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1. Near-Optimal Reinforcement Learning with Self-Play under Adaptivity Constraints

   Qiao, Dan; Wang, Yu-Xiang (July 2024, Proceedings of Machine Learning Research)

   We study the problem of multi-agent reinforcement learning (MARL) with adaptivity constraints -- a new problem motivated by real-world applications where deployments of new policies are costly and the number of policy updates must be minimized. For two-player zero-sum Markov Games, we design a (policy) elimination based algorithm that achieves a regret of O˜(H3S2ABK‾‾‾‾‾‾‾‾‾‾√), while the batch complexity is only O(H+loglogK). In the above, S denotes the number of states, A,B are the number of actions for the two players respectively, H is the horizon and K is the number of episodes. Furthermore, we prove a batch complexity lower bound Ω(HlogAK+loglogK) for all algorithms with O˜(K‾‾√) regret bound, which matches our upper bound up to logarithmic factors. As a byproduct, our techniques naturally extend to learning bandit games and reward-free MARL within near optimal batch complexity. To the best of our knowledge, these are the first line of results towards understanding MARL with low adaptivity. 

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2. DOPE: Doubly Optimistic and Pessimistic Exploration for Safe Reinforcement Learning

   Bura, Archana; HasanzadeZonuzy, Aria; Kalathil, Dileep; Shakkottai, Srinivas; Chamberland, Jean-Francois (November 2022, Advances in neural information processing systems)

   Safe reinforcement learning is extremely challenging--not only must the agent explore an unknown environment, it must do so while ensuring no safety constraint violations. We formulate this safe reinforcement learning (RL) problem using the framework of a finite-horizon Constrained Markov Decision Process (CMDP) with an unknown transition probability function, where we model the safety requirements as constraints on the expected cumulative costs that must be satisfied during all episodes of learning. We propose a model-based safe RL algorithm that we call Doubly Optimistic and Pessimistic Exploration (DOPE), and show that it achieves an objective regret $$\tilde{O}(|\mathcal{S}|\sqrt{|\mathcal{A}| K})$$ without violating the safety constraints during learning, where $$|\mathcal{S}|$$ is the number of states, $$|\mathcal{A}|$$ is the number of actions, and $$K$$ is the number of learning episodes. Our key idea is to combine a reward bonus for exploration (optimism) with a conservative constraint (pessimism), in addition to the standard optimistic model-based exploration. DOPE is not only able to improve the objective regret bound, but also shows a significant empirical performance improvement as compared to earlier optimism-pessimism approaches. 

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3. Is Long Horizon RL More Difficult Than Short Horizon RL?

   Wang, Ruosong; Du, Simon S.; Yang, Lin; Kakade, Sham (January 2020, Advances in neural information processing systems)

   null (Ed.)

   Learning to plan for long horizons is a central challenge in episodic reinforcement learning problems. A fundamental question is to understand how the difficulty of the problem scales as the horizon increases. Here the natural measure of sample complexity is a normalized one: we are interested in the \emph{number of episodes} it takes to provably discover a policy whose value is eps near to that of the optimal value, where the value is measured by the \emph{normalized} cumulative reward in each episode. In a COLT 2018 open problem, Jiang and Agarwal conjectured that, for tabular, episodic reinforcement learning problems, there exists a sample complexity lower bound which exhibits a polynomial dependence on the horizon --- a conjecture which is consistent with all known sample complexity upper bounds. This work refutes this conjecture, proving that tabular, episodic reinforcement learning is possible with a sample complexity that scales only \emph{logarithmically} with the planning horizon. In other words, when the values are appropriately normalized (to lie in the unit interval), this results shows that long horizon RL is no more difficult than short horizon RL, at least in a minimax sense. Our analysis introduces two ideas: (i) the construction of an eps-net for near-optimal policies whose log-covering number scales only logarithmically with the planning horizon, and (ii) the Online Trajectory Synthesis algorithm, which adaptively evaluates all policies in a given policy class and enjoys a sample complexity that scales logarithmically with the cardinality of the given policy class. Both may be of independent interest. 

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4. Settling the Sample Complexity of Online Reinforcement Learning

   https://doi.org/10.1145/3733592  

   Zhang, Zihan; Chen, Yuxin; Lee, Jason; Du, Simon S (May 2025, Journal of the ACM)

   A central issue lying at the heart of online reinforcement learning (RL) is data efficiency. While a number of recent works achieved asymptotically minimal regret in online RL, the optimality of these results is only guaranteed in a “large-sample” regime, imposing enormous burn-in cost in order for their algorithms to operate optimally. How to achieve minimax-optimal regret without incurring any burn-in cost has been an open problem in RL theory. We settle this problem for finite-horizon inhomogeneous Markov decision processes. Specifically, we prove that a modified version ofMVP(Monotonic Value Propagation), an optimistic model-based algorithm proposed by Zhang et al. [82], achieves a regret on the order of (modulo log factors)\begin{equation*} \min \big \lbrace \sqrt {SAH^3K}, \,HK \big \rbrace,\end{equation*}whereSis the number of states,Ais the number of actions,His the horizon length, andKis the total number of episodes. This regret matches the minimax lower bound for the entire range of sample sizeK≥ 1, essentially eliminating any burn-in requirement. It also translates to a PAC sample complexity (i.e., the number of episodes needed to yield ε-accuracy) of\(\frac{SAH^3}{\varepsilon ^2} \)up to log factor, which is minimax-optimal for the full ε-range. Further, we extend our theory to unveil the influences of problem-dependent quantities like the optimal value/cost and certain variances. The key technical innovation lies in a novel analysis paradigm (based on a new concept called “profiles”) to decouple complicated statistical dependency across the sample trajectories — a long-standing challenge facing the analysis of online RL in the sample-starved regime. 

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5. Randomized Exploration in Cooperative Multi-Agent Reinforcement Learning

   Hsu, Hao-Lun; Wang, Weixin; Pajic, Miroslav; Xu, Pan (September 2024, Advances in Neural Information Processing Systems)

   We present the first study on provably efficient randomized exploration in cooperative multi-agent reinforcement learning (MARL). We propose a unified algorithm framework for randomized exploration in parallel Markov Decision Processes (MDPs), and two Thompson Sampling (TS)-type algorithms, CoopTS-PHE and CoopTS-LMC, incorporating the perturbed-history exploration (PHE) strategy and the Langevin Monte Carlo exploration (LMC) strategy, respectively, which are flexible in design and easy to implement in practice. For a special class of parallel MDPs where the transition is (approximately) linear, we theoretically prove that both CoopTS-PHE and CoopTS-LMC achieve a $$\widetilde{\mathcal{O}}(d^{3/2}H^2\sqrt{MK})$$ regret bound with communication complexity $$\widetilde{\mathcal{O}}(dHM^2)$$, where $$d$$ is the feature dimension, $$H$$ is the horizon length, $$M$$ is the number of agents, and $$K$$ is the number of episodes. This is the first theoretical result for randomized exploration in cooperative MARL. We evaluate our proposed method on multiple parallel RL environments, including a deep exploration problem (i.e., $$N$$-chain), a video game, and a real-world problem in energy systems. Our experimental results support that our framework can achieve better performance, even under conditions of misspecified transition models. Additionally, we establish a connection between our unified framework and the practical application of federated learning. 

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