than demanding strict string matching with the SFT data demonstration. We theoretically show that these mechanisms incentivize strong learning signals with high natural gradient norm, while maximally preserving policy probability ordering on actions unrelated to training tasks. In comparison to standard SFT on identical data, we demonstrate that PivotRL achieves +4.17% higher in-domain accuracy on average across four agentic domains, and +10.04% higher OOD accuracy in non-agentic tasks. Notably, on agentic coding tasks, PivotRL achieves competitive accuracy with E2E RL with 4x fewer rollout turns. PivotRL is adopted by NVIDIA's Nemotron-3-Super-120B-A12B, acting as the workhorse in production-scale agentic post-training.

Evan Frick, Tianle Li, Connor Chen et al. · berkeley

We introduce a new benchmark for reward models that quantifies their ability to produce strong language models through RLHF (Reinforcement Learning from Human Feedback). The gold-standard approach is to run a full RLHF training pipeline and directly probe downstream LLM performance. However, this process is prohibitively expensive. To address this, we build a predictive model of downstream LLM performance by evaluating the reward model on proxy tasks. These proxy tasks consist of a large-scale human preference and a verifiable correctness preference dataset, in which we measure 12 metrics across 12 domains. To investigate which reward model metrics are most correlated to gold-standard RLHF outcomes, we launch an end-to-end RLHF experiment on a large-scale crowdsourced human preference platform to view real reward model downstream performance as ground truth. Ultimately, we compile our data and findings into Preference Proxy Evaluations (PPE), the first reward model benchmark explicitly linked to post-RLHF real-world human preference performance, which we open-source for public use and further development. Our code and evaluations can be found at https://github.com/lmarena/PPE .

Hanlin Zhu, Baihe Huang, Shaolun Zhang et al.

Auto-regressive large language models (LLMs) show impressive capacities to solve many complex reasoning tasks while struggling with some simple logical reasoning tasks such as inverse search: when trained on '$A \to B$' (e.g., 'Tom is the parent of John'), LLM fails to directly conclude '$B \gets A$' (e.g., 'John is the child of Tom') during inference even if the two sentences are semantically identical, which is known as the 'reversal curse'. In this paper, we theoretically analyze the reversal curse via the training dynamics of (stochastic) gradient descent for two auto-regressive models: (1) a bilinear model that can be viewed as a simplification of a one-layer transformer; (2) one-layer transformers under certain assumptions. Our analysis reveals that for both models, the reversal curse is a consequence of the (effective) model weights 'asymmetry', i.e., the increase of weights from a token $A$ to token $B$ during training does not necessarily cause the increase of the weights from $B$ to $A$, which is caused by the training dynamics under certain choice of loss function and the optimization space of model parameters. Moreover, our analysis can be naturally applied to other logical reasoning tasks such as chain-of-thought (COT), which provides a new perspective different from previous work that focuses on expressivity. Finally, we conduct experiments to validate our theory on multi-layer transformers under different settings. Our code is available at https://github.com/marlo-z/reversal_curse_analysis/.

Baihe Huang, Eric Xu, Kannan Ramchandran et al.

The proliferation of Large Language Models (LLMs) necessitates efficient mechanisms to distinguish machine-generated content from human text. While statistical watermarking has emerged as a promising solution, existing methods suffer from two critical limitations: the lack of a principled approach for selecting sampling distributions and the reliance on fixed-horizon hypothesis testing, which precludes valid early stopping. In this paper, we bridge this gap by developing the first e-value-based watermarking framework, Anchored E-Watermarking, that unifies optimal sampling with anytime-valid inference. Unlike traditional approaches where optional stopping invalidates Type-I error guarantees, our framework enables valid, anytime-inference by constructing a test supermartingale for the detection process. By leveraging an anchor distribution to approximate the target model, we characterize the optimal e-value with respect to the worst-case log-growth rate and derive the optimal expected stopping time. Our theoretical claims are substantiated by simulations and evaluations on established benchmarks, showing that our framework can significantly enhance sample efficiency, reducing the average token budget required for detection by 13-15% relative to state-of-the-art baselines.

Tianjun Zhang, Paria Rashidinejad, Jiantao Jiao et al.

