Simon S. Du

Tongzhou Wang, Simon S. Du, Antonio Torralba et al. · mit

The ability to separate signal from noise, and reason with clean abstractions, is critical to intelligence. With this ability, humans can efficiently perform real world tasks without considering all possible nuisance factors.How can artificial agents do the same? What kind of information can agents safely discard as noises? In this work, we categorize information out in the wild into four types based on controllability and relation with reward, and formulate useful information as that which is both controllable and reward-relevant. This framework clarifies the kinds information removed by various prior work on representation learning in reinforcement learning (RL), and leads to our proposed approach of learning a Denoised MDP that explicitly factors out certain noise distractors. Extensive experiments on variants of DeepMind Control Suite and RoboDesk demonstrate superior performance of our denoised world model over using raw observations alone, and over prior works, across policy optimization control tasks as well as the non-control task of joint position regression.

Jikai Jin, Zhiyuan Li, Kaifeng Lyu et al. · stanford, tsinghua

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics (Li et al., 2020) and follows an incremental learning procedure (Gissin et al., 2019): GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

Jifan Zhang, Yifang Chen, Gregory Canal et al. · uw

Labeled data are critical to modern machine learning applications, but obtaining labels can be expensive. To mitigate this cost, machine learning methods, such as transfer learning, semi-supervised learning and active learning, aim to be label-efficient: achieving high predictive performance from relatively few labeled examples. While obtaining the best label-efficiency in practice often requires combinations of these techniques, existing benchmark and evaluation frameworks do not capture a concerted combination of all such techniques. This paper addresses this deficiency by introducing LabelBench, a new computationally-efficient framework for joint evaluation of multiple label-efficient learning techniques. As an application of LabelBench, we introduce a novel benchmark of state-of-the-art active learning methods in combination with semi-supervised learning for fine-tuning pretrained vision transformers. Our benchmark demonstrates better label-efficiencies than previously reported in active learning. LabelBench's modular codebase is open-sourced for the broader community to contribute label-efficient learning methods and benchmarks. The repository can be found at: https://github.com/EfficientTraining/LabelBench.

Kaifeng Lyu, Jikai Jin, Zhiyuan Li et al. · stanford, tsinghua

Recent work by Power et al. (2022) highlighted a surprising "grokking" phenomenon in learning arithmetic tasks: a neural net first "memorizes" the training set, resulting in perfect training accuracy but near-random test accuracy, and after training for sufficiently longer, it suddenly transitions to perfect test accuracy. This paper studies the grokking phenomenon in theoretical setups and shows that it can be induced by a dichotomy of early and late phase implicit biases. Specifically, when training homogeneous neural nets with large initialization and small weight decay on both classification and regression tasks, we prove that the training process gets trapped at a solution corresponding to a kernel predictor for a long time, and then a very sharp transition to min-norm/max-margin predictors occurs, leading to a dramatic change in test accuracy.

Haoyuan Cai, Tengyu Ma, Simon Du · stanford

We revisit the incremental autonomous exploration problem proposed by Lim & Auer (2012). In this setting, the agent aims to learn a set of near-optimal goal-conditioned policies to reach the $L$-controllable states: states that are incrementally reachable from an initial state $s_0$ within $L$ steps in expectation. We introduce a new algorithm with stronger sample complexity bounds than existing ones. Furthermore, we also prove the first lower bound for the autonomous exploration problem. In particular, the lower bound implies that our proposed algorithm, Value-Aware Autonomous Exploration, is nearly minimax-optimal when the number of $L$-controllable states grows polynomially with respect to $L$. Key in our algorithm design is a connection between autonomous exploration and multi-goal stochastic shortest path, a new problem that naturally generalizes the classical stochastic shortest path problem. This new problem and its connection to autonomous exploration can be of independent interest.

Yuandong Tian, Yiping Wang, Zhenyu Zhang et al.

We propose Joint MLP/Attention (JoMA) dynamics, a novel mathematical framework to understand the training procedure of multilayer Transformer architectures. This is achieved by integrating out the self-attention layer in Transformers, producing a modified dynamics of MLP layers only. JoMA removes unrealistic assumptions in previous analysis (e.g., lack of residual connection) and predicts that the attention first becomes sparse (to learn salient tokens), then dense (to learn less salient tokens) in the presence of nonlinear activations, while in the linear case, it is consistent with existing works that show attention becomes sparse over time. We leverage JoMA to qualitatively explains how tokens are combined to form hierarchies in multilayer Transformers, when the input tokens are generated by a latent hierarchical generative model. Experiments on models trained from real-world dataset (Wikitext2/Wikitext103) and various pre-trained models (OPT, Pythia) verify our theoretical findings. Code can be found in https://github.com/facebookresearch/luckmatters/tree/yuandong3.

Runlong Zhou, Zihan Zhang, Simon S. Du · tsinghua

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

Jiaqi Yang, Qi Lei, Jason D. Lee et al. · tsinghua

We give novel algorithms for multi-task and lifelong linear bandits with shared representation. Specifically, we consider the setting where we play $M$ linear bandits with dimension $d$, each for $T$ rounds, and these $M$ bandit tasks share a common $k(\ll d)$ dimensional linear representation. For both the multi-task setting where we play the tasks concurrently, and the lifelong setting where we play tasks sequentially, we come up with novel algorithms that achieve $\widetilde{O}\left(d\sqrt{kMT} + kM\sqrt{T}\right)$ regret bounds, which matches the known minimax regret lower bound up to logarithmic factors and closes the gap in existing results [Yang et al., 2021]. Our main technique include a more efficient estimator for the low-rank linear feature extractor and an accompanied novel analysis for this estimator.

Rui Lu, Andrew Zhao, Simon S. Du et al. · tsinghua

While multitask representation learning has become a popular approach in reinforcement learning (RL) to boost the sample efficiency, the theoretical understanding of why and how it works is still limited. Most previous analytical works could only assume that the representation function is already known to the agent or from linear function class, since analyzing general function class representation encounters non-trivial technical obstacles such as generalization guarantee, formulation of confidence bound in abstract function space, etc. However, linear-case analysis heavily relies on the particularity of linear function class, while real-world practice usually adopts general non-linear representation functions like neural networks. This significantly reduces its applicability. In this work, we extend the analysis to general function class representations. Specifically, we consider an agent playing $M$ contextual bandits (or MDPs) concurrently and extracting a shared representation function $φ$ from a specific function class $Φ$ using our proposed Generalized Functional Upper Confidence Bound algorithm (GFUCB). We theoretically validate the benefit of multitask representation learning within general function class for bandits and linear MDP for the first time. Lastly, we conduct experiments to demonstrate the effectiveness of our algorithm with neural net representation.

