Lin F. Yang

Sharan Vaswani, Lin F. Yang, Csaba Szepesvári · deepmind

In contrast to the advances in characterizing the sample complexity for solving Markov decision processes (MDPs), the optimal statistical complexity for solving constrained MDPs (CMDPs) remains unknown. We resolve this question by providing minimax upper and lower bounds on the sample complexity for learning near-optimal policies in a discounted CMDP with access to a generative model (simulator). In particular, we design a model-based algorithm that addresses two settings: (i) relaxed feasibility, where small constraint violations are allowed, and (ii) strict feasibility, where the output policy is required to satisfy the constraint. For (i), we prove that our algorithm returns an $ε$-optimal policy with probability $1 - δ$, by making $\tilde{O}\left(\frac{S A \log(1/δ)}{(1 - γ)^3 ε^2}\right)$ queries to the generative model, thus matching the sample-complexity for unconstrained MDPs. For (ii), we show that the algorithm's sample complexity is upper-bounded by $\tilde{O} \left(\frac{S A \, \log(1/δ)}{(1 - γ)^5 \, ε^2 ζ^2} \right)$ where $ζ$ is the problem-dependent Slater constant that characterizes the size of the feasible region. Finally, we prove a matching lower-bound for the strict feasibility setting, thus obtaining the first near minimax optimal bounds for discounted CMDPs. Our results show that learning CMDPs is as easy as MDPs when small constraint violations are allowed, but inherently more difficult when we demand zero constraint violation.

Masoud Monajatipoor, Liunian Harold Li, Mozhdeh Rouhsedaghat et al.

Large-scale language models have shown the ability to adapt to a new task via conditioning on a few demonstrations (i.e., in-context learning). However, in the vision-language domain, most large-scale pre-trained vision-language (VL) models do not possess the ability to conduct in-context learning. How can we enable in-context learning for VL models? In this paper, we study an interesting hypothesis: can we transfer the in-context learning ability from the language domain to VL domain? Specifically, we first meta-trains a language model to perform in-context learning on NLP tasks (as in MetaICL); then we transfer this model to perform VL tasks by attaching a visual encoder. Our experiments suggest that indeed in-context learning ability can be transferred cross modalities: our model considerably improves the in-context learning capability on VL tasks and can even compensate for the size of the model significantly. On VQA, OK-VQA, and GQA, our method could outperform the baseline model while having 20 times fewer parameters.

Yunfan Li, Yiran Wang, Yu Cheng et al.

Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow convergence rates and poor sample complexity. Hence it is important to design provably sample efficient algorithms for policy optimization. Yet, recent advances for this problems have only been successful in tabular and linear setting, whose benign structures cannot be generalized to non-linearly parameterized policies. In this paper, we address this problem by leveraging recent advances in value-based algorithms, including bounded eluder-dimension and online sensitivity sampling, to design a low-switching sample-efficient policy optimization algorithm, LPO, with general non-linear function approximation. We show that, our algorithm obtains an $\varepsilon$-optimal policy with only $\widetilde{O}(\frac{\text{poly}(d)}{\varepsilon^3})$ samples, where $\varepsilon$ is the suboptimality gap and $d$ is a complexity measure of the function class approximating the policy. This drastically improves previously best-known sample bound for policy optimization algorithms, $\widetilde{O}(\frac{\text{poly}(d)}{\varepsilon^8})$. Moreover, we empirically test our theory with deep neural nets to show the benefits of the theoretical inspiration.

Jinghan Wang, Mengdi Wang, Lin F. Yang

This work considers the sample complexity of obtaining an $\varepsilon$-optimal policy in an average reward Markov Decision Process (AMDP), given access to a generative model (simulator). When the ground-truth MDP is weakly communicating, we prove an upper bound of $\widetilde O(H \varepsilon^{-3} \ln \frac{1}δ)$ samples per state-action pair, where $H := sp(h^*)$ is the span of bias of any optimal policy, $\varepsilon$ is the accuracy and $δ$ is the failure probability. This bound improves the best-known mixing-time-based approaches in [Jin & Sidford 2021], which assume the mixing-time of every deterministic policy is bounded. The core of our analysis is a proper reduction bound from AMDP problems to discounted MDP (DMDP) problems, which may be of independent interests since it allows the application of DMDP algorithms for AMDP in other settings. We complement our upper bound by proving a minimax lower bound of $Ω(|\mathcal S| |\mathcal A| H \varepsilon^{-2} \ln \frac{1}δ)$ total samples, showing that a linear dependent on $H$ is necessary and that our upper bound matches the lower bound in all parameters of $(|\mathcal S|, |\mathcal A|, H, \ln \frac{1}δ)$ up to some logarithmic factors.

Osama A. Hanna, Lin F. Yang, Christina Fragouli

In this paper, we address the stochastic contextual linear bandit problem, where a decision maker is provided a context (a random set of actions drawn from a distribution). The expected reward of each action is specified by the inner product of the action and an unknown parameter. The goal is to design an algorithm that learns to play as close as possible to the unknown optimal policy after a number of action plays. This problem is considered more challenging than the linear bandit problem, which can be viewed as a contextual bandit problem with a \emph{fixed} context. Surprisingly, in this paper, we show that the stochastic contextual problem can be solved as if it is a linear bandit problem. In particular, we establish a novel reduction framework that converts every stochastic contextual linear bandit instance to a linear bandit instance, when the context distribution is known. When the context distribution is unknown, we establish an algorithm that reduces the stochastic contextual instance to a sequence of linear bandit instances with small misspecifications and achieves nearly the same worst-case regret bound as the algorithm that solves the misspecified linear bandit instances. As a consequence, our results imply a $O(d\sqrt{T\log T})$ high-probability regret bound for contextual linear bandits, making progress in resolving an open problem in (Li et al., 2019), (Li et al., 2021). Our reduction framework opens up a new way to approach stochastic contextual linear bandit problems, and enables improved regret bounds in a number of instances including the batch setting, contextual bandits with misspecifications, contextual bandits with sparse unknown parameters, and contextual bandits with adversarial corruption.

Haochen Zhang, Xi Chen, Lin F. Yang

Decentralized exchanges (DEXs) are a cornerstone of decentralized finance (DeFi), allowing users to trade cryptocurrencies without the need for third-party authorization. Investors are incentivized to deposit assets into liquidity pools, against which users can trade directly, while paying fees to liquidity providers (LPs). However, a number of unresolved issues related to capital efficiency and market risk hinder DeFi's further development. Uniswap V3, a leading and groundbreaking DEX project, addresses capital efficiency by enabling LPs to concentrate their liquidity within specific price ranges for deposited assets. Nevertheless, this approach exacerbates market risk, as LPs earn trading fees only when asset prices are within these predetermined brackets. To mitigate this issue, this paper introduces a deep reinforcement learning (DRL) solution designed to adaptively adjust these price ranges, maximizing profits and mitigating market risks. Our approach also neutralizes price-change risks by hedging the liquidity position through a rebalancing portfolio in a centralized futures exchange. The DRL policy aims to optimize trading fees earned by LPs against associated costs, such as gas fees and hedging expenses, which is referred to as loss-versus-rebalancing (LVR). Using simulations with a profit-and-loss (PnL) benchmark, our method demonstrates superior performance in ETH/USDC and ETH/USDT pools compared to existing baselines. We believe that this strategy not only offers investors a valuable asset management tool but also introduces a new incentive mechanism for DEX designers.