In online reinforcement learning (RL), efficient exploration remains particularly challenging in high-dimensional environments with sparse rewards. In low-dimensional environments, where tabular parameterization is possible, count-based upper confidence bound (UCB) exploration methods achieve minimax near-optimal rates. However, it remains unclear how to efficiently implement UCB in realistic RL tasks that involve non-linear function approximation. To address this, we propose a new exploration approach via \textit{maximizing} the deviation of the occupancy of the next policy from the explored regions. We add this term as an adaptive regularizer to the standard RL objective to balance exploration vs. exploitation. We pair the new objective with a provably convergent algorithm, giving rise to a new intrinsic reward that adjusts existing bonuses. The proposed intrinsic reward is easy to implement and combine with other existing RL algorithms to conduct exploration. As a proof of concept, we evaluate the new intrinsic reward on tabular examples across a variety of model-based and model-free algorithms, showing improvements over count-only exploration strategies. When tested on navigation and locomotion tasks from MiniGrid and DeepMind Control Suite benchmarks, our approach significantly improves sample efficiency over state-of-the-art methods. Our code is available at https://github.com/tianjunz/MADE.

Bohan Lyu, Yucheng Yang, Siqiao Huang et al.

Modern AI progress has been driven by ML methods that are generalizable across settings and scalable to larger regimes. As large language models demonstrate advanced capabilities in reasoning, coding, and engineering tasks, it is increasingly important to understand whether they can discover such methods rather than only apply existing ones. We introduce MLS-Bench, a benchmark for evaluating whether AI systems can invent generalizable and scalable ML methods. MLS-Bench contains 140 tasks across 12 domains, each requiring an agent to improve one targeted component of an ML system or algorithm and demonstrate that the improvement generalizes across controlled settings and scales. We find that current agents remain far from reliably surpassing human-designed methods, and that engineering-style tuning is easier for them than genuine method invention. We further study the effects of test-time scaling, adaptive compute allocation, and context provision on agents' discovery performance, together with case studies of their behavior. Our analyses suggest that the bottleneck is not only in proposing new methods, but also in the scientific insight needed to plan, validate, and scale claims about them. More search, compute, or context alone does not remove this bottleneck. We build and maintain a community platform for cumulative and comparable iteration, and release the data and code at https://mls-bench.com.

Banghua Zhu, Michael I. Jordan, Jiantao Jiao

Reinforcement Learning from Human Feedback (RLHF) is a pivotal technique that aligns language models closely with human-centric values. The initial phase of RLHF involves learning human values using a reward model from ranking data. It is observed that the performance of the reward model degrades after one epoch of training, and optimizing too much against the learned reward model eventually hinders the true objective. This paper delves into these issues, leveraging the theoretical insights to design improved reward learning algorithm termed 'Iterative Data Smoothing' (IDS). The core idea is that during each training epoch, we not only update the model with the data, but also update the date using the model, replacing hard labels with soft labels. Our empirical findings highlight the superior performance of this approach over the traditional methods.

DiJia Su, Hanlin Zhu, Yingchen Xu et al.

Large Language Models (LLMs) excel at reasoning and planning when trained on chainof-thought (CoT) data, where the step-by-step thought process is explicitly outlined by text tokens. However, this results in lengthy inputs where many words support textual coherence rather than core reasoning information, and processing these inputs consumes substantial computation resources. In this work, we propose a hybrid representation of the reasoning process, where we partially abstract away the initial reasoning steps using latent discrete tokens generated by VQ-VAE, significantly reducing the length of reasoning traces. We explore the use of latent trace abstractions in two scenarios: 1) training the model from scratch for the Keys-Finding Maze problem, 2) fine-tuning LLMs on this hybrid data with an extended vocabulary including unseen latent tokens, for both logical and mathematical reasoning problems. To facilitate effective learning, we introduce a simple training procedure that randomly mixes latent and text tokens, which enables fast adaptation to new latent tokens. Our approach consistently outperforms the baselines methods in various benchmarks.

Hengyu Fu, Baihe Huang, Virginia Adams et al.

