Entropic Risk-Sensitive Reinforcement Learning: A Meta Regret Framework with Function Approximation

Yingjie Fei, Zhuoran Yang, Zhaoran Wang

Abstract: We study risk-sensitive reinforcement learning with the entropic risk measure and function approximation. We consider the finite-horizon episodic MDP setting, and propose a meta algorithm based on value iteration. We then derive two algorithms for linear and general function approximation, namely RSVI.L and RSVI.G, respectively, as special instances of the meta algorithm. We illustrate that the success of RSVI.L depends crucially on carefully designed feature mapping and regularization that adapt to risk sensitivity. In addition, both RSVI.L and RSVI.G maintain risk-sensitive optimism that facilitates efficient exploration. On the analytic side, we provide regret analysis for the algorithms by developing a meta analytic framework, at the core of which is a risk-sensitive optimism condition. We show that any instance of the meta algorithm that satisfies the condition yields a meta regret bound. We further verify the condition for RSVI.L and RSVI.G under respective function approximation settings to obtain concrete regret bounds that scale sublinearly in the number of episodes.

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