Sanae Amani, Tor Lattimore, András György et al.

We study distributed contextual linear bandits with stochastic contexts, where $N$ agents act cooperatively to solve a linear bandit-optimization problem with $d$-dimensional features over the course of $T$ rounds. For this problem, we derive the first ever information-theoretic lower bound $Ω(dN)$ on the communication cost of any algorithm that performs optimally in a regret minimization setup. We then propose a distributed batch elimination version of the LinUCB algorithm, DisBE-LUCB, where the agents share information among each other through a central server. We prove that the communication cost of DisBE-LUCB matches our lower bound up to logarithmic factors. In particular, for scenarios with known context distribution, the communication cost of DisBE-LUCB is only $\tilde{\mathcal{O}}(dN)$ and its regret is ${\tilde{\mathcal{O}}}(\sqrt{dNT})$, which is of the same order as that incurred by an optimal single-agent algorithm for $NT$ rounds. We also provide similar bounds for practical settings where the context distribution can only be estimated. Therefore, our proposed algorithm is nearly minimax optimal in terms of \emph{both regret and communication cost}. Finally, we propose DecBE-LUCB, a fully decentralized version of DisBE-LUCB, which operates without a central server, where agents share information with their \emph{immediate neighbors} through a carefully designed consensus procedure.

Luyuan Xie, Yan Zhong, Lin Yang et al.

Convolution neural networks (CNNs) have good performance in low-complexity classification tasks such as acoustic scene classifications (ASCs). However, there are few studies on the relationship between the length of target speech and the size of the convolution kernels. In this paper, we combine Selective Kernel Network with Temporal-Convolution (TC-SKNet) to adjust the receptive field of convolution kernels to solve the problem of variable length of target voice while keeping low-complexity. GridMask is a data augmentation strategy by masking part of the raw data or feature area. It can enhance the generalization of the model as the role of dropout. In our experiments, the performance gain brought by GridMask is stronger than spectrum augmentation in ASCs. Finally, we adopt AutoML to search best structure of TC-SKNet and hyperparameters of GridMask for improving the classification performance. As a result, a peak accuracy of 59.87% TC-SKNet is equivalent to that of SOTA, but the parameters only use 20.9 K.

Ningyuan Huang, Soledad Villar, Carey E. Priebe et al.

Graph Neural Networks (GNNs) are powerful deep learning methods for Non-Euclidean data. Popular GNNs are message-passing algorithms (MPNNs) that aggregate and combine signals in a local graph neighborhood. However, shallow MPNNs tend to miss long-range signals and perform poorly on some heterophilous graphs, while deep MPNNs can suffer from issues like over-smoothing or over-squashing. To mitigate such issues, existing works typically borrow normalization techniques from training neural networks on Euclidean data or modify the graph structures. Yet these approaches are not well-understood theoretically and could increase the overall computational complexity. In this work, we draw inspirations from spectral graph embedding and propose $\texttt{PowerEmbed}$ -- a simple layer-wise normalization technique to boost MPNNs. We show $\texttt{PowerEmbed}$ can provably express the top-$k$ leading eigenvectors of the graph operator, which prevents over-smoothing and is agnostic to the graph topology; meanwhile, it produces a list of representations ranging from local features to global signals, which avoids over-squashing. We apply $\texttt{PowerEmbed}$ in a wide range of simulated and real graphs and demonstrate its competitive performance, particularly for heterophilous graphs.

Osama A. Hanna, Lin F. Yang, Christina Fragouli

Contextual linear bandits is a rich and theoretically important model that has many practical applications. Recently, this setup gained a lot of interest in applications over wireless where communication constraints can be a performance bottleneck, especially when the contexts come from a large $d$-dimensional space. In this paper, we consider a distributed memoryless contextual linear bandit learning problem, where the agents who observe the contexts and take actions are geographically separated from the learner who performs the learning while not seeing the contexts. We assume that contexts are generated from a distribution and propose a method that uses $\approx 5d$ bits per context for the case of unknown context distribution and $0$ bits per context if the context distribution is known, while achieving nearly the same regret bound as if the contexts were directly observable. The former bound improves upon existing bounds by a $\log(T)$ factor, where $T$ is the length of the horizon, while the latter achieves information theoretical tightness.

Dingwen Kong, Lin F. Yang

An appropriate reward function is of paramount importance in specifying a task in reinforcement learning (RL). Yet, it is known to be extremely challenging in practice to design a correct reward function for even simple tasks. Human-in-the-loop (HiL) RL allows humans to communicate complex goals to the RL agent by providing various types of feedback. However, despite achieving great empirical successes, HiL RL usually requires too much feedback from a human teacher and also suffers from insufficient theoretical understanding. In this paper, we focus on addressing this issue from a theoretical perspective, aiming to provide provably feedback-efficient algorithmic frameworks that take human-in-the-loop to specify rewards of given tasks. We provide an active-learning-based RL algorithm that first explores the environment without specifying a reward function and then asks a human teacher for only a few queries about the rewards of a task at some state-action pairs. After that, the algorithm guarantees to provide a nearly optimal policy for the task with high probability. We show that, even with the presence of random noise in the feedback, the algorithm only takes $\widetilde{O}(H{{\dim_{R}^2}})$ queries on the reward function to provide an $ε$-optimal policy for any $ε> 0$. Here $H$ is the horizon of the RL environment, and $\dim_{R}$ specifies the complexity of the function class representing the reward function. In contrast, standard RL algorithms require to query the reward function for at least $Ω(\operatorname{poly}(d, 1/ε))$ state-action pairs where $d$ depends on the complexity of the environmental transition.

Jiayi Huang, Han Zhong, Liwei Wang et al.

While numerous works have focused on devising efficient algorithms for reinforcement learning (RL) with uniformly bounded rewards, it remains an open question whether sample or time-efficient algorithms for RL with large state-action space exist when the rewards are \emph{heavy-tailed}, i.e., with only finite $(1+ε)$-th moments for some $ε\in(0,1]$. In this work, we address the challenge of such rewards in RL with linear function approximation. We first design an algorithm, \textsc{Heavy-OFUL}, for heavy-tailed linear bandits, achieving an \emph{instance-dependent} $T$-round regret of $\tilde{O}\big(d T^{\frac{1-ε}{2(1+ε)}} \sqrt{\sum_{t=1}^T ν_t^2} + d T^{\frac{1-ε}{2(1+ε)}}\big)$, the \emph{first} of this kind. Here, $d$ is the feature dimension, and $ν_t^{1+ε}$ is the $(1+ε)$-th central moment of the reward at the $t$-th round. We further show the above bound is minimax optimal when applied to the worst-case instances in stochastic and deterministic linear bandits. We then extend this algorithm to the RL settings with linear function approximation. Our algorithm, termed as \textsc{Heavy-LSVI-UCB}, achieves the \emph{first} computationally efficient \emph{instance-dependent} $K$-episode regret of $\tilde{O}(d \sqrt{H \mathcal{U}^*} K^\frac{1}{1+ε} + d \sqrt{H \mathcal{V}^* K})$. Here, $H$ is length of the episode, and $\mathcal{U}^*, \mathcal{V}^*$ are instance-dependent quantities scaling with the central moment of reward and value functions, respectively. We also provide a matching minimax lower bound $Ω(d H K^{\frac{1}{1+ε}} + d \sqrt{H^3 K})$ to demonstrate the optimality of our algorithm in the worst case. Our result is achieved via a novel robust self-normalized concentration inequality that may be of independent interest in handling heavy-tailed noise in general online regression problems.