Yan Dai, Ruosong Wang, Simon S. Du · tsinghua

It is well-known that for sparse linear bandits, when ignoring the dependency on sparsity which is much smaller than the ambient dimension, the worst-case minimax regret is $\widetildeΘ\left(\sqrt{dT}\right)$ where $d$ is the ambient dimension and $T$ is the number of rounds. On the other hand, in the benign setting where there is no noise and the action set is the unit sphere, one can use divide-and-conquer to achieve $\widetilde{\mathcal O}(1)$ regret, which is (nearly) independent of $d$ and $T$. In this paper, we present the first variance-aware regret guarantee for sparse linear bandits: $\widetilde{\mathcal O}\left(\sqrt{d\sum_{t=1}^T σ_t^2} + 1\right)$, where $σ_t^2$ is the variance of the noise at the $t$-th round. This bound naturally interpolates the regret bounds for the worst-case constant-variance regime (i.e., $σ_t \equiv Ω(1)$) and the benign deterministic regimes (i.e., $σ_t \equiv 0$). To achieve this variance-aware regret guarantee, we develop a general framework that converts any variance-aware linear bandit algorithm to a variance-aware algorithm for sparse linear bandits in a "black-box" manner. Specifically, we take two recent algorithms as black boxes to illustrate that the claimed bounds indeed hold, where the first algorithm can handle unknown-variance cases and the second one is more efficient.

Natalia Zhang, Xinqi Wang, Qiwen Cui et al. · tsinghua

We initiate the study of Preference-Based Multi-Agent Reinforcement Learning (PbMARL), exploring both theoretical foundations and empirical validations. We define the task as identifying the Nash equilibrium from a preference-only offline dataset in general-sum games, a problem marked by the challenge of sparse feedback signals. Our theory establishes the upper complexity bounds for Nash Equilibrium in effective PbMARL, demonstrating that single-policy coverage is inadequate and highlighting the importance of unilateral dataset coverage. These theoretical insights are verified through comprehensive experiments. To enhance the practical performance, we further introduce two algorithmic techniques. (1) We propose a Mean Squared Error (MSE) regularization along the time axis to achieve a more uniform reward distribution and improve reward learning outcomes. (2) We propose an additional penalty based on the distribution of the dataset to incorporate pessimism, improving stability and effectiveness during training. Our findings underscore the multifaceted approach required for PbMARL, paving the way for effective preference-based multi-agent systems.

Yulai Zhao, Jianshu Chen, Simon S. Du · princeton

This paper presents a new statistical analysis aiming to explain the recent superior achievements of the pre-training techniques in natural language processing (NLP). We prove that when the classes of the pre-training task (e.g., different words in the masked language model task) are sufficiently diverse, in the sense that the least singular value of the last linear layer in pre-training (denoted as $\tildeν$) is large, then pre-training can significantly improve the sample efficiency of downstream tasks. Specially, we show the transfer learning excess risk enjoys an $O\left(\frac{1}{\tildeν \sqrt{n}}\right)$ rate, in contrast to the $O\left(\frac{1}{\sqrt{m}}\right)$ rate in the standard supervised learning. Here, $n$ is the number of pre-training data and $m$ is the number of data in the downstream task, and typically $n \gg m$. Our proof relies on a vector-form Rademacher complexity chain rule for disassembling composite function classes and a modified self-concordance condition. These techniques can be of independent interest.

Runlong Zhou, Ruosong Wang, Simon S. Du · tsinghua

We study regret minimization for reinforcement learning (RL) in Latent Markov Decision Processes (LMDPs) with context in hindsight. We design a novel model-based algorithmic framework which can be instantiated with both a model-optimistic and a value-optimistic solver. We prove an $\tilde{O}(\sqrt{\mathsf{Var}^\star M ΓS A K})$ regret bound where $\tilde{O}$ hides logarithm factors, $M$ is the number of contexts, $S$ is the number of states, $A$ is the number of actions, $K$ is the number of episodes, $Γ\le S$ is the maximum transition degree of any state-action pair, and $\mathsf{Var}^\star$ is a variance quantity describing the determinism of the LMDP. The regret bound only scales logarithmically with the planning horizon, thus yielding the first (nearly) horizon-free regret bound for LMDP. This is also the first problem-dependent regret bound for LMDP. Key in our proof is an analysis of the total variance of alpha vectors (a generalization of value functions), which is handled with a truncation method. We complement our positive result with a novel $Ω(\sqrt{\mathsf{Var}^\star M S A K})$ regret lower bound with $Γ= 2$, which shows our upper bound minimax optimal when $Γ$ is a constant for the class of variance-bounded LMDPs. Our lower bound relies on new constructions of hard instances and an argument inspired by the symmetrization technique from theoretical computer science, both of which are technically different from existing lower bound proof for MDPs, and thus can be of independent interest.

Zhiyuan Zeng, Hamish Ivison, Yiping Wang et al.

We introduce Reinforcement Learning (RL) with Adaptive Verifiable Environments (RLVE), an approach using verifiable environments that procedurally generate problems and provide algorithmically verifiable rewards, to scale up RL for language models (LMs). RLVE enables each verifiable environment to dynamically adapt its problem difficulty distribution to the policy model's capabilities as training progresses. In contrast, static data distributions often lead to vanishing learning signals when problems are either too easy or too hard for the policy. To implement RLVE, we create RLVE-Gym, a large-scale suite of 400 verifiable environments carefully developed through manual environment engineering. Using RLVE-Gym, we show that environment scaling, i.e., expanding the collection of training environments, consistently improves generalizable reasoning capabilities. RLVE with joint training across all 400 environments in RLVE-Gym yields a 3.37% absolute average improvement across six reasoning benchmarks, starting from one of the strongest 1.5B reasoning LMs. By comparison, continuing this LM's original RL training yields only a 0.49% average absolute gain despite using over 3x more compute. We release our code publicly.

Simon S. Du, Gauthier Gidel, Michael I. Jordan et al.

We consider the smooth convex-concave bilinearly-coupled saddle-point problem, $\min_{\mathbf{x}}\max_{\mathbf{y}}~F(\mathbf{x}) + H(\mathbf{x},\mathbf{y}) - G(\mathbf{y})$, where one has access to stochastic first-order oracles for $F$, $G$ as well as the bilinear coupling function $H$. Building upon standard stochastic extragradient analysis for variational inequalities, we present a stochastic \emph{accelerated gradient-extragradient (AG-EG)} descent-ascent algorithm that combines extragradient and Nesterov's acceleration in general stochastic settings. This algorithm leverages scheduled restarting to admit a fine-grained nonasymptotic convergence rate that matches known lower bounds by both \citet{ibrahim2020linear} and \citet{zhang2021lower} in their corresponding settings, plus an additional statistical error term for bounded stochastic noise that is optimal up to a constant prefactor. This is the first result that achieves such a relatively mature characterization of optimality in saddle-point optimization.

