Qinghua Liu

Qinghua Liu, Alan Chung, Csaba Szepesvári et al. · deepmind

Applications of Reinforcement Learning (RL), in which agents learn to make a sequence of decisions despite lacking complete information about the latent states of the controlled system, that is, they act under partial observability of the states, are ubiquitous. Partially observable RL can be notoriously difficult -- well-known information-theoretic results show that learning partially observable Markov decision processes (POMDPs) requires an exponential number of samples in the worst case. Yet, this does not rule out the existence of large subclasses of POMDPs over which learning is tractable. In this paper we identify such a subclass, which we call weakly revealing POMDPs. This family rules out the pathological instances of POMDPs where observations are uninformative to a degree that makes learning hard. We prove that for weakly revealing POMDPs, a simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) is sufficient to guarantee polynomial sample complexity. To the best of our knowledge, this is the first provably sample-efficient result for learning from interactions in overcomplete POMDPs, where the number of latent states can be larger than the number of observations.

Aaditya Singh, Adam Fry, Adam Perelman et al. · berkeley, mila

This is the system card published alongside the OpenAI GPT-5 launch, August 2025. GPT-5 is a unified system with a smart and fast model that answers most questions, a deeper reasoning model for harder problems, and a real-time router that quickly decides which model to use based on conversation type, complexity, tool needs, and explicit intent (for example, if you say 'think hard about this' in the prompt). The router is continuously trained on real signals, including when users switch models, preference rates for responses, and measured correctness, improving over time. Once usage limits are reached, a mini version of each model handles remaining queries. This system card focuses primarily on gpt-5-thinking and gpt-5-main, while evaluations for other models are available in the appendix. The GPT-5 system not only outperforms previous models on benchmarks and answers questions more quickly, but -- more importantly -- is more useful for real-world queries. We've made significant advances in reducing hallucinations, improving instruction following, and minimizing sycophancy, and have leveled up GPT-5's performance in three of ChatGPT's most common uses: writing, coding, and health. All of the GPT-5 models additionally feature safe-completions, our latest approach to safety training to prevent disallowed content. Similarly to ChatGPT agent, we have decided to treat gpt-5-thinking as High capability in the Biological and Chemical domain under our Preparedness Framework, activating the associated safeguards. While we do not have definitive evidence that this model could meaningfully help a novice to create severe biological harm -- our defined threshold for High capability -- we have chosen to take a precautionary approach.

Qinghua Liu, Csaba Szepesvári, Chi Jin · deepmind

This paper considers the challenging tasks of Multi-Agent Reinforcement Learning (MARL) under partial observability, where each agent only sees her own individual observations and actions that reveal incomplete information about the underlying state of system. This paper studies these tasks under the general model of multiplayer general-sum Partially Observable Markov Games (POMGs), which is significantly larger than the standard model of Imperfect Information Extensive-Form Games (IIEFGs). We identify a rich subclass of POMGs -- weakly revealing POMGs -- in which sample-efficient learning is tractable. In the self-play setting, we prove that a simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) is sufficient to find approximate Nash equilibria, correlated equilibria, as well as coarse correlated equilibria of weakly revealing POMGs, in a polynomial number of samples when the number of agents is small. In the setting of playing against adversarial opponents, we show that a variant of our optimistic MLE algorithm is capable of achieving sublinear regret when being compared against the optimal maximin policies. To our best knowledge, this work provides the first line of sample-efficient results for learning POMGs.