Diffusion Language Models (DLMs) have recently emerged as a strong alternative to autoregressive language models (LMs). DLMs offer comparable accuracy with faster inference speed via parallel decoding. However, standard DLM decoding strategies relying on high-confidence tokens encounter an inherent information-theoretic bottleneck that restricts decoding progress and ultimately slows generation. We demonstrate both theoretically and empirically that prioritizing high-confidence tokens is inherently inefficient. High-probability tokens carry negligible information and strictly relying on them limits the effective progress made in each decoding round. We prove that the number of decoding rounds must grow linearly with the sample's total information (negative log-likelihood) and inversely with the per-round information budget, establishing a bits-to-rounds principle. We also propose Explore-Then-Exploit (ETE), a training-free decoding strategy that maximizes information throughput and decoding efficiency. ETE combines cross-block decoding with targeted exploration of high-uncertainty tokens to reshape the conditional distribution and trigger cascades of confident predictions. Experiments verify our theoretical bounds and demonstrate that ETE consistently reduces the required number of decoding rounds compared to confidence-only baselines without compromising generation quality.

Tianhao Wu, Janice Lan, Weizhe Yuan et al. · meta-ai

LLMs are typically trained to answer user questions or follow instructions similarly to how human experts respond. However, in the standard alignment framework they lack the basic ability of explicit thinking before answering. Thinking is important for complex questions that require reasoning and planning -- but can be applied to any task. We propose a training method for equipping existing LLMs with such thinking abilities for general instruction following without use of additional human data. We achieve this by an iterative search and optimization procedure that explores the space of possible thought generations, allowing the model to learn how to think without direct supervision. For each instruction, the thought candidates are scored using a judge model to evaluate their responses only, and then optimized via preference optimization. We show that this procedure leads to superior performance on AlpacaEval and Arena-Hard, and shows gains from thinking on non-reasoning categories such as marketing, health and general knowledge, in addition to more traditional reasoning & problem-solving tasks.

Nived Rajaraman, Jiantao Jiao, Kannan Ramchandran

While there has been a large body of research attempting to circumvent tokenization for language modeling (Clark et al., 2022; Xue et al., 2022), the current consensus is that it is a necessary initial step for designing state-of-the-art performant language models. In this paper, we investigate tokenization from a theoretical point of view by studying the behavior of transformers on simple data generating processes. When trained on data drawn from certain simple $k^{\text{th}}$-order Markov processes for $k > 1$, transformers exhibit a surprising phenomenon - in the absence of tokenization, they empirically fail to learn the right distribution and predict characters according to a unigram model (Makkuva et al., 2024). With the addition of tokenization, however, we empirically observe that transformers break through this barrier and are able to model the probabilities of sequences drawn from the source near-optimally, achieving small cross-entropy loss. With this observation as starting point, we study the end-to-end cross-entropy loss achieved by transformers with and without tokenization. With the appropriate tokenization, we show that even the simplest unigram models (over tokens) learnt by transformers are able to model the probability of sequences drawn from $k^{\text{th}}$-order Markov sources near optimally. Our analysis provides a justification for the use of tokenization in practice through studying the behavior of transformers on Markovian data.

Tianyu Guo, Druv Pai, Yu Bai et al.

Practitioners have consistently observed three puzzling phenomena in transformer-based large language models (LLMs): attention sinks, value-state drains, and residual-state peaks, collectively referred to as extreme-token phenomena. These phenomena are characterized by certain so-called "sink tokens" receiving disproportionately high attention weights, exhibiting significantly smaller value states, and having much larger residual-state norms than those of other tokens. These extreme tokens give rise to various challenges in LLM inference, quantization, and interpretability. We elucidate the mechanisms behind extreme-token phenomena. First, we show that these phenomena arise in very simple architectures -- transformers with one to three layers -- trained on a toy model, the Bigram-Backcopy (BB) task. In this setting, we identify an active-dormant mechanism, where attention heads become sinks for specific input domains while remaining non-sinks for others. Our theoretical analysis of the training dynamics reveals that these phenomena are driven by a mutual reinforcement mechanism. Building on these insights, we propose strategies to mitigate extreme-token phenomena during pretraining, including replacing softmax with ReLU and Adam with SGD. Next, we extend our analysis to pretrained LLMs, including Llama and OLMo, showing that many attention heads exhibit a similar active-dormant mechanism as in the BB task, and that the mutual reinforcement mechanism also governs the emergence of extreme-token phenomena during LLM pretraining. Our results reveal that many of the static and dynamic properties of extreme-token phenomena predicted by the BB task align with observations in pretrained LLMs.

