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Regularization and Variance-Weighted Regression Achieves Minimax Optimality in Linear MDPs: Theory and Practice
Toshinori Kitamura · Tadashi Kozuno · Yunhao Tang · Nino Vieillard · Michal Valko · Wenhao Yang · Jincheng Mei · Pierre Menard · Mohammad Gheshlaghi Azar · Remi Munos · Olivier Pietquin · Matthieu Geist · Csaba Szepesvari · Wataru Kumagai · Yutaka Matsuo

Tue Jul 25 02:00 PM -- 04:30 PM (PDT) @ Exhibit Hall 1 #700
Mirror descent value iteration (MDVI), an abstraction of Kullback-Leibler (KL) and entropy-regularized reinforcement learning (RL), has served as the basis for recent high-performing practical RL algorithms. However, despite the use of function approximation in practice, the theoretical understanding of MDVI has been limited to tabular Markov decision processes (MDPs). We study MDVI with linear function approximation through its sample complexity required to identify an $\varepsilon$-optimal policy with probability $1-\delta$ under the settings of an infinite-horizon linear MDP, generative model, and G-optimal design. We demonstrate that least-squares regression weighted by the variance of an estimated optimal value function of the next state is crucial to achieving minimax optimality. Based on this observation, we present Variance-Weighted Least-Squares MDVI (VWLS-MDVI), the first theoretical algorithm that achieves nearly minimax optimal sample complexity for infinite-horizon linear MDPs. Furthermore, we propose a practical VWLS algorithm for value-based deep RL, Deep Variance Weighting (DVW). Our experiments demonstrate that DVW improves the performance of popular value-based deep RL algorithms on a set of MinAtar benchmarks.

Author Information

Toshinori Kitamura (The University of Tokyo)
Tadashi Kozuno (Omron Sinic X)
Yunhao Tang (Google DeepMind)
Nino Vieillard (Google Brain)
Michal Valko (Google DeepMind / Inria / MVA)
Wenhao Yang (Peking University)
Jincheng Mei (Google DeepMind)
Pierre Menard (ENS Lyon)
Mohammad Gheshlaghi Azar (Google DeepMind)
Remi Munos (DeepMind)
Olivier Pietquin (Google DeepMind)
Matthieu Geist (Google)
Csaba Szepesvari (DeepMind/University of Alberta)
Wataru Kumagai (The University of Tokyo)
Yutaka Matsuo (University of Tokyo)

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