Shicong Cen, Yuejie Chi, Simon S. Du et al.

Multi-Agent Reinforcement Learning (MARL) -- where multiple agents learn to interact in a shared dynamic environment -- permeates across a wide range of critical applications. While there has been substantial progress on understanding the global convergence of policy optimization methods in single-agent RL, designing and analysis of efficient policy optimization algorithms in the MARL setting present significant challenges, which unfortunately, remain highly inadequately addressed by existing theory. In this paper, we focus on the most basic setting of competitive multi-agent RL, namely two-player zero-sum Markov games, and study equilibrium finding algorithms in both the infinite-horizon discounted setting and the finite-horizon episodic setting. We propose a single-loop policy optimization method with symmetric updates from both agents, where the policy is updated via the entropy-regularized optimistic multiplicative weights update (OMWU) method and the value is updated on a slower timescale. We show that, in the full-information tabular setting, the proposed method achieves a finite-time last-iterate linear convergence to the quantal response equilibrium of the regularized problem, which translates to a sublinear last-iterate convergence to the Nash equilibrium by controlling the amount of regularization. Our convergence results improve upon the best known iteration complexities, and lead to a better understanding of policy optimization in competitive Markov games.

Rui Yuan, Simon S. Du, Robert M. Gower et al.

We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class. Using the compatible function approximation framework, both methods with log-linear policies can be written as inexact versions of the policy mirror descent (PMD) method. We show that both methods attain linear convergence rates and $\tilde{\mathcal{O}}(1/ε^2)$ sample complexities using a simple, non-adaptive geometrically increasing step size, without resorting to entropy or other strongly convex regularization. Lastly, as a byproduct, we obtain sublinear convergence rates for both methods with arbitrary constant step size.

Zihan Zhang, Yuxin Chen, Jason D. Lee et al.

A central issue lying at the heart of online reinforcement learning (RL) is data efficiency. While a number of recent works achieved asymptotically minimal regret in online RL, the optimality of these results is only guaranteed in a ``large-sample'' regime, imposing enormous burn-in cost in order for their algorithms to operate optimally. How to achieve minimax-optimal regret without incurring any burn-in cost has been an open problem in RL theory. We settle this problem for the context of finite-horizon inhomogeneous Markov decision processes. Specifically, we prove that a modified version of Monotonic Value Propagation (MVP), a model-based algorithm proposed by \cite{zhang2020reinforcement}, achieves a regret on the order of (modulo log factors) \begin{equation*} \min\big\{ \sqrt{SAH^3K}, \,HK \big\}, \end{equation*} where $S$ is the number of states, $A$ is the number of actions, $H$ is the planning horizon, and $K$ is the total number of episodes. This regret matches the minimax lower bound for the entire range of sample size $K\geq 1$, essentially eliminating any burn-in requirement. It also translates to a PAC sample complexity (i.e., the number of episodes needed to yield $\varepsilon$-accuracy) of $\frac{SAH^3}{\varepsilon^2}$ up to log factor, which is minimax-optimal for the full $\varepsilon$-range. Further, we extend our theory to unveil the influences of problem-dependent quantities like the optimal value/cost and certain variances. The key technical innovation lies in the development of a new regret decomposition strategy and a novel analysis paradigm to decouple complicated statistical dependency -- a long-standing challenge facing the analysis of online RL in the sample-hungry regime.

Yunchang Yang, Han Zhong, Tianhao Wu et al.

We study stochastic delayed feedback in general multi-agent sequential decision making, which includes bandits, single-agent Markov decision processes (MDPs), and Markov games (MGs). We propose a novel reduction-based framework, which turns any multi-batched algorithm for sequential decision making with instantaneous feedback into a sample-efficient algorithm that can handle stochastic delays in sequential decision making. By plugging different multi-batched algorithms into our framework, we provide several examples demonstrating that our framework not only matches or improves existing results for bandits, tabular MDPs, and tabular MGs, but also provides the first line of studies on delays in sequential decision making with function approximation. In summary, we provide a complete set of sharp results for multi-agent sequential decision making with delayed feedback.

Zihan Zhang, Xiangyang Ji, Simon S. Du

This paper gives the first polynomial-time algorithm for tabular Markov Decision Processes (MDP) that enjoys a regret bound \emph{independent on the planning horizon}. Specifically, we consider tabular MDP with $S$ states, $A$ actions, a planning horizon $H$, total reward bounded by $1$, and the agent plays for $K$ episodes. We design an algorithm that achieves an $O\left(\mathrm{poly}(S,A,\log K)\sqrt{K}\right)$ regret in contrast to existing bounds which either has an additional $\mathrm{polylog}(H)$ dependency~\citep{zhang2020reinforcement} or has an exponential dependency on $S$~\citep{li2021settling}. Our result relies on a sequence of new structural lemmas establishing the approximation power, stability, and concentration property of stationary policies, which can have applications in other problems related to Markov chains.

Qiwen Cui, Kaiqing Zhang, Simon S. Du

We propose a new model, independent linear Markov game, for multi-agent reinforcement learning with a large state space and a large number of agents. This is a class of Markov games with independent linear function approximation, where each agent has its own function approximation for the state-action value functions that are marginalized by other players' policies. We design new algorithms for learning the Markov coarse correlated equilibria (CCE) and Markov correlated equilibria (CE) with sample complexity bounds that only scale polynomially with each agent's own function class complexity, thus breaking the curse of multiagents. In contrast, existing works for Markov games with function approximation have sample complexity bounds scale with the size of the \emph{joint action space} when specialized to the canonical tabular Markov game setting, which is exponentially large in the number of agents. Our algorithms rely on two key technical innovations: (1) utilizing policy replay to tackle non-stationarity incurred by multiple agents and the use of function approximation; (2) separating learning Markov equilibria and exploration in the Markov games, which allows us to use the full-information no-regret learning oracle instead of the stronger bandit-feedback no-regret learning oracle used in the tabular setting. Furthermore, we propose an iterative-best-response type algorithm that can learn pure Markov Nash equilibria in independent linear Markov potential games. In the tabular case, by adapting the policy replay mechanism for independent linear Markov games, we propose an algorithm with $\widetilde{O}(ε^{-2})$ sample complexity to learn Markov CCE, which improves the state-of-the-art result $\widetilde{O}(ε^{-3})$ in Daskalakis et al. 2022, where $ε$ is the desired accuracy, and also significantly improves other problem parameters.