Runyu Zhang, Qinghua Liu, Huan Wang et al. · salesforce

This paper studies policy optimization algorithms for multi-agent reinforcement learning. We begin by proposing an algorithm framework for two-player zero-sum Markov Games in the full-information setting, where each iteration consists of a policy update step at each state using a certain matrix game algorithm, and a value update step with a certain learning rate. This framework unifies many existing and new policy optimization algorithms. We show that the state-wise average policy of this algorithm converges to an approximate Nash equilibrium (NE) of the game, as long as the matrix game algorithms achieve low weighted regret at each state, with respect to weights determined by the speed of the value updates. Next, we show that this framework instantiated with the Optimistic Follow-The-Regularized-Leader (OFTRL) algorithm at each state (and smooth value updates) can find an $\mathcal{\widetilde{O}}(T^{-5/6})$ approximate NE in $T$ iterations, and a similar algorithm with slightly modified value update rule achieves a faster $\mathcal{\widetilde{O}}(T^{-1})$ convergence rate. These improve over the current best $\mathcal{\widetilde{O}}(T^{-1/2})$ rate of symmetric policy optimization type algorithms. We also extend this algorithm to multi-player general-sum Markov Games and show an $\mathcal{\widetilde{O}}(T^{-3/4})$ convergence rate to Coarse Correlated Equilibria (CCE). Finally, we provide a numerical example to verify our theory and investigate the importance of smooth value updates, and find that using "eager" value updates instead (equivalent to the independent natural policy gradient algorithm) may significantly slow down the convergence, even on a simple game with $H=2$ layers.

Chung-Wei Lee, Qinghua Liu, Yasin Abbasi-Yadkori et al. · deepmind

We consider a contextual bandit problem with $S$ contexts and $K$ actions. In each round $t=1,2,\dots$, the learner observes a random context and chooses an action based on its past experience. The learner then observes a random reward whose mean is a function of the context and the action for the round. Under the assumption that the contexts can be lumped into $r\le \min\{S,K\}$ groups such that the mean reward for the various actions is the same for any two contexts that are in the same group, we give an algorithm that outputs an $ε$-optimal policy after using at most $\widetilde O(r (S +K )/ε^2)$ samples with high probability and provide a matching $Ω(r(S+K)/ε^2)$ lower bound. In the regret minimization setting, we give an algorithm whose cumulative regret up to time $T$ is bounded by $\widetilde O(\sqrt{r^3(S+K)T})$. To the best of our knowledge, we are the first to show the near-optimal sample complexity in the PAC setting and $\widetilde O(\sqrt{{poly}(r)(S+K)T})$ minimax regret in the online setting for this problem. We also show our algorithms can be applied to more general low-rank bandits and get improved regret bounds in some scenarios.

Yuanhao Wang, Qinghua Liu, Chi Jin

Reinforcement learning from Human Feedback (RLHF) learns from preference signals, while standard Reinforcement Learning (RL) directly learns from reward signals. Preferences arguably contain less information than rewards, which makes preference-based RL seemingly more difficult. This paper theoretically proves that, for a wide range of preference models, we can solve preference-based RL directly using existing algorithms and techniques for reward-based RL, with small or no extra costs. Specifically, (1) for preferences that are drawn from reward-based probabilistic models, we reduce the problem to robust reward-based RL that can tolerate small errors in rewards; (2) for general arbitrary preferences where the objective is to find the von Neumann winner, we reduce the problem to multiagent reward-based RL which finds Nash equilibria for factored Markov games with a restricted set of policies. The latter case can be further reduced to adversarial MDP when preferences only depend on the final state. We instantiate all reward-based RL subroutines by concrete provable algorithms, and apply our theory to a large class of models including tabular MDPs and MDPs with generic function approximation. We further provide guarantees when K-wise comparisons are available.

Yuanhao Wang, Qinghua Liu, Yu Bai et al.

A unique challenge in Multi-Agent Reinforcement Learning (MARL) is the curse of multiagency, where the description length of the game as well as the complexity of many existing learning algorithms scale exponentially with the number of agents. While recent works successfully address this challenge under the model of tabular Markov Games, their mechanisms critically rely on the number of states being finite and small, and do not extend to practical scenarios with enormous state spaces where function approximation must be used to approximate value functions or policies. This paper presents the first line of MARL algorithms that provably resolve the curse of multiagency under function approximation. We design a new decentralized algorithm -- V-Learning with Policy Replay, which gives the first polynomial sample complexity results for learning approximate Coarse Correlated Equilibria (CCEs) of Markov Games under decentralized linear function approximation. Our algorithm always outputs Markov CCEs, and achieves an optimal rate of $\widetilde{\mathcal{O}}(ε^{-2})$ for finding $ε$-optimal solutions. Also, when restricted to the tabular case, our result improves over the current best decentralized result $\widetilde{\mathcal{O}}(ε^{-3})$ for finding Markov CCEs. We further present an alternative algorithm -- Decentralized Optimistic Policy Mirror Descent, which finds policy-class-restricted CCEs using a polynomial number of samples. In exchange for learning a weaker version of CCEs, this algorithm applies to a wider range of problems under generic function approximation, such as linear quadratic games and MARL problems with low ''marginal'' Eluder dimension.