Baihe Huang, Hanlin Zhu, Banghua Zhu et al.

We study statistical watermarking by formulating it as a hypothesis testing problem, a general framework which subsumes all previous statistical watermarking methods. Key to our formulation is a coupling of the output tokens and the rejection region, realized by pseudo-random generators in practice, that allows non-trivial trade-offs between the Type I error and Type II error. We characterize the Uniformly Most Powerful (UMP) watermark in the general hypothesis testing setting and the minimax Type II error in the model-agnostic setting. In the common scenario where the output is a sequence of $n$ tokens, we establish nearly matching upper and lower bounds on the number of i.i.d. tokens required to guarantee small Type I and Type II errors. Our rate of $Θ(h^{-1} \log (1/h))$ with respect to the average entropy per token $h$ highlights potentials for improvement from the rate of $h^{-2}$ in the previous works. Moreover, we formulate the robust watermarking problem where the user is allowed to perform a class of perturbations on the generated texts, and characterize the optimal Type II error of robust UMP tests via a linear programming problem. To the best of our knowledge, this is the first systematic statistical treatment on the watermarking problem with near-optimal rates in the i.i.d. setting, which might be of interest for future works.

Hanlin Zhu, Shibo Hao, Zhiting Hu et al.

Large Language Models (LLMs) have demonstrated remarkable performance in many applications, including challenging reasoning problems via chain-of-thoughts (CoTs) techniques that generate ``thinking tokens'' before answering the questions. While existing theoretical works demonstrate that CoTs with discrete tokens boost the capability of LLMs, recent work on continuous CoTs lacks a theoretical understanding of why it outperforms discrete counterparts in various reasoning tasks such as directed graph reachability, a fundamental graph reasoning problem that includes many practical domain applications as special cases. In this paper, we prove that a two-layer transformer with $D$ steps of continuous CoTs can solve the directed graph reachability problem, where $D$ is the diameter of the graph, while the best known result of constant-depth transformers with discrete CoTs requires $O(n^2)$ decoding steps where $n$ is the number of vertices ($D<n$). In our construction, each continuous thought vector is a superposition state that encodes multiple search frontiers simultaneously (i.e., parallel breadth-first search (BFS)), while discrete CoTs must choose a single path sampled from the superposition state, which leads to sequential search that requires many more steps and may be trapped into local solutions. We also performed extensive experiments to verify that our theoretical construction aligns well with the empirical solution obtained via training dynamics. Notably, encoding of multiple search frontiers as a superposition state automatically emerges in training continuous CoTs, without explicit supervision to guide the model to explore multiple paths simultaneously.

Banghua Zhu, Norman Mu, Jiantao Jiao et al.

Generative AI's expanding footprint across numerous industries has led to both excitement and increased scrutiny. This paper delves into the unique security challenges posed by Generative AI, and outlines potential research directions for managing these risks.

Tianyu Guo, Hanlin Zhu, Ruiqi Zhang et al.

``Socrates is human. All humans are mortal. Therefore, Socrates is mortal.'' This form of argument illustrates a typical pattern of two-hop reasoning. Formally, two-hop reasoning refers to the process of inferring a conclusion by making two logical steps, each connecting adjacent concepts, such that the final conclusion depends on the integration of both steps. It is one of the most fundamental components of human reasoning and plays a crucial role in both formal logic and everyday decision-making. Despite recent progress in large language models (LLMs), we surprisingly find that they can fail at solving simple two-hop reasoning problems when distractors are present. We observe on a synthetic dataset that pre-trained LLMs often resort to random guessing among all plausible conclusions. However, after few steps of fine-tuning, models achieve near-perfect accuracy and exhibit strong length generalization. To understand the underlying mechanisms, we train a 3-layer Transformer from scratch on a synthetic two-hop reasoning task and reverse-engineer its internal information flow. We observe a clear progression in the attention logits throughout training. This pictures a sharp phase transition from an initial stage of random guessing to the emergence of a structured sequential query mechanism, where the model first retrieves the preceding and the bridge concepts in the early layers and then uses them to infer the final answer. Finally, we show that these dynamics can be captured by a minimal three-parameter attention-only network.

