Bayesian Bellman Operators

TL;DR

This paper introduces Bayesian Bellman Operators (BBO) to characterize uncertainty in the Bellman operator, providing theoretical insights and demonstrating improved exploration in continuous control tasks over traditional methods.

Contribution

The paper presents a novel BBO framework that shifts the focus from posterior over value functions to the Bellman operator, offering new theoretical analysis and practical algorithms for Bayesian RL.

Findings

Bayesian solutions are consistent with frequentist RL solutions.

BBO-based algorithms exhibit advanced deep exploration capabilities.

BBO methods outperform regularized actor-critic algorithms in continuous control tasks.

Abstract

We introduce a novel perspective on Bayesian reinforcement learning (RL); whereas existing approaches infer a posterior over the transition distribution or Q-function, we characterise the uncertainty in the Bellman operator. Our Bayesian Bellman operator (BBO) framework is motivated by the insight that when bootstrapping is introduced, model-free approaches actually infer a posterior over Bellman operators, not value functions. In this paper, we use BBO to provide a rigorous theoretical analysis of model-free Bayesian RL to better understand its relationshipto established frequentist RL methodologies. We prove that Bayesian solutions are consistent with frequentist RL solutions, even when approximate inference isused, and derive conditions for which convergence properties hold. Empirically, we demonstrate that algorithms derived from the BBO framework have sophisticated deep exploration properties that enable them to solve continuous control tasks at which state-of-the-art regularised actor-critic algorithms fail catastrophically