Jialin Dong, Lin F. Yang

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in $\mathbb{R}^d$ that approximate the rewards in a bandit or RL with a uniform error of $\varepsilon$, searching for an $O(\varepsilon)$-optimal action requires pulling at least $Ω(\exp(d))$ queries. Furthermore, Lattimore et al. (2020) show that a degraded $O(\varepsilon\sqrt{d})$-optimal solution can be learned within $\operatorname{poly}(d/\varepsilon)$ queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the $\varepsilon\sqrt{d}$ barrier. In this paper, we address this question by showing that algorithms can obtain $O(\varepsilon)$-optimal actions by querying $O(\varepsilon^{-s}d^s)$ actions, where $s$ is the sparsity parameter, removing the $\exp(d)$-dependence. We then establish information-theoretical lower bounds, i.e., $Ω(\exp(s))$, to show that our upper bound on sample complexity is nearly tight if one demands an error $ O(s^δ\varepsilon)$ for $0<δ<1$. For $δ\geq 1$, we further show that $\operatorname{poly}(s/\varepsilon)$ queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

Sanae Amani, Lin F. Yang, Ching-An Cheng

We study lifelong reinforcement learning (RL) in a regret minimization setting of linear contextual Markov decision process (MDP), where the agent needs to learn a multi-task policy while solving a streaming sequence of tasks. We propose an algorithm, called UCB Lifelong Value Distillation (UCBlvd), that provably achieves sublinear regret for any sequence of tasks, which may be adaptively chosen based on the agent's past behaviors. Remarkably, our algorithm uses only sublinear number of planning calls, which means that the agent eventually learns a policy that is near optimal for multiple tasks (seen or unseen) without the need of deliberate planning. A key to this property is a new structural assumption that enables computation sharing across tasks during exploration. Specifically, for $K$ task episodes of horizon $H$, our algorithm has a regret bound $\tilde{\mathcal{O}}(\sqrt{(d^3+d^\prime d)H^4K})$ based on $\mathcal{O}(dH\log(K))$ number of planning calls, where $d$ and $d^\prime$ are the feature dimensions of the dynamics and rewards, respectively. This theoretical guarantee implies that our algorithm can enable a lifelong learning agent to accumulate experiences and learn to rapidly solve new tasks.

Min Gan, Guang-Yong Chen, Yang Yi et al.

The proliferation of saddle points, rather than poor local minima, is increasingly understood to be a primary obstacle in large-scale non-convex optimization for machine learning. Variable elimination algorithms, like Variable Projection (VarPro), have long been observed to exhibit superior convergence and robustness in practice, yet a principled understanding of why they so effectively navigate these complex energy landscapes has remained elusive. In this work, we provide a rigorous geometric explanation by comparing the optimization landscapes of the original and reduced formulations. Through a rigorous analysis based on Hessian inertia and the Schur complement, we prove that variable elimination fundamentally reshapes the critical point structure of the objective function, revealing that local maxima in the reduced landscape are created from, and correspond directly to, saddle points in the original formulation. Our findings are illustrated on the canonical problem of non-convex matrix factorization, visualized directly on two-parameter neural networks, and finally validated in training deep Residual Networks, where our approach yields dramatic improvements in stability and convergence to superior minima. This work goes beyond explaining an existing method; it establishes landscape simplification via saddle point transformation as a powerful principle that can guide the design of a new generation of more robust and efficient optimization algorithms.

Sanae Amani, Khushbu Pahwa, Vladimir Braverman et al.

Recently, DARPA launched the ShELL program, which aims to explore how experience sharing can benefit distributed lifelong learning agents in adapting to new challenges. In this paper, we address this issue by conducting both theoretical and empirical research on distributed multi-task reinforcement learning (RL), where a group of $N$ agents collaboratively solves $M$ tasks without prior knowledge of their identities. We approach the problem by formulating it as linearly parameterized contextual Markov decision processes (MDPs), where each task is represented by a context that specifies the transition dynamics and rewards. To tackle this problem, we propose an algorithm called DistMT-LSVI. First, the agents identify the tasks, and then they exchange information through a central server to derive $ε$-optimal policies for the tasks. Our research demonstrates that to achieve $ε$-optimal policies for all $M$ tasks, a single agent using DistMT-LSVI needs to run a total number of episodes that is at most $\tilde{\mathcal{O}}({d^3H^6(ε^{-2}+c_{\rm sep}^{-2})}\cdot M/N)$, where $c_{\rm sep}>0$ is a constant representing task separability, $H$ is the horizon of each episode, and $d$ is the feature dimension of the dynamics and rewards. Notably, DistMT-LSVI improves the sample complexity of non-distributed settings by a factor of $1/N$, as each agent independently learns $ε$-optimal policies for all $M$ tasks using $\tilde{\mathcal{O}}(d^3H^6Mε^{-2})$ episodes. Additionally, we provide numerical experiments conducted on OpenAI Gym Atari environments that validate our theoretical findings.

Ally Yalei Du, Lin F. Yang, Ruosong Wang

The recent work by Dong & Yang (2023) showed for misspecified sparse linear bandits, one can obtain an $O\left(ε\right)$-optimal policy using a polynomial number of samples when the sparsity is a constant, where $ε$ is the misspecification error. This result is in sharp contrast to misspecified linear bandits without sparsity, which require an exponential number of samples to get the same guarantee. In order to study whether the analog result is possible in the reinforcement learning setting, we consider the following problem: assuming the optimal $Q$-function is a $d$-dimensional linear function with sparsity $k$ and misspecification error $ε$, whether we can obtain an $O\left(ε\right)$-optimal policy using number of samples polynomially in the feature dimension $d$. We first demonstrate why the standard approach based on Bellman backup or the existing optimistic value function elimination approach such as OLIVE (Jiang et al., 2017) achieves suboptimal guarantees for this problem. We then design a novel elimination-based algorithm to show one can obtain an $O\left(Hε\right)$-optimal policy with sample complexity polynomially in the feature dimension $d$ and planning horizon $H$. Lastly, we complement our upper bound with an $\widetildeΩ\left(Hε\right)$ suboptimality lower bound, giving a complete picture of this problem.

