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1. Towards instance-optimal offline reinforcement learning with pessimism

   Yin, Ming ; Wang, Yu-Xiang ( December 2021 , Advances in neural information processing systems)

   We study the \emph{offline reinforcement learning} (offline RL) problem, where the goal is to learn a reward-maximizing policy in an unknown \emph{Markov Decision Process} (MDP) using the data coming from a policy $\mu$. In particular, we consider the sample complexity problems of offline RL for the finite horizon MDPs. Prior works derive the information-theoretical lower bounds based on different data-coverage assumptions and their upper bounds are expressed by the covering coefficients which lack the explicit characterization of system quantities. In this work, we analyze the \emph{Adaptive Pessimistic Value Iteration} (APVI) algorithm and derive the suboptimality upper bound that nearly matches $ O\left(\sum_{h=1}^H\sum_{s_h,a_h}d^{\pi^\star}_h(s_h,a_h)\sqrt{\frac{\mathrm{Var}_{P_{s_h,a_h}}{(V^\star_{h+1}+r_h)}}{d^\mu_h(s_h,a_h)}}\sqrt{\frac{1}{n}}\right). $ We also prove an information-theoretical lower bound to show this quantity is required under the weak assumption that $d^\mu_h(s_h,a_h)>0$ if $d^{\pi^\star}_h(s_h,a_h)>0$. Here $\pi^\star$ is a optimal policy, $\mu$ is the behavior policy and $d(s_h,a_h)$ is the marginal state-action probability. We call this adaptive bound the \emph{intrinsic offline reinforcement learning bound} since it directly implies all the existing optimal results: minimax rate under uniform data-coverage assumption, horizon-free setting, single policy concentrability, and the tight problem-dependent results. Later, we extend the result to the \emph{assumption-free} regime (where we make no assumption on $ \mu$) and obtain the assumption-free intrinsicmore »bound. Due to its generic form, we believe the intrinsic bound could help illuminate what makes a specific problem hard and reveal the fundamental challenges in offline RL.« less
2. Optimal Uniform OPE and Model-based Offline Reinforcement Learning in Time-Homogeneous, Reward-Free and Task-Agnostic Settings

   Yin, Ming ; Wang, Yu-Xiang ( October 2021 , Advances in neural information processing systems)

   This work studies the statistical limits of uniform convergence for offline policy evaluation (OPE) problems with model-based methods (for episodic MDP) and provides a unified framework towards optimal learning for several well-motivated offline tasks. Uniform OPE supΠ|Qπ−Q̂ π|<ϵ is a stronger measure than the point-wise OPE and ensures offline learning when Π contains all policies (the global class). In this paper, we establish an Ω(H2S/dmϵ2) lower bound (over model-based family) for the global uniform OPE and our main result establishes an upper bound of Õ (H2/dmϵ2) for the \emph{local} uniform convergence that applies to all \emph{near-empirically optimal} policies for the MDPs with \emph{stationary} transition. Here dm is the minimal marginal state-action probability. Critically, the highlight in achieving the optimal rate Õ (H2/dmϵ2) is our design of \emph{singleton absorbing MDP}, which is a new sharp analysis tool that works with the model-based approach. We generalize such a model-based framework to the new settings: offline task-agnostic and the offline reward-free with optimal complexity Õ (H2log(K)/dmϵ2) (K is the number of tasks) and Õ (H2S/dmϵ2) respectively. These results provide a unified solution for simultaneously solving different offline RL problems.
3. Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity

   Shi, Laixi ; Li, Gen ; Wei, Yuting ; Chen, Yuxin ; Chi, Yuejie ( January 2022 , Proceedings of the 39th International Conference on Machine Learning)