Qinghua Liu, Yuanhao Wang, Chi Jin

An ideal strategy in zero-sum games should not only grant the player an average reward no less than the value of Nash equilibrium, but also exploit the (adaptive) opponents when they are suboptimal. While most existing works in Markov games focus exclusively on the former objective, it remains open whether we can achieve both objectives simultaneously. To address this problem, this work studies no-regret learning in Markov games with adversarial opponents when competing against the best fixed policy in hindsight. Along this direction, we present a new complete set of positive and negative results: When the policies of the opponents are revealed at the end of each episode, we propose new efficient algorithms achieving $\sqrt{K}$-regret bounds when either (1) the baseline policy class is small or (2) the opponent's policy class is small. This is complemented with an exponential lower bound when neither conditions are true. When the policies of the opponents are not revealed, we prove a statistical hardness result even in the most favorable scenario when both above conditions are true. Our hardness result is much stronger than the existing hardness results which either only involve computational hardness, or require further restrictions on the algorithms.

Zihan Ding, Dijia Su, Qinghua Liu et al.

This paper proposes new, end-to-end deep reinforcement learning algorithms for learning two-player zero-sum Markov games. Different from prior efforts on training agents to beat a fixed set of opponents, our objective is to find the Nash equilibrium policies that are free from exploitation by even the adversarial opponents. We propose (a) Nash-DQN algorithm, which integrates the deep learning techniques from single DQN into the classic Nash Q-learning algorithm for solving tabular Markov games; (b) Nash-DQN-Exploiter algorithm, which additionally adopts an exploiter to guide the exploration of the main agent. We conduct experimental evaluation on tabular examples as well as various two-player Atari games. Our empirical results demonstrate that (i) the policies found by many existing methods including Neural Fictitious Self Play and Policy Space Response Oracle can be prone to exploitation by adversarial opponents; (ii) the output policies of our algorithms are robust to exploitation, and thus outperform existing methods.

Qinghua Liu, Rui Zhang, Yao Xie

Distributed change-point detection has been a fundamental problem when performing real-time monitoring using sensor-networks. We propose a distributed detection algorithm, where each sensor only exchanges CUSUM statistic with their neighbors based on the average consensus scheme, and an alarm is raised when local consensus statistic exceeds a pre-specified global threshold. We provide theoretical performance bounds showing that the performance of the fully distributed scheme can match the centralized algorithms under some mild conditions. Numerical experiments demonstrate the good performance of the algorithm especially in detecting asynchronous changes.

Qinghua Liu, Yuxiang Jiang

The increasing scale of model size and continuous improvement of performance herald the arrival of the Big Model era. In this report, we explore what and how the big model training works by diving into training objectives and training methodologies. Specifically,training objectives describe how to leverage web-scale data to develop extremely capable and incredibly large models based on self-supervised learning, and training methodologies which are based on distributed training describe how to make big model training a reality. We summarize the existing training methodologies into three main categories: training parallelism, memory-saving technologies, and model sparsity design. Training parallelism can be categorized into data, pipeline, and tensor parallelism according to the dimension of parallelism that takes place. Memory-saving technologies are orthogonal and complementary to training parallelism. And model sparsity design further scales up the model size with a constant computational cost. A continuously updated paper list of big model training is provided at https://github.com/qhliu26/BM-Training.

Haoyan Xu, Ruizhi Qian, Jiate Li et al.

