On the Global Convergence of Risk-Averse Policy Gradient Methods with Dynamic Time-Consistent Risk Measures

Risk-sensitive reinforcement learning (RL) has become a popular tool to control the risk of uncertain outcomes and ensure reliable performance in various sequential decision-making problems. While policy gradient methods have been developed for risk-sensitive RL, it remains unclear if these methods enjoy the same global convergence guarantees as in the risk-neutral case. In this paper, we consider a class of dynamic time-consistent risk measures, called Expected Conditional Risk Measures (ECRMs), and derive policy gradient updates for ECRM-based objective functions. Under both constrained direct parameterization and unconstrained softmax parameterization, we provide global convergence of the corresponding risk-averse policy gradient algorithms. We further test a risk-averse variant of REINFORCE algorithm on a stochastic Cliffwalk environment to demonstrate the efficacy of our algorithm and the importance of risk control.

Risk-Averse Reinforcement Learning via Dynamic Time-Consistent Risk Measures

Traditional reinforcement learning (RL) aims to maximize the expected total reward, while the risk of uncertain outcomes needs to be controlled to ensure reliable performance in a risk-averse setting. In this paper, we consider the problem of maximizing dynamic risk of a sequence of rewards in infinite-horizon Markov Decision Processes (MDPs). We adapt the Expected Conditional Risk Measures (ECRMs) to the infinite-horizon risk-averse MDP and prove its time consistency. Using a convex combination of expectation and conditional value-at-risk (CVaR) as a special one-step conditional risk measure, we reformulate the risk-averse MDP as a risk-neutral counterpart with augmented action space and manipulation on the immediate rewards. We further prove that the related Bellman operator is a contraction mapping, which guarantees the convergence of any value-based RL algorithms. Accordingly, we develop a risk-averse deep Q-learning framework, and our numerical studies based on two simple MDPs show that the risk-averse setting can reduce the variance and enhance robustness of the results.