Hanlin Zhu, Banghua Zhu, Jiantao Jiao

Large language models (LLMs) have achieved huge success in numerous natural language process (NLP) tasks. However, it faces the challenge of significant resource consumption during inference. In this paper, we aim to improve the inference efficiency of LLMs by prompt caching, i.e., if the current prompt can be answered by the same response of a previous prompt, one can directly utilize that previous response without calling the LLM. Specifically, we focus on the prediction accuracy of prompt caching for single-round question-answering tasks via embedding similarity. The existing embeddings of prompts mostly focus on whether two prompts are semantically similar, which is not necessarily equivalent to whether the same response can answer them. Therefore, we propose a distillation-based method to fine-tune the existing embeddings for better caching prediction. Theoretically, we provide finite-sample guarantees for the convergence of our method under different types of loss functions. Empirically, we carefully construct a hard dataset based on Kwiatkowski et al. (2019) where the existing embedding model (Wang et al., 2022) only achieves an AUC of 0.51. We then fine-tune the above embedding model, which significantly improves the AUC of caching prediction from 0.51 to 0.81. We also conduct simulations demonstrating that our trained models achieve better caching efficiency than the previous embedding model.

Yixiao Huang, Hanlin Zhu, Tianyu Guo et al.

Large language models (LLMs) can acquire new knowledge through fine-tuning, but this process exhibits a puzzling duality: models can generalize remarkably from new facts, yet are also prone to hallucinating incorrect information. However, the reasons for this phenomenon remain poorly understood. In this work, we argue that both behaviors stem from a single mechanism known as out-of-context reasoning (OCR): the ability to deduce implications by associating concepts, even those without a causal link. Our experiments across five prominent LLMs confirm that OCR indeed drives both generalization and hallucination, depending on whether the associated concepts are causally related. To build a rigorous theoretical understanding of this phenomenon, we then formalize OCR as a synthetic factual recall task. We empirically show that a one-layer single-head attention-only transformer with factorized output and value matrices can learn to solve this task, while a model with combined weights cannot, highlighting the crucial role of matrix factorization. Our theoretical analysis shows that the OCR capability can be attributed to the implicit bias of gradient descent, which favors solutions that minimize the nuclear norm of the combined output-value matrix. This mathematical structure explains why the model learns to associate facts and implications with high sample efficiency, regardless of whether the correlation is causal or merely spurious. Ultimately, our work provides a theoretical foundation for understanding the OCR phenomenon, offering a new lens for analyzing and mitigating undesirable behaviors from knowledge injection.

Hanlin Zhu, Shibo Hao, Zhiting Hu et al.

Previous work shows that the chain of continuous thought (continuous CoT) improves the reasoning capability of large language models (LLMs) by enabling implicit parallel thinking, and a subsequent work provided theoretical insight by showing that a two-layer transformer equipped with continuous CoT can efficiently solve directed graph reachability by maintaining a superposition of multiple reasoning traces in the continuous thought. However, it remains unclear how the superposition mechanism is naturally learned from gradient-based training methods. To fill this gap, we theoretically analyze the training dynamics of a simplified two-layer transformer on the directed graph reachability problem to unveil how the superposition mechanism emerges during training in two training stages -- (i) a thought-generation stage that autoregressively expands the continuous thought, and (ii) a prediction stage that converts the thought into the final answer. Our analysis reveals that during training using continuous thought, the index-matching logit, an important quantity which reflects the strength of the model's local search ability, will first increase and then remain bounded under mild assumptions. The bounded index-matching logit effectively balances exploration and exploitation during the reasoning process: the model will exploit local problem structures to identify plausible search traces, and assign comparable weights to multiple such traces to explore when it is uncertain about which solution is correct, which results in superposition. Our experimental results tracking the growth of logits further validate our theory.