Graph machine learning has advanced rapidly in tasks such as link prediction, anomaly detection, and node classification. As models scale up, pretrained graph models have become valuable intellectual assets because they encode extensive computation and domain expertise. Building on these advances, Graph Foundation Models (GFMs) mark a major step forward by jointly pretraining graph and text encoders on massive and diverse data. This unifies structural and semantic understanding, enables zero-shot inference, and supports applications such as fraud detection and biomedical analysis. However, the high pretraining cost and broad cross-domain knowledge in GFMs also make them attractive targets for model extraction attacks (MEAs). Prior work has focused only on small graph neural networks trained on a single graph, leaving the security implications for large-scale and multimodal GFMs largely unexplored. This paper presents the first systematic study of MEAs against GFMs. We formalize a black-box threat model and define six practical attack scenarios covering domain-level and graph-specific extraction goals, architectural mismatch, limited query budgets, partial node access, and training data discrepancies. To instantiate these attacks, we introduce a lightweight extraction method that trains an attacker encoder using supervised regression of graph embeddings. Even without contrastive pretraining data, this method learns an encoder that stays aligned with the victim text encoder and preserves its zero-shot inference ability on unseen graphs. Experiments on seven datasets show that the attacker can approximate the victim model using only a tiny fraction of its original training cost, with almost no loss in accuracy. These findings reveal that GFMs greatly expand the MEA surface and highlight the need for deployment-aware security defenses in large-scale graph learning systems.

Audrey Huang, Adam Block, Qinghua Liu et al.

Inference-time computation offers a powerful axis for scaling the performance of language models. However, naively increasing computation in techniques like Best-of-N sampling can lead to performance degradation due to reward hacking. Toward a theoretical understanding of how to best leverage additional computation, we focus on inference-time alignment, which we formalize as the problem of improving the quality of responses drawn from a pre-trained policy, given a prompt of interest and access to an imperfect reward model. We analyze the performance of inference-time alignment algorithms in terms of (i) response quality, and (ii) compute, and provide new results that highlight the importance of the pre-trained policy's coverage over high-quality responses for performance and compute scaling: 1. We show that Best-of-$N$ alignment with an ideal choice for $N$ can achieve optimal performance under stringent notions of coverage, but provably suffers from reward hacking when $N$ is large, and fails to achieve tight guarantees under more realistic coverage conditions. 2. We introduce $\texttt{InferenceTimePessimism}$, a new algorithm which mitigates reward hacking through deliberate use of inference-time compute, implementing the principle of pessimism in the face of uncertainty via rejection sampling; we prove that its performance is optimal and does not degrade with $N$, meaning it is scaling-monotonic. We complement our theoretical results with an experimental evaluation that demonstrate the benefits of $\texttt{InferenceTimePessimism}$ across a variety of tasks and models.

Paul Boniol, Qinghua Liu, Mingyi Huang et al.

Recent advances in data collection technology, accompanied by the ever-rising volume and velocity of streaming data, underscore the vital need for time series analytics. In this regard, time-series anomaly detection has been an important activity, entailing various applications in fields such as cyber security, financial markets, law enforcement, and health care. While traditional literature on anomaly detection is centered on statistical measures, the increasing number of machine learning algorithms in recent years call for a structured, general characterization of the research methods for time-series anomaly detection. This survey groups and summarizes anomaly detection existing solutions under a process-centric taxonomy in the time series context. In addition to giving an original categorization of anomaly detection methods, we also perform a meta-analysis of the literature and outline general trends in time-series anomaly detection research.

Paul Boniol, Ashwin K. Krishna, Marine Bruel et al.