Yunfan Li, Lin Yang

The success of reinforcement learning (RL) crucially depends on effective function approximation when dealing with complex ground-truth models. Existing sample-efficient RL algorithms primarily employ three approaches to function approximation: policy-based, value-based, and model-based methods. However, in the face of model misspecification (a disparity between the ground-truth and optimal function approximators), it is shown that policy-based approaches can be robust even when the policy function approximation is under a large locally-bounded misspecification error, with which the function class may exhibit a $Ω(1)$ approximation error in specific states and actions, but remains small on average within a policy-induced state distribution. Yet it remains an open question whether similar robustness can be achieved with value-based and model-based approaches, especially with general function approximation. To bridge this gap, in this paper we present a unified theoretical framework for addressing model misspecification in RL. We demonstrate that, through meticulous algorithm design and sophisticated analysis, value-based and model-based methods employing general function approximation can achieve robustness under local misspecification error bounds. In particular, they can attain a regret bound of $\widetilde{O}\left(\text{poly}(d H)(\sqrt{K} + Kζ) \right)$, where $d$ represents the complexity of the function class, $H$ is the episode length, $K$ is the total number of episodes, and $ζ$ denotes the local bound for misspecification error. Furthermore, we propose an algorithmic framework that can achieve the same order of regret bound without prior knowledge of $ζ$, thereby enhancing its practical applicability.

Jiayi Huang, Han Zhong, Liwei Wang et al.

To tackle long planning horizon problems in reinforcement learning with general function approximation, we propose the first algorithm, termed as UCRL-WVTR, that achieves both \emph{horizon-free} and \emph{instance-dependent}, since it eliminates the polynomial dependency on the planning horizon. The derived regret bound is deemed \emph{sharp}, as it matches the minimax lower bound when specialized to linear mixture MDPs up to logarithmic factors. Furthermore, UCRL-WVTR is \emph{computationally efficient} with access to a regression oracle. The achievement of such a horizon-free, instance-dependent, and sharp regret bound hinges upon (i) novel algorithm designs: weighted value-targeted regression and a high-order moment estimator in the context of general function approximation; and (ii) fine-grained analyses: a novel concentration bound of weighted non-linear least squares and a refined analysis which leads to the tight instance-dependent bound. We also conduct comprehensive experiments to corroborate our theoretical findings.

Osama A. Hanna, Merve Karakas, Lin F. Yang et al.

Multi-Armed Bandit (MAB) systems are witnessing an upswing in applications within multi-agent distributed environments, leading to the advancement of collaborative MAB algorithms. In such settings, communication between agents executing actions and the primary learner making decisions can hinder the learning process. A prevalent challenge in distributed learning is action erasure, often induced by communication delays and/or channel noise. This results in agents possibly not receiving the intended action from the learner, subsequently leading to misguided feedback. In this paper, we introduce novel algorithms that enable learners to interact concurrently with distributed agents across heterogeneous action erasure channels with different action erasure probabilities. We illustrate that, in contrast to existing bandit algorithms, which experience linear regret, our algorithms assure sub-linear regret guarantees. Our proposed solutions are founded on a meticulously crafted repetition protocol and scheduling of learning across heterogeneous channels. To our knowledge, these are the first algorithms capable of effectively learning through heterogeneous action erasure channels. We substantiate the superior performance of our algorithm through numerical experiments, emphasizing their practical significance in addressing issues related to communication constraints and delays in multi-agent environments.

Jinhang Chai, Elynn Chen, Lin Yang

To bridge the gap between empirical success and theoretical understanding in transfer reinforcement learning (RL), we study a principled approach with provable performance guarantees. We introduce a novel composite MDP framework where high-dimensional transition dynamics are modeled as the sum of a low-rank component representing shared structure and a sparse component capturing task-specific variations. This relaxes the common assumption of purely low-rank transition models, allowing for more realistic scenarios where tasks share core dynamics but maintain individual variations. We introduce UCB-TQL (Upper Confidence Bound Transfer Q-Learning), designed for transfer RL scenarios where multiple tasks share core linear MDP dynamics but diverge along sparse dimensions. When applying UCB-TQL to a target task after training on a source task with sufficient trajectories, we achieve a regret bound of $\tilde{O}(\sqrt{eH^5N})$ that scales independently of the ambient dimension. Here, $N$ represents the number of trajectories in the target task, while $e$ quantifies the sparse differences between tasks. This result demonstrates substantial improvement over single task RL by effectively leveraging their structural similarities. Our theoretical analysis provides rigorous guarantees for how UCB-TQL simultaneously exploits shared dynamics while adapting to task-specific variations.

Lawrence Liu, Alexander Liu, Mengdi Wang et al.

Large language models (LLMs) present significant deployment challenges due to their immense computational and memory requirements. While semi-structured pruning, particularly 2:4 sparsity, offers a path to practical hardware acceleration, existing methods often incur substantial performance degradation. To bridge this gap, we introduce ARMOR: (Adaptive Representation with Matrix-factORization), a novel one-shot post-training pruning algorithm. Instead of directly pruning weights, ARMOR factorizes each weight matrix into a 2:4 sparse core wrapped by two low-overhead, block diagonal matrices. These wrappers act as efficient pre and post-transformation error correctors, offering greater flexibility to preserve model quality compared to conventional 2:4 pruning techniques. The sparse core and block diagonal wrappers are chosen through a block coordinate descent algorithm that minimizes a layer-wise proxy loss. We theoretically prove this optimization is guaranteed to converge to a solution with a proxy loss less than or equal to state-of-the-art pruning algorithms. Experiments on Llama (Touvron et al., 2023; Dubey et al., 2024) and Qwen (Yang et al., 2025) model families demonstrate that ARMOR consistently and significantly outperforms state-of-the-art 2:4 pruning methods across a wide range of downstream tasks and perplexity evaluations. ARMOR achieves this superior performance while retaining the inference speedups and substantial memory usage reductions of 2:4 pruning, establishing a more effective trade-off between model compression and task accuracy

Yukuan Wei, Xudong Li, Lin F. Yang

Recent advances have significantly improved our understanding of the sample complexity of learning in average-reward Markov decision processes (AMDPs) under the generative model. However, much less is known about the constrained average-reward MDP (CAMDP), where policies must satisfy long-run average constraints. In this work, we address this gap by studying the sample complexity of learning an $ε$-optimal policy in CAMDPs under a generative model. We propose a model-based algorithm that operates under two settings: (i) relaxed feasibility, which allows small constraint violations, and (ii) strict feasibility, where the output policy satisfies the constraint. We show that our algorithm achieves sample complexities of $\tilde{O}\left(\frac{S A (B+H)}{ ε^2}\right)$ and $\tilde{O} \left(\frac{S A (B+H)}{ε^2 ζ^2} \right)$ under the relaxed and strict feasibility settings, respectively. Here, $ζ$ is the Slater constant indicating the size of the feasible region, $H$ is the span bound of the bias function, and $B$ is the transient time bound. Moreover, a matching lower bound of $\tildeΩ\left(\frac{S A (B+H)}{ ε^2ζ^2}\right)$ for the strict feasibility case is established, thus providing the first minimax-optimal bounds for CAMDPs. Our results close the theoretical gap in understanding the complexity of constrained average-reward MDPs.

Merve Karakas, Osama Hanna, Lin F. Yang et al.

