Model-free deep reinforcement learning (RL) algorithms have achieved tremendous success on a range of challenging tasks. However, safety concerns remain when these methods are deployed on real-world applications, necessitating risk-aware agents. A common utility for learning such risk-aware agents is the entropic risk measure, but current policy gradient methods optimizing this measure must perform high-variance and numerically unstable updates. As a result, existing risk-sensitive model-free approaches are limited to simple tasks and tabular settings. In this paper, we provide a comprehensive theoretical justification for policy gradient methods on the entropic risk measure, including on- and off-policy gradient theorems for the stochastic and deterministic policy settings. Motivated by theory, we propose risk-sensitive exponential actor-critic (rsEAC), an off-policy model-free approach that incorporates novel procedures to avoid the explicit representation of exponential value functions and their gradients, and optimizes its policy w.r.t. the entropic risk measure. In this way, we show that rsEAC produces more numerically stable updates compared to existing approaches and reliably learns risk-sensitive policies in challenging risky variants of continuous tasks in MuJoCo.

Risk-sensitive reinforcement learning (RL) with an entropic risk measure typically requires knowledge of the transition kernel or performs unstable updates w.r.t. exponential Bellman equations. As a consequence, algorithms that optimize this objective have been restricted to tabular or low-dimensional continuous environments. In this work we leverage the connection between the entropic risk measure and the RL-as-inference framework to develop a risk-sensitive variational actor-critic algorithm (rsVAC). Our work extends the variational framework to incorporate stochastic rewards and proposes a variational model-based actor-critic approach that modulates policy risk via a risk parameter. We consider, both, the risk-seeking and risk-averse regimes and present rsVAC learning variants for each setting. Our experiments demonstrate that this approach produces risk-sensitive policies and yields improvements in both tabular and risk-aware variants of complex continuous control tasks in MuJoCo.