Anomaly detection (AD) is a fundamental task for time-series analytics with important implications for the downstream performance of many applications. In contrast to other domains where AD mainly focuses on point-based anomalies (i.e., outliers in standalone observations), AD for time series is also concerned with range-based anomalies (i.e., outliers spanning multiple observations). Nevertheless, it is common to use traditional point-based information retrieval measures, such as Precision, Recall, and F-score, to assess the quality of methods by thresholding the anomaly score to mark each point as an anomaly or not. However, mapping discrete labels into continuous data introduces unavoidable shortcomings, complicating the evaluation of range-based anomalies. Notably, the choice of evaluation measure may significantly bias the experimental outcome. Despite over six decades of attention, there has never been a large-scale systematic quantitative and qualitative analysis of time-series AD evaluation measures. This paper extensively evaluates quality measures for time-series AD to assess their robustness under noise, misalignments, and different anomaly cardinality ratios. Our results indicate that measures producing quality values independently of a threshold (i.e., AUC-ROC and AUC-PR) are more suitable for time-series AD. Motivated by this observation, we first extend the AUC-based measures to account for range-based anomalies. Then, we introduce a new family of parameter-free and threshold-independent measures, Volume Under the Surface (VUS), to evaluate methods while varying parameters. We also introduce two optimized implementations for VUS that reduce significantly the execution time of the initial implementation. Our findings demonstrate that our four measures are significantly more robust in assessing the quality of time-series AD methods.

Edward S. Hu, Kwangjun Ahn, Qinghua Liu et al.

We introduce the "Belief State Transformer", a next-token predictor that takes both a prefix and suffix as inputs, with a novel objective of predicting both the next token for the prefix and the previous token for the suffix. The Belief State Transformer effectively learns to solve challenging problems that conventional forward-only transformers struggle with, in a domain-independent fashion. Key to this success is learning a compact belief state that captures all relevant information necessary for accurate predictions. Empirical ablations show that each component of the model is essential in difficult scenarios where standard Transformers fall short. For the task of story writing with known prefixes and suffixes, our approach outperforms the Fill-in-the-Middle method for reaching known goals and demonstrates improved performance even when the goals are unknown. Altogether, the Belief State Transformer enables more efficient goal-conditioned decoding, better test-time inference, and high-quality text representations on small scale problems. Website: https://edwhu.github.io/bst-website

Qinghua Liu, Sam Heshmati, Zheda Mai et al.

Effective analysis of time series data presents significant challenges due to the complex temporal dependencies and cross-channel interactions in multivariate data. Inspired by the way human analysts visually inspect time series to uncover hidden patterns, we ask: can incorporating visual representations enhance automated time-series analysis? Recent advances in multimodal large language models have demonstrated impressive generalization and visual understanding capability, yet their application to time series remains constrained by the modality gap between continuous numerical data and discrete natural language. To bridge this gap, we introduce MLLM4TS, a novel framework that leverages multimodal large language models for general time-series analysis by integrating a dedicated vision branch. Each time-series channel is rendered as a horizontally stacked color-coded line plot in one composite image to capture spatial dependencies across channels, and a temporal-aware visual patch alignment strategy then aligns visual patches with their corresponding time segments. MLLM4TS fuses fine-grained temporal details from the numerical data with global contextual information derived from the visual representation, providing a unified foundation for multimodal time-series analysis. Extensive experiments on standard benchmarks demonstrate the effectiveness of MLLM4TS across both predictive tasks (e.g., classification) and generative tasks (e.g., anomaly detection and forecasting). These results underscore the potential of integrating visual modalities with pretrained language models to achieve robust and generalizable time-series analysis.

Jiachen Hu, Qinghua Liu, Chi Jin

Despite the remarkable success of Transformer-based architectures in various sequential modeling tasks, such as natural language processing, computer vision, and robotics, their ability to learn basic sequential models, like Hidden Markov Models (HMMs), is still unclear. This paper investigates the performance of Transformers in learning HMMs and their variants through extensive experimentation and compares them to Recurrent Neural Networks (RNNs). We show that Transformers consistently underperform RNNs in both training speed and testing accuracy across all tested HMM models. There are even challenging HMM instances where Transformers struggle to learn, while RNNs can successfully do so. Our experiments further reveal the relation between the depth of Transformers and the longest sequence length it can effectively learn, based on the types and the complexity of HMMs. To address the limitation of transformers in modeling HMMs, we demonstrate that a variant of the Chain-of-Thought (CoT), called $\textit{block CoT}$ in the training phase, can help transformers to reduce the evaluation error and to learn longer sequences at a cost of increasing the training time. Finally, we complement our empirical findings by theoretical results proving the expressiveness of transformers in approximating HMMs with logarithmic depth.