We study a distributed multi-armed bandit (MAB) problem over arm erasure channels, motivated by the increasing adoption of MAB algorithms over communication-constrained networks. In this setup, the learner communicates the chosen arm to play to an agent over an erasure channel with probability $ε\in [0,1)$; if an erasure occurs, the agent continues pulling the last successfully received arm; the learner always observes the reward of the arm pulled. In past work, we considered the case where the agent cannot convey feedback to the learner, and thus the learner does not know whether the arm played is the requested or the last successfully received one. In this paper, we instead consider the case where the agent can send feedback to the learner on whether the arm request was received, and thus the learner exactly knows which arm was played. Surprisingly, we prove that erasure feedback does not improve the worst-case regret upper bound order over the previously studied no-feedback setting. In particular, we prove a regret lower bound of $Ω(\sqrt{KT} + K / (1 - ε))$, where $K$ is the number of arms and $T$ the time horizon, that matches no-feedback upper bounds up to logarithmic factors. We note however that the availability of feedback enables simpler algorithm designs that may achieve better constants (albeit not better order) regret bounds; we design one such algorithm and evaluate its performance numerically.

Yiran Wang, Chenshu Liu, Yunfan Li et al.

The exploration \& exploitation dilemma poses significant challenges in reinforcement learning (RL). Recently, curiosity-based exploration methods achieved great success in tackling hard-exploration problems. However, they necessitate extensive hyperparameter tuning on different environments, which heavily limits the applicability and accessibility of this line of methods. In this paper, we characterize this problem via analysis of the agent behavior, concluding the fundamental difficulty of choosing a proper hyperparameter. We then identify the difficulty and the instability of the optimization when the agent learns with curiosity. We propose our method, hyperparameter robust exploration (\textbf{Hyper}), which extensively mitigates the problem by effectively regularizing the visitation of the exploration and decoupling the exploitation to ensure stable training. We theoretically justify that \textbf{Hyper} is provably efficient under function approximation setting and empirically demonstrate its appealing performance and robustness in various environments.

Tian Tian, Lin F. Yang, Csaba Szepesvári

The constrained Markov decision process (CMDP) framework emerges as an important reinforcement learning approach for imposing safety or other critical objectives while maximizing cumulative reward. However, the current understanding of how to learn efficiently in a CMDP environment with a potentially infinite number of states remains under investigation, particularly when function approximation is applied to the value functions. In this paper, we address the learning problem given linear function approximation with $q_π$-realizability, where the value functions of all policies are linearly representable with a known feature map, a setting known to be more general and challenging than other linear settings. Utilizing a local-access model, we propose a novel primal-dual algorithm that, after $\tilde{O}(\text{poly}(d) ε^{-3})$ queries, outputs with high probability a policy that strictly satisfies the constraints while nearly optimizing the value with respect to a reward function. Here, $d$ is the feature dimension and $ε> 0$ is a given error. The algorithm relies on a carefully crafted off-policy evaluation procedure to evaluate the policy using historical data, which informs policy updates through policy gradients and conserves samples. To our knowledge, this is the first result achieving polynomial sample complexity for CMDP in the $q_π$-realizable setting.

Osama Hanna, Merve Karakas, Lin F. Yang et al.

We consider a novel multi-arm bandit (MAB) setup, where a learner needs to communicate the actions to distributed agents over erasure channels, while the rewards for the actions are directly available to the learner through external sensors. In our model, while the distributed agents know if an action is erased, the central learner does not (there is no feedback), and thus does not know whether the observed reward resulted from the desired action or not. We propose a scheme that can work on top of any (existing or future) MAB algorithm and make it robust to action erasures. Our scheme results in a worst-case regret over action-erasure channels that is at most a factor of $O(1/\sqrt{1-ε})$ away from the no-erasure worst-case regret of the underlying MAB algorithm, where $ε$ is the erasure probability. We also propose a modification of the successive arm elimination algorithm and prove that its worst-case regret is $\Tilde{O}(\sqrt{KT}+K/(1-ε))$, which we prove is optimal by providing a matching lower bound.

Amin Karbasi, Grigoris Velegkas, Lin F. Yang et al.

We initiate the mathematical study of replicability as an algorithmic property in the context of reinforcement learning (RL). We focus on the fundamental setting of discounted tabular MDPs with access to a generative model. Inspired by Impagliazzo et al. [2022], we say that an RL algorithm is replicable if, with high probability, it outputs the exact same policy after two executions on i.i.d. samples drawn from the generator when its internal randomness is the same. We first provide an efficient $ρ$-replicable algorithm for $(\varepsilon, δ)$-optimal policy estimation with sample and time complexity $\widetilde O\left(\frac{N^3\cdot\log(1/δ)}{(1-γ)^5\cdot\varepsilon^2\cdotρ^2}\right)$, where $N$ is the number of state-action pairs. Next, for the subclass of deterministic algorithms, we provide a lower bound of order $Ω\left(\frac{N^3}{(1-γ)^3\cdot\varepsilon^2\cdotρ^2}\right)$. Then, we study a relaxed version of replicability proposed by Kalavasis et al. [2023] called TV indistinguishability. We design a computationally efficient TV indistinguishable algorithm for policy estimation whose sample complexity is $\widetilde O\left(\frac{N^2\cdot\log(1/δ)}{(1-γ)^5\cdot\varepsilon^2\cdotρ^2}\right)$. At the cost of $\exp(N)$ running time, we transform these TV indistinguishable algorithms to $ρ$-replicable ones without increasing their sample complexity. Finally, we introduce the notion of approximate-replicability where we only require that two outputted policies are close under an appropriate statistical divergence (e.g., Renyi) and show an improved sample complexity of $\widetilde O\left(\frac{N\cdot\log(1/δ)}{(1-γ)^5\cdot\varepsilon^2\cdotρ^2}\right)$.

Jinyuan Chang, Jing He, Lin Yang et al.

We consider to model matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further refined approach which projects it into a lower-dimensional full-ranked eigenequation. This refined method improves significantly the finite-sample performance of the estimation. The asymptotic theory has been established under a general setting without the stationarity. It shows, for example, that all the component coefficient vectors in the CP-decomposition are estimated consistently with certain convergence rates. The proposed model and the estimation method are also illustrated with both simulated and real data; showing effective dimension-reduction in modelling and forecasting matrix time series.

Yucong Zhang, Qinjian Lin, Weiqing Wang et al.

This paper introduces an online speaker diarization system that can handle long-time audio with low latency. We enable Agglomerative Hierarchy Clustering (AHC) to work in an online fashion by introducing a label matching algorithm. This algorithm solves the inconsistency between output labels and hidden labels that are generated each turn. To ensure the low latency in the online setting, we introduce a variant of AHC, namely chkpt-AHC, to cluster the speakers. In addition, we propose a speaker embedding graph to exploit a graph-based re-clustering method, further improving the performance. In the experiment, we evaluate our systems on both DIHARD3 and VoxConverse datasets. The experimental results show that our proposed online systems have better performance than our baseline online system and have comparable performance to our offline systems. We find out that the framework combining the chkpt-AHC method and the label matching algorithm works well in the online setting. Moreover, the chkpt-AHC method greatly reduces the time cost, while the graph-based re-clustering method helps improve the performance.