Qiwen Cui, Simon S. Du

This paper considers offline multi-agent reinforcement learning. We propose the strategy-wise concentration principle which directly builds a confidence interval for the joint strategy, in contrast to the point-wise concentration principle that builds a confidence interval for each point in the joint action space. For two-player zero-sum Markov games, by exploiting the convexity of the strategy-wise bonus, we propose a computationally efficient algorithm whose sample complexity enjoys a better dependency on the number of actions than the prior methods based on the point-wise bonus. Furthermore, for offline multi-agent general-sum Markov games, based on the strategy-wise bonus and a novel surrogate function, we give the first algorithm whose sample complexity only scales $\sum_{i=1}^mA_i$ where $A_i$ is the action size of the $i$-th player and $m$ is the number of players. In sharp contrast, the sample complexity of methods based on the point-wise bonus would scale with the size of the joint action space $Π_{i=1}^m A_i$ due to the curse of multiagents. Lastly, all of our algorithms can naturally take a pre-specified strategy class $Π$ as input and output a strategy that is close to the best strategy in $Π$. In this setting, the sample complexity only scales with $\log |Π|$ instead of $\sum_{i=1}^mA_i$.

Weihang Xu, Simon S. Du

We revisit the problem of learning a single neuron with ReLU activation under Gaussian input with square loss. We particularly focus on the over-parameterization setting where the student network has $n\ge 2$ neurons. We prove the global convergence of randomly initialized gradient descent with a $O\left(T^{-3}\right)$ rate. This is the first global convergence result for this problem beyond the exact-parameterization setting ($n=1$) in which the gradient descent enjoys an $\exp(-Ω(T))$ rate. Perhaps surprisingly, we further present an $Ω\left(T^{-3}\right)$ lower bound for randomly initialized gradient flow in the over-parameterization setting. These two bounds jointly give an exact characterization of the convergence rate and imply, for the first time, that over-parameterization can exponentially slow down the convergence rate. To prove the global convergence, we need to tackle the interactions among student neurons in the gradient descent dynamics, which are not present in the exact-parameterization case. We use a three-phase structure to analyze GD's dynamics. Along the way, we prove gradient descent automatically balances student neurons, and use this property to deal with the non-smoothness of the objective function. To prove the convergence rate lower bound, we construct a novel potential function that characterizes the pairwise distances between the student neurons (which cannot be done in the exact-parameterization case). We show this potential function converges slowly, which implies the slow convergence rate of the loss function.

Zhen Zhang, Liangcai Su, Zhuo Chen et al.

Deep research agents have achieved remarkable progress on complex information seeking tasks. Even long ReAct style rollouts explore only a single trajectory, while recent state of the art systems scale inference time compute via parallel search and aggregation. Yet deep research answers are composed of complementary pieces of evidence, which parallel rollouts often duplicate rather than complete, yielding diminishing returns while pushing the aggregation context toward the model's limit. We propose Argus, an agentic system in which a Searcher and a Navigator cooperate to treat deep research as assembling a jigsaw from complementary evidence pieces, rather than brute forcing the whole answer in parallel. The Searcher collects evidence traces for a given sub-query through ReAct-style interaction. The Navigator maintains a shared evidence graph, verifying which pieces are still missing, dispatching Searchers to gather them, and reasoning over the completed graph to produce a source-traced final answer. We train the Navigator with reinforcement learning to verify, dispatch, and synthesize, while independently training the Searcher to remain a standard ReAct agent. The resulting Navigator supports rollouts with a single Searcher or many in parallel without retraining. With both Searcher and Navigator built on a 35B-A3B MoE backbone, Argus gains 5.5 points with a single Searcher and 12.7 points with 8 parallel Searchers, averaged over eight benchmarks. With 64 Searchers it reaches 86.2 on BrowseComp, surpassing every proprietary agent we benchmark, while the Navigator's reasoning context stays under 21.5K tokens.

Qiwen Cui, Zhihan Xiong, Maryam Fazel et al.

In this paper, we investigate Nash-regret minimization in congestion games, a class of games with benign theoretical structure and broad real-world applications. We first propose a centralized algorithm based on the optimism in the face of uncertainty principle for congestion games with (semi-)bandit feedback, and obtain finite-sample guarantees. Then we propose a decentralized algorithm via a novel combination of the Frank-Wolfe method and G-optimal design. By exploiting the structure of the congestion game, we show the sample complexity of both algorithms depends only polynomially on the number of players and the number of facilities, but not the size of the action set, which can be exponentially large in terms of the number of facilities. We further define a new problem class, Markov congestion games, which allows us to model the non-stationarity in congestion games. We propose a centralized algorithm for Markov congestion games, whose sample complexity again has only polynomial dependence on all relevant problem parameters, but not the size of the action set.

Xinqi Wang, Qiwen Cui, Simon S. Du

This paper presents a systematic study on gap-dependent sample complexity in offline reinforcement learning. Prior work showed when the density ratio between an optimal policy and the behavior policy is upper bounded (the optimal policy coverage assumption), then the agent can achieve an $O\left(\frac{1}{ε^2}\right)$ rate, which is also minimax optimal. We show under the optimal policy coverage assumption, the rate can be improved to $O\left(\frac{1}ε\right)$ when there is a positive sub-optimality gap in the optimal $Q$-function. Furthermore, we show when the visitation probabilities of the behavior policy are uniformly lower bounded for states where an optimal policy's visitation probabilities are positive (the uniform optimal policy coverage assumption), the sample complexity of identifying an optimal policy is independent of $\frac{1}ε$. Lastly, we present nearly-matching lower bounds to complement our gap-dependent upper bounds.

Yiping Wang, Yifang Chen, Kevin Jamieson et al.

To leverage the copious amount of data from source tasks and overcome the scarcity of the target task samples, representation learning based on multi-task pretraining has become a standard approach in many applications. However, up until now, most existing works design a source task selection strategy from a purely empirical perspective. Recently, \citet{chen2022active} gave the first active multi-task representation learning (A-MTRL) algorithm which adaptively samples from source tasks and can provably reduce the total sample complexity using the L2-regularized-target-source-relevance parameter $ν^2$. But their work is theoretically suboptimal in terms of total source sample complexity and is less practical in some real-world scenarios where sparse training source task selection is desired. In this paper, we address both issues. Specifically, we show the strict dominance of the L1-regularized-relevance-based ($ν^1$-based) strategy by giving a lower bound for the $ν^2$-based strategy. When $ν^1$ is unknown, we propose a practical algorithm that uses the LASSO program to estimate $ν^1$. Our algorithm successfully recovers the optimal result in the known case. In addition to our sample complexity results, we also characterize the potential of our $ν^1$-based strategy in sample-cost-sensitive settings. Finally, we provide experiments on real-world computer vision datasets to illustrate the effectiveness of our proposed method.