Qinghua Liu, Gellért Weisz, András György et al.

While policy optimization algorithms have played an important role in recent empirical success of Reinforcement Learning (RL), the existing theoretical understanding of policy optimization remains rather limited -- they are either restricted to tabular MDPs or suffer from highly suboptimal sample complexity, especial in online RL where exploration is necessary. This paper proposes a simple efficient policy optimization framework -- Optimistic NPG for online RL. Optimistic NPG can be viewed as a simple combination of the classic natural policy gradient (NPG) algorithm [Kakade, 2001] with optimistic policy evaluation subroutines to encourage exploration. For $d$-dimensional linear MDPs, Optimistic NPG is computationally efficient, and learns an $\varepsilon$-optimal policy within $\tilde{O}(d^2/\varepsilon^3)$ samples, which is the first computationally efficient algorithm whose sample complexity has the optimal dimension dependence $\tildeΘ(d^2)$. It also improves over state-of-the-art results of policy optimization algorithms [Zanette et al., 2021] by a factor of $d$. In the realm of general function approximation, which subsumes linear MDPs, Optimistic NPG, to our best knowledge, stands as the first policy optimization algorithm that achieves polynomial sample complexity for learning near-optimal policies.

Qinghua Liu, Praneeth Netrapalli, Csaba Szepesvári et al.

This paper introduces a simple efficient learning algorithms for general sequential decision making. The algorithm combines Optimism for exploration with Maximum Likelihood Estimation for model estimation, which is thus named OMLE. We prove that OMLE learns the near-optimal policies of an enormously rich class of sequential decision making problems in a polynomial number of samples. This rich class includes not only a majority of known tractable model-based Reinforcement Learning (RL) problems (such as tabular MDPs, factored MDPs, low witness rank problems, tabular weakly-revealing/observable POMDPs and multi-step decodable POMDPs), but also many new challenging RL problems especially in the partially observable setting that were not previously known to be tractable. Notably, the new problems addressed by this paper include (1) observable POMDPs with continuous observation and function approximation, where we achieve the first sample complexity that is completely independent of the size of observation space; (2) well-conditioned low-rank sequential decision making problems (also known as Predictive State Representations (PSRs)), which include and generalize all known tractable POMDP examples under a more intrinsic representation; (3) general sequential decision making problems under SAIL condition, which unifies our existing understandings of model-based RL in both fully observable and partially observable settings. SAIL condition is identified by this paper, which can be viewed as a natural generalization of Bellman/witness rank to address partial observability. This paper also presents a reward-free variant of OMLE algorithm, which learns approximate dynamic models that enable the computation of near-optimal policies for all reward functions simultaneously.

Qinghua Liu, Yating Huang, Yunzhe Hao et al.

Multi-modal cues, including spatial information, facial expression and voiceprint, are introduced to the speech separation and speaker extraction tasks to serve as complementary information to achieve better performance. However, the introduction of these cues brings about an increasing number of parameters and model complexity, which makes it harder to deploy these models on resource-constrained devices. In this paper, we alleviate the aforementioned problem by proposing a Lightweight Multi-modal framework for Speaker Extraction (LiMuSE). We propose to use GC-equipped TCN, which incorporates Group Communication (GC) and Temporal Convolutional Network (TCN) in the Context Codec module, the audio block and the fusion block. The experiments on the MC_GRID dataset demonstrate that LiMuSE achieves on par or better performance with a much smaller number of parameters and less model complexity. We further investigate the impacts of the quantization of LiMuSE. Our code and dataset are provided.

Chi Jin, Qinghua Liu, Yuanhao Wang et al.