Yuanzhi Li, Ruosong Wang, Lin F. Yang

Recently there is a surge of interest in understanding the horizon-dependence of the sample complexity in reinforcement learning (RL). Notably, for an RL environment with horizon length $H$, previous work have shown that there is a probably approximately correct (PAC) algorithm that learns an $O(1)$-optimal policy using $\mathrm{polylog}(H)$ episodes of environment interactions when the number of states and actions is fixed. It is yet unknown whether the $\mathrm{polylog}(H)$ dependence is necessary or not. In this work, we resolve this question by developing an algorithm that achieves the same PAC guarantee while using only $O(1)$ episodes of environment interactions, completely settling the horizon-dependence of the sample complexity in RL. We achieve this bound by (i) establishing a connection between value functions in discounted and finite-horizon Markov decision processes (MDPs) and (ii) a novel perturbation analysis in MDPs. We believe our new techniques are of independent interest and could be applied in related questions in RL.

Han Zhong, Jiayi Huang, Lin F. Yang et al.

Despite a large amount of effort in dealing with heavy-tailed error in machine learning, little is known when moments of the error can become non-existential: the random noise $η$ satisfies Pr$\left[|η| > |y|\right] \le 1/|y|^α$ for some $α> 0$. We make the first attempt to actively handle such super heavy-tailed noise in bandit learning problems: We propose a novel robust statistical estimator, mean of medians, which estimates a random variable by computing the empirical mean of a sequence of empirical medians. We then present a generic reductionist algorithmic framework for solving bandit learning problems (including multi-armed and linear bandit problem): the mean of medians estimator can be applied to nearly any bandit learning algorithm as a black-box filtering for its reward signals and obtain similar regret bound as if the reward is sub-Gaussian. We show that the regret bound is near-optimal even with very heavy-tailed noise. We also empirically demonstrate the effectiveness of the proposed algorithm, which further corroborates our theoretical results.

Weichao Mao, Lin F. Yang, Kaiqing Zhang et al.

Multi-agent reinforcement learning (MARL) algorithms often suffer from an exponential sample complexity dependence on the number of agents, a phenomenon known as \emph{the curse of multiagents}. In this paper, we address this challenge by investigating sample-efficient model-free algorithms in \emph{decentralized} MARL, and aim to improve existing algorithms along this line. For learning (coarse) correlated equilibria in general-sum Markov games, we propose \emph{stage-based} V-learning algorithms that significantly simplify the algorithmic design and analysis of recent works, and circumvent a rather complicated no-\emph{weighted}-regret bandit subroutine. For learning Nash equilibria in Markov potential games, we propose an independent policy gradient algorithm with a decentralized momentum-based variance reduction technique. All our algorithms are decentralized in that each agent can make decisions based on only its local information. Neither communication nor centralized coordination is required during learning, leading to a natural generalization to a large number of agents. We also provide numerical simulations to corroborate our theoretical findings.

Qingjian Lin, Lin Yang, Xuyang Wang et al.

With the development of deep learning, automatic speaker verification has made considerable progress over the past few years. However, to design a lightweight and robust system with limited computational resources is still a challenging problem. Traditionally, a speaker verification system is symmetrical, indicating that the same embedding extraction model is applied for both enrollment and verification in inference. In this paper, we come up with an innovative asymmetric structure, which takes the large-scale ECAPA-TDNN model for enrollment and the small-scale ECAPA-TDNNLite model for verification. As a symmetrical system, our proposed ECAPA-TDNNLite model achieves an EER of 3.07% on the Voxceleb1 original test set with only 11.6M FLOPS. Moreover, the asymmetric structure further reduces the EER to 2.31%, without increasing any computational costs during verification.

Junhong Shen, Lin F. Yang

Recently, deep reinforcement learning (RL) has achieved remarkable empirical success by integrating deep neural networks into RL frameworks. However, these algorithms often require a large number of training samples and admit little theoretical understanding. To mitigate these issues, we propose a theoretically principled nearest neighbor (NN) function approximator that can improve the value networks in deep RL methods. Inspired by human similarity judgments, the NN approximator estimates the action values using rollouts on past observations and can provably obtain a small regret bound that depends only on the intrinsic complexity of the environment. We present (1) Nearest Neighbor Actor-Critic (NNAC), an online policy gradient algorithm that demonstrates the practicality of combining function approximation with deep RL, and (2) a plug-and-play NN update module that aids the training of existing deep RL methods. Experiments on classical control and MuJoCo locomotion tasks show that the NN-accelerated agents achieve higher sample efficiency and stability than the baseline agents. Based on its theoretical benefits, we believe that the NN approximator can be further applied to other complex domains to speed-up learning.

Xiaoyu Chen, Jiachen Hu, Lin F. Yang et al.

Although model-based reinforcement learning (RL) approaches are considered more sample efficient, existing algorithms are usually relying on sophisticated planning algorithm to couple tightly with the model-learning procedure. Hence the learned models may lack the ability of being re-used with more specialized planners. In this paper we address this issue and provide approaches to learn an RL model efficiently without the guidance of a reward signal. In particular, we take a plug-in solver approach, where we focus on learning a model in the exploration phase and demand that \emph{any planning algorithm} on the learned model can give a near-optimal policy. Specicially, we focus on the linear mixture MDP setting, where the probability transition matrix is a (unknown) convex combination of a set of existing models. We show that, by establishing a novel exploration algorithm, the plug-in approach learns a model by taking $\tilde{O}(d^2H^3/ε^2)$ interactions with the environment and \emph{any} $ε$-optimal planner on the model gives an $O(ε)$-optimal policy on the original model. This sample complexity matches lower bounds for non-plug-in approaches and is \emph{statistically optimal}. We achieve this result by leveraging a careful maximum total-variance bound using Bernstein inequality and properties specified to linear mixture MDP.

Jingfeng Wu, Vladimir Braverman, Lin F. Yang

For the problem of task-agnostic reinforcement learning (RL), an agent first collects samples from an unknown environment without the supervision of reward signals, then is revealed with a reward and is asked to compute a corresponding near-optimal policy. Existing approaches mainly concern the worst-case scenarios, in which no structural information of the reward/transition-dynamics is utilized. Therefore the best sample upper bound is $\propto\widetilde{\mathcal{O}}(1/ε^2)$, where $ε>0$ is the target accuracy of the obtained policy, and can be overly pessimistic. To tackle this issue, we provide an efficient algorithm that utilizes a gap parameter, $ρ>0$, to reduce the amount of exploration. In particular, for an unknown finite-horizon Markov decision process, the algorithm takes only $\widetilde{\mathcal{O}} (1/ε\cdot (H^3SA / ρ+ H^4 S^2 A) )$ episodes of exploration, and is able to obtain an $ε$-optimal policy for a post-revealed reward with sub-optimality gap at least $ρ$, where $S$ is the number of states, $A$ is the number of actions, and $H$ is the length of the horizon, obtaining a nearly \emph{quadratic saving} in terms of $ε$. We show that, information-theoretically, this bound is nearly tight for $ρ< Θ(1/(HS))$ and $H>1$. We further show that $\propto\widetilde{\mathcal{O}}(1)$ sample bound is possible for $H=1$ (i.e., multi-armed bandit) or with a sampling simulator, establishing a stark separation between those settings and the RL setting.