Haotian Ye, Xiaoyu Chen, Liwei Wang et al.

Generalization in Reinforcement Learning (RL) aims to learn an agent during training that generalizes to the target environment. This paper studies RL generalization from a theoretical aspect: how much can we expect pre-training over training environments to be helpful? When the interaction with the target environment is not allowed, we certify that the best we can obtain is a near-optimal policy in an average sense, and we design an algorithm that achieves this goal. Furthermore, when the agent is allowed to interact with the target environment, we give a surprising result showing that asymptotically, the improvement from pre-training is at most a constant factor. On the other hand, in the non-asymptotic regime, we design an efficient algorithm and prove a distribution-based regret bound in the target environment that is independent of the state-action space.

Haozhe Jiang, Qiwen Cui, Zhihan Xiong et al.

We investigate learning the equilibria in non-stationary multi-agent systems and address the challenges that differentiate multi-agent learning from single-agent learning. Specifically, we focus on games with bandit feedback, where testing an equilibrium can result in substantial regret even when the gap to be tested is small, and the existence of multiple optimal solutions (equilibria) in stationary games poses extra challenges. To overcome these obstacles, we propose a versatile black-box approach applicable to a broad spectrum of problems, such as general-sum games, potential games, and Markov games, when equipped with appropriate learning and testing oracles for stationary environments. Our algorithms can achieve $\widetilde{O}\left(Δ^{1/4}T^{3/4}\right)$ regret when the degree of nonstationarity, as measured by total variation $Δ$, is known, and $\widetilde{O}\left(Δ^{1/5}T^{4/5}\right)$ regret when $Δ$ is unknown, where $T$ is the number of rounds. Meanwhile, our algorithm inherits the favorable dependence on number of agents from the oracles. As a side contribution that may be independent of interest, we show how to test for various types of equilibria by a black-box reduction to single-agent learning, which includes Nash equilibria, correlated equilibria, and coarse correlated equilibria.

Zhaoyi Zhou, Chuning Zhu, Runlong Zhou et al. · tsinghua

Off-policy dynamic programming (DP) techniques such as $Q$-learning have proven to be important in sequential decision-making problems. In the presence of function approximation, however, these techniques often diverge due to the absence of Bellman completeness in the function classes considered, a crucial condition for the success of DP-based methods. In this paper, we show how off-policy learning techniques based on return-conditioned supervised learning (RCSL) are able to circumvent these challenges of Bellman completeness, converging under significantly more relaxed assumptions inherited from supervised learning. We prove there exists a natural environment in which if one uses two-layer multilayer perceptron as the function approximator, the layer width needs to grow linearly with the state space size to satisfy Bellman completeness while a constant layer width is enough for RCSL. These findings take a step towards explaining the superior empirical performance of RCSL methods compared to DP-based methods in environments with near-optimal datasets. Furthermore, in order to learn from sub-optimal datasets, we propose a simple framework called MBRCSL, granting RCSL methods the ability of dynamic programming to stitch together segments from distinct trajectories. MBRCSL leverages learned dynamics models and forward sampling to accomplish trajectory stitching while avoiding the need for Bellman completeness that plagues all dynamic programming algorithms. We propose both theoretical analysis and experimental evaluation to back these claims, outperforming state-of-the-art model-free and model-based offline RL algorithms across several simulated robotics problems.

Yifang Chen, Yingbing Huang, Simon S. Du et al.

Representation learning based on multi-task pretraining has become a powerful approach in many domains. In particular, task-aware representation learning aims to learn an optimal representation for a specific target task by sampling data from a set of source tasks, while task-agnostic representation learning seeks to learn a universal representation for a class of tasks. In this paper, we propose a general and versatile algorithmic and theoretic framework for \textit{active representation learning}, where the learner optimally chooses which source tasks to sample from. This framework, along with a tractable meta algorithm, allows most arbitrary target and source task spaces (from discrete to continuous), covers both task-aware and task-agnostic settings, and is compatible with deep representation learning practices. We provide several instantiations under this framework, from bilinear and feature-based nonlinear to general nonlinear cases. In the bilinear case, by leveraging the non-uniform spectrum of the task representation and the calibrated source-target relevance, we prove that the sample complexity to achieve $\varepsilon$-excess risk on target scales with $ (k^*)^2 \|v^*\|_2^2 \varepsilon^{-2}$ where $k^*$ is the effective dimension of the target and $\|v^*\|_2^2 \in (0,1]$ represents the connection between source and target space. Compared to the passive one, this can save up to $\frac{1}{d_W}$ of sample complexity, where $d_W$ is the task space dimension. Finally, we demonstrate different instantiations of our meta algorithm in synthetic datasets and robotics problems, from pendulum simulations to real-world drone flight datasets. On average, our algorithms outperform baselines by $20\%-70\%$.

Ruizhe Shi, Minhak Song, Runlong Zhou et al. · tsinghua

We present a fine-grained theoretical analysis of the performance gap between reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) under a representation gap. Our study decomposes this gap into two sources: an explicit representation gap under exact optimization and an implicit representation gap under finite samples. In the exact optimization setting, we characterize how the relative capacities of the reward and policy model classes influence the final policy qualities. We show that RLHF, DPO, or online DPO can outperform one another depending on type of model mis-specifications. Notably, online DPO can outperform both RLHF and standard DPO when the reward and policy model classes are isomorphic and both mis-specified. In the approximate optimization setting, we provide a concrete construction where the ground-truth reward is implicitly sparse and show that RLHF requires significantly fewer samples than DPO to recover an effective reward model, highlighting a statistical advantage of two-stage learning. Together, these results provide a comprehensive understanding of the performance gap between RLHF and DPO under various settings, and offer practical insights into when each method is preferred.

Ruizhe Shi, Runlong Zhou, Simon S. Du · tsinghua

Direct Preference Optimization (DPO) has emerged as a stable, scalable, and efficient solution for language model alignment. Despite its empirical success, the optimization properties, particularly the impact of samplers on its convergence rates, remain under-explored. In this paper, we provide a rigorous analysis of DPO's convergence rates with different sampling strategies under the exact gradient setting, revealing a surprising separation: uniform sampling achieves $\textbf{linear}$ convergence, while our proposed online sampler achieves $\textbf{quadratic}$ convergence. We further adapt the sampler to practical settings by incorporating posterior distributions and logit mixing, demonstrating improvements over previous methods. For example, it outperforms vanilla DPO by over $7.4$% on Safe-RLHF dataset. Our results not only offer insights into the theoretical understanding of DPO but also pave the way for further algorithm designs.

