Xianjun Yu

Xian Yu, Lei Ying

Risk-sensitive reinforcement learning (RL) has become a popular tool for controlling the risk of uncertain outcomes and ensuring reliable performance in highly stochastic sequential decision-making problems. While it has been shown that policy gradient methods can find globally optimal policies in the risk-neutral setting, it remains unclear if the risk-averse variants enjoy the same global convergence guarantees. In this paper, we consider a class of dynamic time-consistent risk measures, named Expected Conditional Risk Measures (ECRMs), and derive natural policy gradient (NPG) updates for ECRMs-based RL problems. We provide global optimality and iteration complexity of the proposed risk-averse NPG algorithm with softmax parameterization and entropy regularization under both exact and inexact policy evaluation. Furthermore, we test our risk-averse NPG algorithm on a stochastic Cliffwalk environment to demonstrate the efficacy of our method.

Minheng Xiao, Xian Yu, Lei Ying

Risk-sensitive reinforcement learning (RL) is crucial for maintaining reliable performance in high-stakes applications. While traditional RL methods aim to learn a point estimate of the random cumulative cost, distributional RL (DRL) seeks to estimate the entire distribution of it, which leads to a unified framework for handling different risk measures. However, developing policy gradient methods for risk-sensitive DRL is inherently more complex as it involves finding the gradient of a probability measure. This paper introduces a new policy gradient method for risk-sensitive DRL with general coherent risk measures, where we provide an analytical form of the probability measure's gradient for any distribution. For practical use, we design a categorical distributional policy gradient algorithm (CDPG) that approximates any distribution by a categorical family supported on some fixed points. We further provide a finite-support optimality guarantee and a finite-iteration convergence guarantee under inexact policy evaluation and gradient estimation. Through experiments on stochastic Cliffwalk and CartPole environments, we illustrate the benefits of considering a risk-sensitive setting in DRL.