A major challenge of multiagent reinforcement learning (MARL) is the curse of multiagents, where the size of the joint action space scales exponentially with the number of agents. This remains to be a bottleneck for designing efficient MARL algorithms even in a basic scenario with finitely many states and actions. This paper resolves this challenge for the model of episodic Markov games. We design a new class of fully decentralized algorithms -- V-learning, which provably learns Nash equilibria (in the two-player zero-sum setting), correlated equilibria and coarse correlated equilibria (in the multiplayer general-sum setting) in a number of samples that only scales with $\max_{i\in[m]} A_i$, where $A_i$ is the number of actions for the $i^{\rm th}$ player. This is in sharp contrast to the size of the joint action space which is $\prod_{i=1}^m A_i$. V-learning (in its basic form) is a new class of single-agent RL algorithms that convert any adversarial bandit algorithm with suitable regret guarantees into a RL algorithm. Similar to the classical Q-learning algorithm, it performs incremental updates to the value functions. Different from Q-learning, it only maintains the estimates of V-values instead of Q-values. This key difference allows V-learning to achieve the claimed guarantees in the MARL setting by simply letting all agents run V-learning independently.

Chi Jin, Qinghua Liu, Tiancheng Yu

Modern reinforcement learning (RL) commonly engages practical problems with large state spaces, where function approximation must be deployed to approximate either the value function or the policy. While recent progresses in RL theory address a rich set of RL problems with general function approximation, such successes are mostly restricted to the single-agent setting. It remains elusive how to extend these results to multi-agent RL, especially due to the new challenges arising from its game-theoretical nature. This paper considers two-player zero-sum Markov Games (MGs). We propose a new algorithm that can provably find the Nash equilibrium policy using a polynomial number of samples, for any MG with low multi-agent Bellman-Eluder dimension -- a new complexity measure adapted from its single-agent version (Jin et al., 2021). A key component of our new algorithm is the exploiter, which facilitates the learning of the main player by deliberately exploiting her weakness. Our theoretical framework is generic, which applies to a wide range of models including but not limited to tabular MGs, MGs with linear or kernel function approximation, and MGs with rich observations.

Chi Jin, Qinghua Liu, Sobhan Miryoosefi

Finding the minimal structural assumptions that empower sample-efficient learning is one of the most important research directions in Reinforcement Learning (RL). This paper advances our understanding of this fundamental question by introducing a new complexity measure -- Bellman Eluder (BE) dimension. We show that the family of RL problems of low BE dimension is remarkably rich, which subsumes a vast majority of existing tractable RL problems including but not limited to tabular MDPs, linear MDPs, reactive POMDPs, low Bellman rank problems as well as low Eluder dimension problems. This paper further designs a new optimization-based algorithm -- GOLF, and reanalyzes a hypothesis elimination-based algorithm -- OLIVE (proposed in Jiang et al., 2017). We prove that both algorithms learn the near-optimal policies of low BE dimension problems in a number of samples that is polynomial in all relevant parameters, but independent of the size of state-action space. Our regret and sample complexity results match or improve the best existing results for several well-known subclasses of low BE dimension problems.

Qinghua Liu, Zhou Lu

Leveraging algorithmic stability to derive sharp generalization bounds is a classic and powerful approach in learning theory. Since Vapnik and Chervonenkis [1974] first formalized the idea for analyzing SVMs, it has been utilized to study many fundamental learning algorithms (e.g., $k$-nearest neighbors [Rogers and Wagner, 1978], stochastic gradient method [Hardt et al., 2016], linear regression [Maurer, 2017], etc). In a recent line of great works by Feldman and Vondrak [2018, 2019] as well as Bousquet et al. [2020b], they prove a high probability generalization upper bound of order $\tilde{\mathcal{O}}(γ+\frac{L}{\sqrt{n}})$ for any uniformly $γ$-stable algorithm and $L$-bounded loss function. Although much progress was achieved in proving generalization upper bounds for stable algorithms, our knowledge of lower bounds is rather limited. In fact, there is no nontrivial lower bound known ever since the study of uniform stability [Bousquet and Elisseeff, 2002], to the best of our knowledge. In this paper we fill the gap by proving a tight generalization lower bound of order $Ω(γ+\frac{L}{\sqrt{n}})$, which matches the best known upper bound up to logarithmic factors

Qinghua Liu, Tiancheng Yu, Yu Bai et al.

