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Risk-sensitive reinforcement learning (RL) has become a popular tool tocontrol the risk of uncertain outcomes and ensure reliable performance invarious sequential decision-making problems. While policy gradient methods havebeen developed for risk-sensitive RL, it remains unclear if these methods enjoythe same global convergence guarantees as in the risk-neutral case. In thispaper, we consider a class of dynamic time-consistent risk measures, calledExpected Conditional Risk Measures (ECRMs), and derive policy gradient updatesfor ECRM-based objective functions. Under both constrained directparameterization and unconstrained softmax parameterization, we provide globalconvergence and iteration complexities of the corresponding risk-averse policygradient algorithms. We further test risk-averse variants of REINFORCE andactor-critic algorithms to demonstrate the efficacy of our method and theimportance of risk control.

On the Global Convergence of Risk-Averse Policy Gradient Methods with Expected Conditional Risk Measures