Online Bayesian Risk-Averse Reinforcement Learning
This work addresses uncertainty in RL for applications requiring risk-aware decision-making, but it is incremental as it builds on existing Bayesian and risk-averse frameworks.
The paper tackles the problem of epistemic uncertainty in reinforcement learning by proposing a Bayesian risk-averse approach, deriving asymptotic normality to show it pessimistically underestimates value functions, and achieves sub-linear regret bounds in online RL and contextual multi-arm bandits.
In this paper, we study the Bayesian risk-averse formulation in reinforcement learning (RL). To address the epistemic uncertainty due to a lack of data, we adopt the Bayesian Risk Markov Decision Process (BRMDP) to account for the parameter uncertainty of the unknown underlying model. We derive the asymptotic normality that characterizes the difference between the Bayesian risk value function and the original value function under the true unknown distribution. The results indicate that the Bayesian risk-averse approach tends to pessimistically underestimate the original value function. This discrepancy increases with stronger risk aversion and decreases as more data become available. We then utilize this adaptive property in the setting of online RL as well as online contextual multi-arm bandits (CMAB), a special case of online RL. We provide two procedures using posterior sampling for both the general RL problem and the CMAB problem. We establish a sub-linear regret bound, with the regret defined as the conventional regret for both the RL and CMAB settings. Additionally, we establish a sub-linear regret bound for the CMAB setting with the regret defined as the Bayesian risk regret. Finally, we conduct numerical experiments to demonstrate the effectiveness of the proposed algorithm in addressing epistemic uncertainty and verifying the theoretical properties.