Model-based algorithms -- algorithms that explore the environment through building and utilizing an estimated model -- are widely used in reinforcement learning practice and theoretically shown to achieve optimal sample efficiency for single-agent reinforcement learning in Markov Decision Processes (MDPs). However, for multi-agent reinforcement learning in Markov games, the current best known sample complexity for model-based algorithms is rather suboptimal and compares unfavorably against recent model-free approaches. In this paper, we present a sharp analysis of model-based self-play algorithms for multi-agent Markov games. We design an algorithm -- Optimistic Nash Value Iteration (Nash-VI) for two-player zero-sum Markov games that is able to output an $ε$-approximate Nash policy in $\tilde{\mathcal{O}}(H^3SAB/ε^2)$ episodes of game playing, where $S$ is the number of states, $A,B$ are the number of actions for the two players respectively, and $H$ is the horizon length. This significantly improves over the best known model-based guarantee of $\tilde{\mathcal{O}}(H^4S^2AB/ε^2)$, and is the first that matches the information-theoretic lower bound $Ω(H^3S(A+B)/ε^2)$ except for a $\min\{A,B\}$ factor. In addition, our guarantee compares favorably against the best known model-free algorithm if $\min \{A,B\}=o(H^3)$, and outputs a single Markov policy while existing sample-efficient model-free algorithms output a nested mixture of Markov policies that is in general non-Markov and rather inconvenient to store and execute. We further adapt our analysis to designing a provably efficient task-agnostic algorithm for zero-sum Markov games, and designing the first line of provably sample-efficient algorithms for multi-player general-sum Markov games.

Jianyu Wang, Qinghua Liu, Hao Liang et al.

In federated optimization, heterogeneity in the clients' local datasets and computation speeds results in large variations in the number of local updates performed by each client in each communication round. Naive weighted aggregation of such models causes objective inconsistency, that is, the global model converges to a stationary point of a mismatched objective function which can be arbitrarily different from the true objective. This paper provides a general framework to analyze the convergence of federated heterogeneous optimization algorithms. It subsumes previously proposed methods such as FedAvg and FedProx and provides the first principled understanding of the solution bias and the convergence slowdown due to objective inconsistency. Using insights from this analysis, we propose FedNova, a normalized averaging method that eliminates objective inconsistency while preserving fast error convergence.

Chi Jin, Sham M. Kakade, Akshay Krishnamurthy et al.

Partial observability is a common challenge in many reinforcement learning applications, which requires an agent to maintain memory, infer latent states, and integrate this past information into exploration. This challenge leads to a number of computational and statistical hardness results for learning general Partially Observable Markov Decision Processes (POMDPs). This work shows that these hardness barriers do not preclude efficient reinforcement learning for rich and interesting subclasses of POMDPs. In particular, we present a sample-efficient algorithm, OOM-UCB, for episodic finite undercomplete POMDPs, where the number of observations is larger than the number of latent states and where exploration is essential for learning, thus distinguishing our results from prior works. OOM-UCB achieves an optimal sample complexity of $\tilde{\mathcal{O}}(1/\varepsilon^2)$ for finding an $\varepsilon$-optimal policy, along with being polynomial in all other relevant quantities. As an interesting special case, we also provide a computationally and statistically efficient algorithm for POMDPs with deterministic state transitions.

Gen Li, Qinghua Liu, Yuantao Gu

Dimensionality reduction is in demand to reduce the complexity of solving large-scale problems with data lying in latent low-dimensional structures in machine learning and computer version. Motivated by such need, in this work we study the Restricted Isometry Property (RIP) of Gaussian random projections for low-dimensional subspaces in $\mathbb{R}^N$, and rigorously prove that the projection Frobenius norm distance between any two subspaces spanned by the projected data in $\mathbb{R}^n$ ($n<N$) remain almost the same as the distance between the original subspaces with probability no less than $1 - {\rm e}^{-\mathcal{O}(n)}$. Previously the well-known Johnson-Lindenstrauss (JL) Lemma and RIP for sparse vectors have been the foundation of sparse signal processing including Compressed Sensing. As an analogy to JL Lemma and RIP for sparse vectors, this work allows the use of random projections to reduce the ambient dimension with the theoretical guarantee that the distance between subspaces after compression is well preserved.