   Offline or batch reinforcement learning seeks to learn a near-optimal policy using history data without active exploration of the environment. To counter the insufficient coverage and sample scarcity of many offline datasets, the principle of pessimism has been recently introduced to mitigate high bias of the estimated values. While pessimistic variants of model-based algorithms (e.g., value iteration with lower confidence bounds) have been theoretically investigated, their model-free counterparts — which do not require explicit model estimation — have not been adequately studied, especially in terms of sample efficiency. To address this inadequacy, we study a pessimistic variant of Q-learning in the context of finite-horizon Markov decision processes, and characterize its sample complexity under the single-policy concentrability assumption which does not require the full coverage of the state-action space. In addition, a variance-reduced pessimistic Q-learning algorithm is proposed to achieve near-optimal sample complexity. Altogether, this work highlights the efficiency of model-free algorithms in offline RL when used in conjunction with pessimism and variance reduction.
4. Reinforcement Learning with Sparse Rewards using Guidance from Offline Demonstration

   Rengarajan, D. ; Vaidya, G. ; Sarvesh, A. ; Kalathil, D. ; Shakkottai, S ( April 2022 , International Conference on Learning Representations (ICLR))

   A major challenge in real-world reinforcement learning (RL) is the sparsity of reward feedback. Often, what is available is an intuitive but sparse reward function that only indicates whether the task is completed partially or fully. However, the lack of carefully designed, fine grain feedback implies that most existing RL algorithms fail to learn an acceptable policy in a reasonable time frame. This is because of the large number of exploration actions that the policy has to perform before it gets any useful feedback that it can learn from. In this work, we address this challenging problem by developing an algorithm that exploits the offline demonstration data generated by a sub-optimal behavior policy for faster and efficient online RL in such sparse reward settings. The proposed algorithm, which we call the Learning Online with Guidance Offline (LOGO) algorithm, merges a policy improvement step with an additional policy guidance step by using the offline demonstration data. The key idea is that by obtaining guidance from - not imitating - the offline data, LOGO orients its policy in the manner of the sub-optimal policy, while yet being able to learn beyond and approach optimality. We provide a theoretical analysis of our algorithm,more »and provide a lower bound on the performance improvement in each learning episode. We also extend our algorithm to the even more challenging incomplete observation setting, where the demonstration data contains only a censored version of the true state observation. We demonstrate the superior performance of our algorithm over state-of-the-art approaches on a number of benchmark environments with sparse rewards and censored state. Further, we demonstrate the value of our approach via implementing LOGO on a mobile robot for trajectory tracking and obstacle avoidance, where it shows excellent performance.« less
5. Learning Zero-Sum Simultaneous-Move Markov Games Using Function Approximation and Correlated Equilibrium

   https://doi.org/10.1287/moor.2022.1268  

   Xie, Qiaomin ; Chen, Yudong ; Wang, Zhaoran ; Yang, Zhuoran ( June 2022 , Mathematics of Operations Research)

   We develop provably efficient reinforcement learning algorithms for two-player zero-sum finite-horizon Markov games with simultaneous moves. To incorporate function approximation, we consider a family of Markov games where the reward function and transition kernel possess a linear structure. Both the offline and online settings of the problems are considered. In the offline setting, we control both players and aim to find the Nash equilibrium by minimizing the duality gap. In the online setting, we control a single player playing against an arbitrary opponent and aim to minimize the regret. For both settings, we propose an optimistic variant of the least-squares minimax value iteration algorithm. We show that our algorithm is computationally efficient and provably achieves an [Formula: see text] upper bound on the duality gap and regret, where d is the linear dimension, H the horizon and T the total number of timesteps. Our results do not require additional assumptions on the sampling model. Our setting requires overcoming several new challenges that are absent in Markov decision processes or turn-based Markov games. In particular, to achieve optimism with simultaneous moves, we construct both upper and lower confidence bounds of the value function, and then compute the optimistic policy by solvingmore »a general-sum matrix game with these bounds as the payoff matrices. As finding the Nash equilibrium of a general-sum game is computationally hard, our algorithm instead solves for a coarse correlated equilibrium (CCE), which can be obtained efficiently. To our best knowledge, such a CCE-based scheme for optimism has not appeared in the literature and might be of interest in its own right.« less