Haque Ishfaq, Qiwen Cui, Viet Nguyen et al.

We propose a model-free reinforcement learning algorithm inspired by the popular randomized least squares value iteration (RLSVI) algorithm as well as the optimism principle. Unlike existing upper-confidence-bound (UCB) based approaches, which are often computationally intractable, our algorithm drives exploration by simply perturbing the training data with judiciously chosen i.i.d. scalar noises. To attain optimistic value function estimation without resorting to a UCB-style bonus, we introduce an optimistic reward sampling procedure. When the value functions can be represented by a function class $\mathcal{F}$, our algorithm achieves a worst-case regret bound of $\widetilde{O}(\mathrm{poly}(d_EH)\sqrt{T})$ where $T$ is the time elapsed, $H$ is the planning horizon and $d_E$ is the $\textit{eluder dimension}$ of $\mathcal{F}$. In the linear setting, our algorithm reduces to LSVI-PHE, a variant of RLSVI, that enjoys an $\widetilde{\mathcal{O}}(\sqrt{d^3H^3T})$ regret. We complement the theory with an empirical evaluation across known difficult exploration tasks.

Dingwen Kong, Ruslan Salakhutdinov, Ruosong Wang et al.

Most of the existing works for reinforcement learning (RL) with general function approximation (FA) focus on understanding the statistical complexity or regret bounds. However, the computation complexity of such approaches is far from being understood -- indeed, a simple optimization problem over the function class might be as well intractable. In this paper, we tackle this problem by establishing an efficient online sub-sampling framework that measures the information gain of data points collected by an RL algorithm and uses the measurement to guide exploration. For a value-based method with complexity-bounded function class, we show that the policy only needs to be updated for $\propto\operatorname{poly}\log(K)$ times for running the RL algorithm for $K$ episodes while still achieving a small near-optimal regret bound. In contrast to existing approaches that update the policy for at least $Ω(K)$ times, our approach drastically reduces the number of optimization calls in solving for a policy. When applied to settings in \cite{wang2020reinforcement} or \cite{jin2021bellman}, we improve the overall time complexity by at least a factor of $K$. Finally, we show the generality of our online sub-sampling technique by applying it to the reward-free RL setting and multi-agent RL setting.

Sanae Amani, Christos Thrampoulidis, Lin F. Yang

Safety in reinforcement learning has become increasingly important in recent years. Yet, existing solutions either fail to strictly avoid choosing unsafe actions, which may lead to catastrophic results in safety-critical systems, or fail to provide regret guarantees for settings where safety constraints need to be learned. In this paper, we address both problems by first modeling safety as an unknown linear cost function of states and actions, which must always fall below a certain threshold. We then present algorithms, termed SLUCB-QVI and RSLUCB-QVI, for episodic Markov decision processes (MDPs) with linear function approximation. We show that SLUCB-QVI and RSLUCB-QVI, while with \emph{no safety violation}, achieve a $\tilde{\mathcal{O}}\left(κ\sqrt{d^3H^3T}\right)$ regret, nearly matching that of state-of-the-art unsafe algorithms, where $H$ is the duration of each episode, $d$ is the dimension of the feature mapping, $κ$ is a constant characterizing the safety constraints, and $T$ is the total number of action plays. We further present numerical simulations that corroborate our theoretical findings.

Jialin Dong, Da Zheng, Lin F. Yang et al.

Graph neural networks (GNNs) are powerful tools for learning from graph data and are widely used in various applications such as social network recommendation, fraud detection, and graph search. The graphs in these applications are typically large, usually containing hundreds of millions of nodes. Training GNN models on such large graphs efficiently remains a big challenge. Despite a number of sampling-based methods have been proposed to enable mini-batch training on large graphs, these methods have not been proved to work on truly industry-scale graphs, which require GPUs or mixed-CPU-GPU training. The state-of-the-art sampling-based methods are usually not optimized for these real-world hardware setups, in which data movement between CPUs and GPUs is a bottleneck. To address this issue, we propose Global Neighborhood Sampling that aims at training GNNs on giant graphs specifically for mixed-CPU-GPU training. The algorithm samples a global cache of nodes periodically for all mini-batches and stores them in GPUs. This global cache allows in-GPU importance sampling of mini-batches, which drastically reduces the number of nodes in a mini-batch, especially in the input layer, to reduce data copy between CPU and GPU and mini-batch computation without compromising the training convergence rate or model accuracy. We provide a highly efficient implementation of this method and show that our implementation outperforms an efficient node-wise neighbor sampling baseline by a factor of 2X-4X on giant graphs. It outperforms an efficient implementation of LADIES with small layers by a factor of 2X-14X while achieving much higher accuracy than LADIES.We also theoretically analyze the proposed algorithm and show that with cached node data of a proper size, it enjoys a comparable convergence rate as the underlying node-wise sampling method.

Fei Feng, Wotao Yin, Alekh Agarwal et al.

Policy optimization methods remain a powerful workhorse in empirical Reinforcement Learning (RL), with a focus on neural policies that can easily reason over complex and continuous state and/or action spaces. Theoretical understanding of strategic exploration in policy-based methods with non-linear function approximation, however, is largely missing. In this paper, we address this question by designing ENIAC, an actor-critic method that allows non-linear function approximation in the critic. We show that under certain assumptions, e.g., a bounded eluder dimension $d$ for the critic class, the learner finds a near-optimal policy in $O(\poly(d))$ exploration rounds. The method is robust to model misspecification and strictly extends existing works on linear function approximation. We also develop some computational optimizations of our approach with slightly worse statistical guarantees and an empirical adaptation building on existing deep RL tools. We empirically evaluate this adaptation and show that it outperforms prior heuristics inspired by linear methods, establishing the value via correctly reasoning about the agent's uncertainty under non-linear function approximation.

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.

Minbo Gao, Tianle Xie, Simon S. Du et al.

Many real-world applications, such as those in medical domains, recommendation systems, etc, can be formulated as large state space reinforcement learning problems with only a small budget of the number of policy changes, i.e., low switching cost. This paper focuses on the linear Markov Decision Process (MDP) recently studied in [Yang et al 2019, Jin et al 2020] where the linear function approximation is used for generalization on the large state space. We present the first algorithm for linear MDP with a low switching cost. Our algorithm achieves an $\widetilde{O}\left(\sqrt{d^3H^4K}\right)$ regret bound with a near-optimal $O\left(d H\log K\right)$ global switching cost where $d$ is the feature dimension, $H$ is the planning horizon and $K$ is the number of episodes the agent plays. Our regret bound matches the best existing polynomial algorithm by [Jin et al 2020] and our switching cost is exponentially smaller than theirs. When specialized to tabular MDP, our switching cost bound improves those in [Bai et al 2019, Zhang et al 20020]. We complement our positive result with an $Ω\left(dH/\log d\right)$ global switching cost lower bound for any no-regret algorithm.