Haozhe Jiang, Qiwen Cui, Zhihan Xiong et al.

This paper investigates when one can efficiently recover an approximate Nash Equilibrium (NE) in offline congestion games. The existing dataset coverage assumption in offline general-sum games inevitably incurs a dependency on the number of actions, which can be exponentially large in congestion games. We consider three different types of feedback with decreasing revealed information. Starting from the facility-level (a.k.a., semi-bandit) feedback, we propose a novel one-unit deviation coverage condition and give a pessimism-type algorithm that can recover an approximate NE. For the agent-level (a.k.a., bandit) feedback setting, interestingly, we show the one-unit deviation coverage condition is not sufficient. On the other hand, we convert the game to multi-agent linear bandits and show that with a generalized data coverage assumption in offline linear bandits, we can efficiently recover the approximate NE. Lastly, we consider a novel type of feedback, the game-level feedback where only the total reward from all agents is revealed. Again, we show the coverage assumption for the agent-level feedback setting is insufficient in the game-level feedback setting, and with a stronger version of the data coverage assumption for linear bandits, we can recover an approximate NE. Together, our results constitute the first study of offline congestion games and imply formal separations between different types of feedback.

Ruizhe Shi, Yuyao Liu, Yanjie Ze et al.

Offline reinforcement learning (RL) aims to find a near-optimal policy using pre-collected datasets. In real-world scenarios, data collection could be costly and risky; therefore, offline RL becomes particularly challenging when the in-domain data is limited. Given recent advances in Large Language Models (LLMs) and their few-shot learning prowess, this paper introduces $\textbf{La}$nguage Models for $\textbf{Mo}$tion Control ($\textbf{LaMo}$), a general framework based on Decision Transformers to effectively use pre-trained Language Models (LMs) for offline RL. Our framework highlights four crucial components: (1) Initializing Decision Transformers with sequentially pre-trained LMs, (2) employing the LoRA fine-tuning method, in contrast to full-weight fine-tuning, to combine the pre-trained knowledge from LMs and in-domain knowledge effectively, (3) using the non-linear MLP transformation instead of linear projections, to generate embeddings, and (4) integrating an auxiliary language prediction loss during fine-tuning to stabilize the LMs and retain their original abilities on languages. Empirical results indicate $\textbf{LaMo}$ achieves excellent performance in sparse-reward tasks and closes the gap between value-based offline RL methods and decision transformers in dense-reward tasks. In particular, our method demonstrates superior performance in scenarios with limited data samples.

Divyansh Pareek, Simon S. Du, Sewoong Oh · uw

Self-Distillation is a special type of knowledge distillation where the student model has the same architecture as the teacher model. Despite using the same architecture and the same training data, self-distillation has been empirically observed to improve performance, especially when applied repeatedly. For such a process, there is a fundamental question of interest: How much gain is possible by applying multiple steps of self-distillation? To investigate this relative gain, we propose studying the simple but canonical task of linear regression. Our analysis shows that the excess risk achieved by multi-step self-distillation can significantly improve upon a single step of self-distillation, reducing the excess risk by a factor as large as $d$, where $d$ is the input dimension. Empirical results on regression tasks from the UCI repository show a reduction in the learnt model's risk (MSE) by up to 47%.

Yiping Wang, Qing Yang, Zhiyuan Zeng et al. · uw

We show that reinforcement learning with verifiable reward using one training example (1-shot RLVR) is effective in incentivizing the math reasoning capabilities of large language models (LLMs). Applying RLVR to the base model Qwen2.5-Math-1.5B, we identify a single example that elevates model performance on MATH500 from 36.0% to 73.6% (8.6% improvement beyond format correction), and improves the average performance across six common mathematical reasoning benchmarks from 17.6% to 35.7% (7.0% non-format gain). This result matches the performance obtained using the 1.2k DeepScaleR subset (MATH500: 73.6%, average: 35.9%), which contains the aforementioned example. Furthermore, RLVR with only two examples even slightly exceeds these results (MATH500: 74.8%, average: 36.6%). Similar substantial improvements are observed across various models (Qwen2.5-Math-7B, Llama3.2-3B-Instruct, DeepSeek-R1-Distill-Qwen-1.5B), RL algorithms (GRPO and PPO), and different math examples. In addition, we identify some interesting phenomena during 1-shot RLVR, including cross-category generalization, increased frequency of self-reflection, and sustained test performance improvement even after the training accuracy has saturated, a phenomenon we term post-saturation generalization. Moreover, we verify that the effectiveness of 1-shot RLVR primarily arises from the policy gradient loss, distinguishing it from the "grokking" phenomenon. We also show the critical role of promoting exploration (e.g., by incorporating entropy loss with an appropriate coefficient) in 1-shot RLVR training. We also further discuss related observations about format correction, label robustness and prompt modification. These findings can inspire future work on RLVR efficiency and encourage a re-examination of recent progress and the underlying mechanisms in RLVR. All resources are open source at https://github.com/ypwang61/One-Shot-RLVR.

Yifang Chen, Shuohang Wang, Ziyi Yang et al.

Reinforcement learning with human feedback (RLHF), as a widely adopted approach in current large language model pipelines, is \textit{bottlenecked by the size of human preference data}. While traditional methods rely on offline preference dataset constructions, recent approaches have shifted towards online settings, where a learner uses a small amount of labeled seed data and a large pool of unlabeled prompts to iteratively construct new preference data through self-generated responses and high-quality reward/preference feedback. However, most current online algorithms still focus on preference labeling during policy model updating with given feedback oracles, which incurs significant expert query costs. \textit{We are the first to explore cost-effective proxy reward oracles construction strategies for further labeling preferences or rewards with extremely limited labeled data and expert query budgets}. Our approach introduces two key innovations: (1) on-policy query to avoid OOD and imbalance issues in seed data, and (2) active learning to select the most informative data for preference queries. Using these methods, we train a evaluation model with minimal expert-labeled data, which then effectively labels nine times more preference pairs for further RLHF training. For instance, our model using Direct Preference Optimization (DPO) gains around over 1% average improvement on AlpacaEval2, MMLU-5shot and MMLU-0shot, with only 1.7K query cost. Our methodology is orthogonal to other direct expert query-based strategies and therefore might be integrated with them to further reduce query costs.