Baihe Huang, Shanda Li, Tianhao Wu et al.

Test-time scaling paradigms have significantly advanced the capabilities of large language models (LLMs) on complex tasks. Despite their empirical success, theoretical understanding of the sample efficiency of various test-time strategies -- such as self-consistency, best-of-$n$, and self-correction -- remains limited. In this work, we first establish a separation result between two repeated sampling strategies: self-consistency requires $Θ(1/Δ^2)$ samples to produce the correct answer, while best-of-$n$ only needs $Θ(1/Δ)$, where $Δ< 1$ denotes the probability gap between the correct and second most likely answers. Next, we present an expressiveness result for the self-correction approach with verifier feedback: it enables Transformers to simulate online learning over a pool of experts at test time. Therefore, a single Transformer architecture can provably solve multiple tasks without prior knowledge of the specific task associated with a user query, extending the representation theory of Transformers from single-task to multi-task settings. Finally, we empirically validate our theoretical results, demonstrating the practical effectiveness of self-correction methods.

Hanlin Zhu, Tianyu Guo, Song Mei et al.

As LLMs are increasingly deployed as agents, agentic reasoning - the ability to combine tool use, especially search, and reasoning - becomes a critical skill. However, it is hard to disentangle agentic reasoning when evaluated in complex environments and tasks. Current agent benchmarks often mix agentic reasoning with challenging math reasoning, expert-level knowledge, and other advanced capabilities. To fill this gap, we build a novel benchmark, GSM-Agent, where an LLM agent is required to solve grade-school-level reasoning problems, but is only presented with the question in the prompt without the premises that contain the necessary information to solve the task, and needs to proactively collect that information using tools. Although the original tasks are grade-school math problems, we observe that even frontier models like GPT-5 only achieve 67% accuracy. To understand and analyze the agentic reasoning patterns, we propose the concept of agentic reasoning graph: cluster the environment's document embeddings into nodes, and map each tool call to its nearest node to build a reasoning path. Surprisingly, we identify that the ability to revisit a previously visited node, widely taken as a crucial pattern in static reasoning, is often missing for agentic reasoning for many models. Based on the insight, we propose a tool-augmented test-time scaling method to improve LLM's agentic reasoning performance by adding tools to encourage models to revisit. We expect our benchmark and the agentic reasoning framework to aid future studies of understanding and pushing the boundaries of agentic reasoning.

Banghua Zhu, Sai Praneeth Karimireddy, Jiantao Jiao et al.

The creator economy has revolutionized the way individuals can profit through online platforms. In this paper, we initiate the study of online learning in the creator economy by modeling the creator economy as a three-party game between the users, platform, and content creators, with the platform interacting with the content creator under a principal-agent model through contracts to encourage better content. Additionally, the platform interacts with the users to recommend new content, receive an evaluation, and ultimately profit from the content, which can be modeled as a recommender system. Our study aims to explore how the platform can jointly optimize the contract and recommender system to maximize the utility in an online learning fashion. We primarily analyze and compare two families of contracts: return-based contracts and feature-based contracts. Return-based contracts pay the content creator a fraction of the reward the platform gains. In contrast, feature-based contracts pay the content creator based on the quality or features of the content, regardless of the reward the platform receives. We show that under smoothness assumptions, the joint optimization of return-based contracts and recommendation policy provides a regret $Θ(T^{2/3})$. For the feature-based contract, we introduce a definition of intrinsic dimension $d$ to characterize the hardness of learning the contract and provide an upper bound on the regret $\mathcal{O}(T^{(d+1)/(d+2)})$. The upper bound is tight for the linear family.

Banghua Zhu, Jiantao Jiao, Michael I. Jordan

We provide a general framework for designing Generative Adversarial Networks (GANs) to solve high dimensional robust statistics problems, which aim at estimating unknown parameter of the true distribution given adversarially corrupted samples. Prior work focus on the problem of robust mean and covariance estimation when the true distribution lies in the family of Gaussian distributions or elliptical distributions, and analyze depth or scoring rule based GAN losses for the problem. Our work extend these to robust mean estimation, second moment estimation, and robust linear regression when the true distribution only has bounded Orlicz norms, which includes the broad family of sub-Gaussian, sub-Exponential and bounded moment distributions. We also provide a different set of sufficient conditions for the GAN loss to work: we only require its induced distance function to be a cumulative density function of some light-tailed distribution, which is easily satisfied by neural networks with sigmoid activation. In terms of techniques, our proposed GAN losses can be viewed as a smoothed and generalized Kolmogorov-Smirnov distance, which overcomes the computational intractability of the original Kolmogorov-Smirnov distance used in the prior work.