Qiwen Cui, Lin F. Yang

The empirical success of Multi-agent reinforcement learning is encouraging, while few theoretical guarantees have been revealed. In this work, we prove that the plug-in solver approach, probably the most natural reinforcement learning algorithm, achieves minimax sample complexity for turn-based stochastic game (TBSG). Specifically, we plan in an empirical TBSG by utilizing a `simulator' that allows sampling from arbitrary state-action pair. We show that the empirical Nash equilibrium strategy is an approximate Nash equilibrium strategy in the true TBSG and give both problem-dependent and problem-independent bound. We develop absorbing TBSG and reward perturbation techniques to tackle the complex statistical dependence. The key idea is artificially introducing a suboptimality gap in TBSG and then the Nash equilibrium strategy lies in a finite set.

Jingfeng Wu, Vladimir Braverman, Lin F. Yang

In this paper we consider multi-objective reinforcement learning where the objectives are balanced using preferences. In practice, the preferences are often given in an adversarial manner, e.g., customers can be picky in many applications. We formalize this problem as an episodic learning problem on a Markov decision process, where transitions are unknown and a reward function is the inner product of a preference vector with pre-specified multi-objective reward functions. We consider two settings. In the online setting, the agent receives a (adversarial) preference every episode and proposes policies to interact with the environment. We provide a model-based algorithm that achieves a nearly minimax optimal regret bound $\widetilde{\mathcal{O}}\bigl(\sqrt{\min\{d,S\}\cdot H^2 SAK}\bigr)$, where $d$ is the number of objectives, $S$ is the number of states, $A$ is the number of actions, $H$ is the length of the horizon, and $K$ is the number of episodes. Furthermore, we consider preference-free exploration, i.e., the agent first interacts with the environment without specifying any preference and then is able to accommodate arbitrary preference vector up to $ε$ error. Our proposed algorithm is provably efficient with a nearly optimal trajectory complexity $\widetilde{\mathcal{O}}\bigl({\min\{d,S\}\cdot H^3 SA}/{ε^2}\bigr)$. This result partly resolves an open problem raised by \citet{jin2020reward}.

Tianyu Wang, Lin F. Yang

Linear Quadratic Regulators (LQR) achieve enormous successful real-world applications. Very recently, people have been focusing on efficient learning algorithms for LQRs when their dynamics are unknown. Existing results effectively learn to control the unknown system using number of episodes depending polynomially on the system parameters, including the ambient dimension of the states. These traditional approaches, however, become inefficient in common scenarios, e.g., when the states are high-resolution images. In this paper, we propose an algorithm that utilizes the intrinsic system low-rank structure for efficient learning. For problems of rank-$m$, our algorithm achieves a $K$-episode regret bound of order $\widetilde{O}(m^{3/2} K^{1/2})$. Consequently, the sample complexity of our algorithm only depends on the rank, $m$, rather than the ambient dimension, $d$, which can be orders-of-magnitude larger.

Qiwen Cui, Lin F. Yang

It is believed that a model-based approach for reinforcement learning (RL) is the key to reduce sample complexity. However, the understanding of the sample optimality of model-based RL is still largely missing, even for the linear case. This work considers sample complexity of finding an $ε$-optimal policy in a Markov decision process (MDP) that admits a linear additive feature representation, given only access to a generative model. We solve this problem via a plug-in solver approach, which builds an empirical model and plans in this empirical model via an arbitrary plug-in solver. We prove that under the anchor-state assumption, which implies implicit non-negativity in the feature space, the minimax sample complexity of finding an $ε$-optimal policy in a $γ$-discounted MDP is $O(K/(1-γ)^3ε^2)$, which only depends on the dimensionality $K$ of the feature space and has no dependence on the state or action space. We further extend our results to a relaxed setting where anchor-states may not exist and show that a plug-in approach can be sample efficient as well, providing a flexible approach to design model-based algorithms for RL.

Nived Rajaraman, Lin F. Yang, Jiantao Jiao et al.

Imitation learning (IL) aims to mimic the behavior of an expert policy in a sequential decision-making problem given only demonstrations. In this paper, we focus on understanding the minimax statistical limits of IL in episodic Markov Decision Processes (MDPs). We first consider the setting where the learner is provided a dataset of $N$ expert trajectories ahead of time, and cannot interact with the MDP. Here, we show that the policy which mimics the expert whenever possible is in expectation $\lesssim \frac{|\mathcal{S}| H^2 \log (N)}{N}$ suboptimal compared to the value of the expert, even when the expert follows an arbitrary stochastic policy. Here $\mathcal{S}$ is the state space, and $H$ is the length of the episode. Furthermore, we establish a suboptimality lower bound of $\gtrsim |\mathcal{S}| H^2 / N$ which applies even if the expert is constrained to be deterministic, or if the learner is allowed to actively query the expert at visited states while interacting with the MDP for $N$ episodes. To our knowledge, this is the first algorithm with suboptimality having no dependence on the number of actions, under no additional assumptions. We then propose a novel algorithm based on minimum-distance functionals in the setting where the transition model is given and the expert is deterministic. The algorithm is suboptimal by $\lesssim \min \{ H \sqrt{|\mathcal{S}| / N} ,\ |\mathcal{S}| H^{3/2} / N \}$, showing that knowledge of transition improves the minimax rate by at least a $\sqrt{H}$ factor.

Kaiqing Zhang, Sham M. Kakade, Tamer Başar et al.

Model-based reinforcement learning (RL), which finds an optimal policy using an empirical model, has long been recognized as one of the corner stones of RL. It is especially suitable for multi-agent RL (MARL), as it naturally decouples the learning and the planning phases, and avoids the non-stationarity problem when all agents are improving their policies simultaneously using samples. Though intuitive and widely-used, the sample complexity of model-based MARL algorithms has not been fully investigated. In this paper, our goal is to address the fundamental question about its sample complexity. We study arguably the most basic MARL setting: two-player discounted zero-sum Markov games, given only access to a generative model. We show that model-based MARL achieves a sample complexity of $\tilde O(|S||A||B|(1-γ)^{-3}ε^{-2})$ for finding the Nash equilibrium (NE) value up to some $ε$ error, and the $ε$-NE policies with a smooth planning oracle, where $γ$ is the discount factor, and $S,A,B$ denote the state space, and the action spaces for the two agents. We further show that such a sample bound is minimax-optimal (up to logarithmic factors) if the algorithm is reward-agnostic, where the algorithm queries state transition samples without reward knowledge, by establishing a matching lower bound. This is in contrast to the usual reward-aware setting, with a $\tildeΩ(|S|(|A|+|B|)(1-γ)^{-3}ε^{-2})$ lower bound, where this model-based approach is near-optimal with only a gap on the $|A|,|B|$ dependence. Our results not only demonstrate the sample-efficiency of this basic model-based approach in MARL, but also elaborate on the fundamental tradeoff between its power (easily handling the more challenging reward-agnostic case) and limitation (less adaptive and suboptimal in $|A|,|B|$), particularly arises in the multi-agent context.