Near-Minimax-Optimal Risk-Sensitive Reinforcement Learning with CVaR

• URL: http://arxiv.org/abs/2302.03201v2
• Date: Wed, 24 May 2023 21:47:10 GMT
• Title: Near-Minimax-Optimal Risk-Sensitive Reinforcement Learning with CVaR
• Authors: Kaiwen Wang and Nathan Kallus and Wen Sun
• Abstract summary: We study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance $tau$. We show the minimax CVaR regret rate is $Omega(sqrttau-1AK)$, where $A$ is the number of actions and $K$ is the number of episodes. We show that our algorithm achieves the optimal regret of $widetilde O(tau-1sqrtSAK)$ under a continuity assumption and in general attains a near
• Score: 58.40575099910538
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance $\tau$. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is $\Omega(\sqrt{\tau^{-1}AK})$, where $A$ is the number of actions and $K$ is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of $\Omega(\sqrt{\tau^{-1}SAK})$ (with normalized cumulative rewards), where $S$ is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of $\widetilde O(\sqrt{\tau^{-1}SAK})$ under a continuity assumption and in general attains a near-optimal regret of $\widetilde O(\tau^{-1}\sqrt{SAK})$, which is minimax-optimal for constant $\tau$. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.

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