Tiantian Wang, Xiang Xiang, Simon S. Du

In federated healthcare systems, Federated Class-Incremental Learning (FCIL) has emerged as a key paradigm, enabling continuous adaptive model learning among distributed clients while safeguarding data privacy. However, in practical applications, data across agent nodes within the distributed framework often exhibits non-independent and identically distributed (non-IID) characteristics, rendering traditional continual learning methods inapplicable. To address these challenges, this paper covers more comprehensive incremental task scenarios and proposes a dynamic memory allocation strategy for exemplar storage based on the data replay mechanism. This strategy fully taps into the inherent potential of data heterogeneity, while taking into account the performance fairness of all participating clients, thereby establishing a balanced and adaptive solution to mitigate catastrophic forgetting. Unlike the fixed allocation of client exemplar memory, the proposed scheme emphasizes the rational allocation of limited storage resources among clients to improve model performance. Furthermore, extensive experiments are conducted on three medical image datasets, and the results demonstrate significant performance improvements compared to existing baseline models.

Shulun Chen, Runlong Zhou, Zihan Zhang et al. · tsinghua

Aligning large language models (LLMs) with human preferences has proven effective for enhancing model capabilities, yet standard preference modeling using the Bradley-Terry model assumes transitivity, overlooking the inherent complexity of human population preferences. Nash learning from human feedback (NLHF) addresses this by framing non-transitive preferences as a two-player zero-sum game, where alignment reduces to finding the Nash equilibrium (NE). However, existing algorithms typically rely on regularization, incurring unavoidable bias when computing the duality gap in the original game. In this work, we provide the first convergence guarantee for Optimistic Multiplicative Weights Update ($\mathtt{OMWU}$) in NLHF, showing that it achieves last-iterate linear convergence after a burn-in phase whenever an NE with full support exists, with an instance-dependent linear convergence rate to the original NE, measured by duality gaps. Compared to prior results in Wei et al. (2020), we do not require the assumption of NE uniqueness. Our analysis identifies a novel marginal convergence behavior, where the probability of rarely played actions grows exponentially from exponentially small values, enabling exponentially better dependence on instance-dependent constants than prior results. Experiments corroborate the theoretical strengths of $\mathtt{OMWU}$ in both tabular and neural policy classes, demonstrating its potential for LLM applications.

Avinandan Bose, Shuyue Stella Li, Faeze Brahman et al.

Cold-start personalization requires inferring user preferences through interaction when no user-specific historical data is available. The core challenge is a routing problem: each task admits dozens of preference dimensions, yet individual users care about only a few, and which ones matter depends on who is asking. With a limited question budget, asking without structure will miss the dimensions that matter. Reinforcement learning is the natural formulation, but in multi-turn settings its terminal reward fails to exploit the factored, per-criterion structure of preference data, and in practice learned policies collapse to static question sequences that ignore user responses. We propose decomposing cold-start elicitation into offline structure learning and online Bayesian inference. Pep (Preference Elicitation with Priors) learns a structured world model of preference correlations offline from complete profiles, then performs training-free Bayesian inference online to select informative questions and predict complete preference profiles, including dimensions never asked about. The framework is modular across downstream solvers and requires only simple belief models. Across medical, mathematical, social, and commonsense reasoning, Pep achieves 80.8% alignment between generated responses and users' stated preferences versus 68.5% for RL, with 3-5x fewer interactions. When two users give different answers to the same question, Pep changes its follow-up 39-62% of the time versus 0-28% for RL. It does so with ~10K parameters versus 8B for RL, showing that the bottleneck in cold-start elicitation is the capability to exploit the factored structure of preference data.

Runlong Zhou, Simon S. Du, Beibin Li · tsinghua

As language models (LMs) demonstrate their capabilities in various fields, their application to tasks requiring multi-round interactions has become increasingly popular. These tasks usually have complex dynamics, so supervised fine-tuning (SFT) on a limited offline dataset does not yield good performance. However, only a few works attempted to directly train the LMs within interactive decision-making environments. We aim to create an effective approach to fine-tune LMs with online reinforcement learning (RL) in these environments. We propose Reflect-RL, a two-player system to fine-tune an LM using SFT and online RL, where a frozen reflection model (player) assists the policy model (player). To generate data for the warm-up SFT stage, we use negative example generation to enhance the error-correction ability of the reflection model. Furthermore, we designed single-prompt action enumeration and applied curriculum learning to allow the policy model to learn more efficiently. Empirically, we verify that Reflect-RL outperforms SFT and online RL without reflection. Testing results indicate GPT-2 XL 1.56B fine-tuned with Reflect-RL outperforms larger open-source LMs, such as Mistral 7B. The benchmarks, dataset, and code involved in this work are publicly available: https://github.com/zhourunlong/Reflect-RL.

Nuoya Xiong, Lijun Ding, Simon S. Du

This paper rigorously shows how over-parameterization changes the convergence behaviors of gradient descent (GD) for the matrix sensing problem, where the goal is to recover an unknown low-rank ground-truth matrix from near-isotropic linear measurements. First, we consider the symmetric setting with the symmetric parameterization where $M^* \in \mathbb{R}^{n \times n}$ is a positive semi-definite unknown matrix of rank $r \ll n$, and one uses a symmetric parameterization $XX^\top$ to learn $M^*$. Here $X \in \mathbb{R}^{n \times k}$ with $k > r$ is the factor matrix. We give a novel $Ω(1/T^2)$ lower bound of randomly initialized GD for the over-parameterized case ($k >r$) where $T$ is the number of iterations. This is in stark contrast to the exact-parameterization scenario ($k=r$) where the convergence rate is $\exp (-Ω(T))$. Next, we study asymmetric setting where $M^* \in \mathbb{R}^{n_1 \times n_2}$ is the unknown matrix of rank $r \ll \min\{n_1,n_2\}$, and one uses an asymmetric parameterization $FG^\top$ to learn $M^*$ where $F \in \mathbb{R}^{n_1 \times k}$ and $G \in \mathbb{R}^{n_2 \times k}$. Building on prior work, we give a global exact convergence result of randomly initialized GD for the exact-parameterization case ($k=r$) with an $\exp (-Ω(T))$ rate. Furthermore, we give the first global exact convergence result for the over-parameterization case ($k>r$) with an $\exp(-Ω(α^2 T))$ rate where $α$ is the initialization scale. This linear convergence result in the over-parameterization case is especially significant because one can apply the asymmetric parameterization to the symmetric setting to speed up from $Ω(1/T^2)$ to linear convergence. On the other hand, we propose a novel method that only modifies one step of GD and obtains a convergence rate independent of $α$, recovering the rate in the exact-parameterization case.

Chuning Zhu, Xinqi Wang, Tyler Han et al.

