KL-Entropy-Regularized RL with a Generative Model is Minimax Optimal
This provides a theoretical foundation for efficient model-free RL algorithms, addressing a key problem for researchers and practitioners in reinforcement learning.
The paper tackles the sample complexity of model-free reinforcement learning with a generative model, showing that mirror descent value iteration (MDVI) with KL divergence and entropy regularization is nearly minimax-optimal for finding an ε-optimal policy when ε is small.
In this work, we consider and analyze the sample complexity of model-free reinforcement learning with a generative model. Particularly, we analyze mirror descent value iteration (MDVI) by Geist et al. (2019) and Vieillard et al. (2020a), which uses the Kullback-Leibler divergence and entropy regularization in its value and policy updates. Our analysis shows that it is nearly minimax-optimal for finding an $\varepsilon$-optimal policy when $\varepsilon$ is sufficiently small. This is the first theoretical result that demonstrates that a simple model-free algorithm without variance-reduction can be nearly minimax-optimal under the considered setting.