Tianhao Wu, Yunchang Yang, Han Zhong et al.

Policy optimization methods are one of the most widely used classes of Reinforcement Learning (RL) algorithms. However, theoretical understanding of these methods remains insufficient. Even in the episodic (time-inhomogeneous) tabular setting, the state-of-the-art theoretical result of policy-based method in \citet{shani2020optimistic} is only $\tilde{O}(\sqrt{S^2AH^4K})$ where $S$ is the number of states, $A$ is the number of actions, $H$ is the horizon, and $K$ is the number of episodes, and there is a $\sqrt{SH}$ gap compared with the information theoretic lower bound $\tildeΩ(\sqrt{SAH^3K})$. To bridge such a gap, we propose a novel algorithm Reference-based Policy Optimization with Stable at Any Time guarantee (\algnameacro), which features the property "Stable at Any Time". We prove that our algorithm achieves $\tilde{O}(\sqrt{SAH^3K} + \sqrt{AH^4K})$ regret. When $S > H$, our algorithm is minimax optimal when ignoring logarithmic factors. To our best knowledge, RPO-SAT is the first computationally efficient, nearly minimax optimal policy-based algorithm for tabular RL.

Yuexiang Zhai, Christina Baek, Zhengyuan Zhou et al.

Many goal-reaching reinforcement learning (RL) tasks have empirically verified that rewarding the agent on subgoals improves convergence speed and practical performance. We attempt to provide a theoretical framework to quantify the computational benefits of rewarding the completion of subgoals, in terms of the number of synchronous value iterations. In particular, we consider subgoals as one-way {\em intermediate states}, which can only be visited once per episode and propose two settings that consider these one-way intermediate states: the one-way single-path (OWSP) and the one-way multi-path (OWMP) settings. In both OWSP and OWMP settings, we demonstrate that adding {\em intermediate rewards} to subgoals is more computationally efficient than only rewarding the agent once it completes the goal of reaching a terminal state. We also reveal a trade-off between computational complexity and the pursuit of the shortest path in the OWMP setting: adding intermediate rewards significantly reduces the computational complexity of reaching the goal but the agent may not find the shortest path, whereas with sparse terminal rewards, the agent finds the shortest path at a significantly higher computational cost. We also corroborate our theoretical results with extensive experiments on the MiniGrid environments using Q-learning and some popular deep RL algorithms.

Jinhyun So, Ramy E. Ali, Basak Guler et al.

Secure aggregation is a critical component in federated learning (FL), which enables the server to learn the aggregate model of the users without observing their local models. Conventionally, secure aggregation algorithms focus only on ensuring the privacy of individual users in a single training round. We contend that such designs can lead to significant privacy leakages over multiple training rounds, due to partial user selection/participation at each round of FL. In fact, we show that the conventional random user selection strategies in FL lead to leaking users' individual models within number of rounds that is linear in the number of users. To address this challenge, we introduce a secure aggregation framework, Multi-RoundSecAgg, with multi-round privacy guarantees. In particular, we introduce a new metric to quantify the privacy guarantees of FL over multiple training rounds, and develop a structured user selection strategy that guarantees the long-term privacy of each user (over any number of training rounds). Our framework also carefully accounts for the fairness and the average number of participating users at each round. Our experiments on MNIST and CIFAR-10 datasets in the IID and the non-IID settings demonstrate the performance improvement over the baselines, both in terms of privacy protection and test accuracy.

Paria Rashidinejad, Banghua Zhu, Cong Ma et al.