Intelligent agents must be generalists, capable of quickly adapting to various tasks. In reinforcement learning (RL), model-based RL learns a dynamics model of the world, in principle enabling transfer to arbitrary reward functions through planning. However, autoregressive model rollouts suffer from compounding error, making model-based RL ineffective for long-horizon problems. Successor features offer an alternative by modeling a policy's long-term state occupancy, reducing policy evaluation under new rewards to linear regression. Yet, zero-shot policy optimization for new tasks with successor features can be challenging. This work proposes a novel class of models, i.e., Distributional Successor Features for Zero-Shot Policy Optimization (DiSPOs), that learn a distribution of successor features of a stationary dataset's behavior policy, along with a policy that acts to realize different successor features achievable within the dataset. By directly modeling long-term outcomes in the dataset, DiSPOs avoid compounding error while enabling a simple scheme for zero-shot policy optimization across reward functions. We present a practical instantiation of DiSPOs using diffusion models and show their efficacy as a new class of transferable models, both theoretically and empirically across various simulated robotics problems. Videos and code available at https://weirdlabuw.github.io/dispo/.

Minrui Luo, Weihang Xu, Xiang Gao et al.

Gradient descent dynamics on the deep matrix factorization problem is extensively studied as a simplified theoretical model for deep neural networks. Although the convergence theory for two-layer matrix factorization is well-established, no global convergence guarantee for general deep matrix factorization under random initialization has been established to date. To address this gap, we provide a polynomial-time global convergence guarantee for randomly initialized gradient descent on four-layer matrix factorization, given certain conditions on the target matrix and a standard balanced regularization term. Our analysis employs new techniques to show saddle-avoidance properties of gradient decent dynamics, and extends previous theories to characterize the change in eigenvalues of layer weights.

Yiping Wang, Shao-Rong Su, Zhiyuan Zeng et al.

Recent advances in large language models (LLMs) have enabled breakthroughs in mathematical discovery, exemplified by AlphaEvolve, a closed-source system that evolves programs to improve bounds on open problems. However, it relies on ensembles of frontier LLMs to achieve new bounds and is a pure inference system that models cannot internalize the evolving strategies. We introduce ThetaEvolve, an open-source framework that simplifies and extends AlphaEvolve to efficiently scale both in-context learning and Reinforcement Learning (RL) at test time, allowing models to continually learn from their experiences in improving open optimization problems. ThetaEvolve features a single LLM, a large program database for enhanced exploration, batch sampling for higher throughput, lazy penalties to discourage stagnant outputs, and optional reward shaping for stable training signals, etc. ThetaEvolve is the first evolving framework that enable a small open-source model, like DeepSeek-R1-0528-Qwen3-8B, to achieve new best-known bounds on open problems (circle packing and first auto-correlation inequality) mentioned in AlphaEvolve. Besides, across two models and four open tasks, we find that ThetaEvolve with RL at test-time consistently outperforms inference-only baselines, and the model indeed learns evolving capabilities, as the RL-trained checkpoints demonstrate faster progress and better final performance on both trained target task and other unseen tasks. We release our code publicly: https://github.com/ypwang61/ThetaEvolve

Divyansh Pareek, Sewoong Oh, Simon S. Du

The success of modern multimodal representation learning relies on internet-scale datasets. Due to the low quality of a large fraction of raw web data, data curation has become a critical step in the training pipeline. Filtering using a trained model (i.e., teacher-based filtering) has emerged as a successful solution, leveraging a pre-trained model to compute quality scores. To explain the empirical success of teacher-based filtering, we characterize the performance of filtered contrastive learning under the standard bimodal data generation model. Denoting $η\in(0,1]$ as the fraction of data with correctly matched modalities among $n$ paired samples, we utilize a linear contrastive learning setup to show a provable benefit of data filtering: $(i)$ the error without filtering is upper and lower bounded by $\frac{1}{η\sqrt{n}}$, and $(ii)$ the error with teacher-based filtering is upper bounded by $\frac{1}{\sqrt{ηn}}$ in the large $η$ regime, and by $\frac{1}{\sqrt{n}}$ in the small $η$ regime.

Rulin Shao, Shuyue Stella Li, Rui Xin et al.

We show that reinforcement learning with verifiable rewards (RLVR) can elicit strong mathematical reasoning in certain models even with spurious rewards that have little, no, or even negative correlation with the correct answer. For example, RLVR improves MATH-500 performance for Qwen2.5-Math-7B in absolute points by 21.4% (random reward), 13.8% (format reward), 24.1% (incorrect label), 26.0% (1-shot RL), and 27.1% (majority voting) -- nearly matching the 29.1% gained with ground truth rewards. However, the spurious rewards that work for Qwen often fail to yield gains with other model families like Llama3 or OLMo2. In particular, we find code reasoning -- thinking in code without actual code execution -- to be a distinctive Qwen2.5-Math behavior that becomes significantly more frequent after RLVR, from 65% to over 90%, even with spurious rewards. Overall, we hypothesize that, given the lack of useful reward signal, RLVR must somehow be surfacing useful reasoning representations learned during pretraining, although the exact mechanism remains a topic for future work. We suggest that future RLVR research should possibly be validated on diverse models rather than a single de facto choice, as we show that it is easy to get significant performance gains on Qwen models even with completely spurious reward signals.

Jiarui Yao, Simon Shaolei Du

Currently, reinforcement learning (RL), especially deep RL, has received more and more attention in the research area. However, the security of RL has been an obvious problem due to the attack manners becoming mature. In order to defend against such adversarial attacks, several practical approaches are developed, such as adversarial training, data filtering, etc. However, these methods are mostly based on empirical algorithms and experiments, without rigorous theoretical analysis of the robustness of the algorithms. In this paper, we develop an algorithm to certify the robustness of a given policy offline with random smoothing, which could be proven and conducted as efficiently as ones without random smoothing. Experiments on different environments confirm the correctness of our algorithm.

Gantavya Bhatt, Yifang Chen, Arnav M. Das et al. · uw

Supervised finetuning (SFT) on instruction datasets has played a crucial role in achieving the remarkable zero-shot generalization capabilities observed in modern large language models (LLMs). However, the annotation efforts required to produce high quality responses for instructions are becoming prohibitively expensive, especially as the number of tasks spanned by instruction datasets continues to increase. Active learning is effective in identifying useful subsets of samples to annotate from an unlabeled pool, but its high computational cost remains a barrier to its widespread applicability in the context of LLMs. To mitigate the annotation cost of SFT and circumvent the computational bottlenecks of active learning, we propose using experimental design. Experimental design techniques select the most informative samples to label, and typically maximize some notion of uncertainty and/or diversity. In our work, we implement a framework that evaluates several existing and novel experimental design techniques and find that these methods consistently yield significant gains in label efficiency with little computational overhead. On generative tasks, our methods achieve the same generalization performance with only $50\%$ of annotation cost required by random sampling.