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Abstract Achieving sample efficiency in online episodic reinforcement learning (RL) requires optimally balancing exploration and exploitation. When it comes to a finite-horizon episodic Markov decision process with $S$ states, $A$ actions and horizon length $H$, substantial progress has been achieved toward characterizing the minimax-optimal regret, which scales on the order of $\sqrt{H^2SAT}$ (modulo log factors) with $T$ the total number of samples. While several competing solution paradigms have been proposed to minimize regret, they are either memory-inefficient, or fall short of optimality unless the sample size exceeds an enormous threshold (e.g. $S^6A^4 \,\mathrm{poly}(H)$ for existing model-free methods). To overcome such a large sample size barrier to efficient RL, we design a novel model-free algorithm, with space complexity $O(SAH)$, that achieves near-optimal regret as soon as the sample size exceeds the order of $SA\,\mathrm{poly}(H)$. In terms of this sample size requirement (also referred to the initial burn-in cost), our method improves—by at least a factor of $S^5A^3$—upon any prior memory-efficient algorithm that is asymptotically regret-optimal. Leveraging the recently introduced variance reduction strategy (also called reference-advantage decomposition), the proposed algorithm employs an early-settled reference update rule, with the aid of two Q-learning sequences with upper and lower confidence bounds. The design principle of our early-settled variance reduction method might be of independent interest to other RL settings that involve intricate exploration–exploitation trade-offs. 

Natural policy gradient (NPG) methods are among the most widely used policy optimization algorithms in contemporary reinforcement learning. This class of methods is often applied in conjunction with entropy regularization—an algorithmic scheme that encourages exploration—and is closely related to soft policy iteration and trust region policy optimization. Despite the empirical success, the theoretical underpinnings for NPG methods remain limited even for the tabular setting. This paper develops nonasymptotic convergence guarantees for entropy-regularized NPG methods under softmax parameterization, focusing on discounted Markov decision processes (MDPs). Assuming access to exact policy evaluation, we demonstrate that the algorithm converges linearly—even quadratically, once it enters a local region around the optimal policy—when computing optimal value functions of the regularized MDP. Moreover, the algorithm is provably stable vis-à-vis inexactness of policy evaluation. Our convergence results accommodate a wide range of learning rates and shed light upon the role of entropy regularization in enabling fast convergence. 

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.