Offline (or batch) reinforcement learning (RL) algorithms seek to learn an optimal policy from a fixed dataset without active data collection. Based on the composition of the offline dataset, two main categories of methods are used: imitation learning which is suitable for expert datasets and vanilla offline RL which often requires uniform coverage datasets. From a practical standpoint, datasets often deviate from these two extremes and the exact data composition is usually unknown a priori. To bridge this gap, we present a new offline RL framework that smoothly interpolates between the two extremes of data composition, hence unifying imitation learning and vanilla offline RL. The new framework is centered around a weak version of the concentrability coefficient that measures the deviation from the behavior policy to the expert policy alone. Under this new framework, we further investigate the question on algorithm design: can one develop an algorithm that achieves a minimax optimal rate and also adapts to unknown data composition? To address this question, we consider a lower confidence bound (LCB) algorithm developed based on pessimism in the face of uncertainty in offline RL. We study finite-sample properties of LCB as well as information-theoretic limits in multi-armed bandits, contextual bandits, and Markov decision processes (MDPs). Our analysis reveals surprising facts about optimality rates. In particular, in all three settings, LCB achieves a faster rate of $1/N$ for nearly-expert datasets compared to the usual rate of $1/\sqrt{N}$ in offline RL, where $N$ is the number of samples in the batch dataset. In the case of contextual bandits with at least two contexts, we prove that LCB is adaptively optimal for the entire data composition range, achieving a smooth transition from imitation learning to offline RL. We further show that LCB is almost adaptively optimal in MDPs.

Nived Rajaraman, Yanjun Han, Lin F. Yang et al.

We study the statistical limits of Imitation Learning (IL) in episodic Markov Decision Processes (MDPs) with a state space $\mathcal{S}$. We focus on the known-transition setting where the learner is provided a dataset of $N$ length-$H$ trajectories from a deterministic expert policy and knows the MDP transition. We establish an upper bound $O(|\mathcal{S}|H^{3/2}/N)$ for the suboptimality using the Mimic-MD algorithm in Rajaraman et al (2020) which we prove to be computationally efficient. In contrast, we show the minimax suboptimality grows as $Ω( H^{3/2}/N)$ when $|\mathcal{S}|\geq 3$ while the unknown-transition setting suffers from a larger sharp rate $Θ(|\mathcal{S}|H^2/N)$ (Rajaraman et al (2020)). The lower bound is established by proving a two-way reduction between IL and the value estimation problem of the unknown expert policy under any given reward function, as well as building connections with linear functional estimation with subsampled observations. We further show that under the additional assumption that the expert is optimal for the true reward function, there exists an efficient algorithm, which we term as Mimic-Mixture, that provably achieves suboptimality $O(1/N)$ for arbitrary 3-state MDPs with rewards only at the terminal layer. In contrast, no algorithm can achieve suboptimality $O(\sqrt{H}/N)$ with high probability if the expert is not constrained to be optimal. Our work formally establishes the benefit of the expert optimal assumption in the known transition setting, while Rajaraman et al (2020) showed it does not help when transitions are unknown.

Cong Ma, Banghua Zhu, Jiantao Jiao et al.

We study the problem of off-policy evaluation in the multi-armed bandit model with bounded rewards, and develop minimax rate-optimal procedures under three settings. First, when the behavior policy is known, we show that the Switch estimator, a method that alternates between the plug-in and importance sampling estimators, is minimax rate-optimal for all sample sizes. Second, when the behavior policy is unknown, we analyze performance in terms of the competitive ratio, thereby revealing a fundamental gap between the settings of known and unknown behavior policies. When the behavior policy is unknown, any estimator must have mean-squared error larger -- relative to the oracle estimator equipped with the knowledge of the behavior policy -- by a multiplicative factor proportional to the support size of the target policy. Moreover, we demonstrate that the plug-in approach achieves this worst-case competitive ratio up to a logarithmic factor. Third, we initiate the study of the partial knowledge setting in which it is assumed that the minimum probability taken by the behavior policy is known. We show that the plug-in estimator is optimal for relatively large values of the minimum probability, but is sub-optimal when the minimum probability is low. In order to remedy this gap, we propose a new estimator based on approximation by Chebyshev polynomials that provably achieves the optimal estimation error. Numerical experiments on both simulated and real data corroborate our theoretical findings.