Bayes-CPACE: PAC Optimal Exploration in Continuous Space Bayes-Adaptive Markov Decision Processes

TL;DR

This paper introduces Bayes-CPACE, the first PAC optimal algorithm for continuous-space BAMDPs, using sampling and Lipschitz continuity to efficiently approximate optimal policies under model uncertainty.

Contribution

It presents a novel PAC optimal algorithm for continuous BAMDPs that leverages sampling and Lipschitz properties to handle intractability.

Findings

Algorithm is proven to be near-optimal.

Empirical results show competitive performance.

Efficient schemes improve computational feasibility.

Abstract

We present the first PAC optimal algorithm for Bayes-Adaptive Markov Decision Processes (BAMDPs) in continuous state and action spaces, to the best of our knowledge. The BAMDP framework elegantly addresses model uncertainty by incorporating Bayesian belief updates into long-term expected return. However, computing an exact optimal Bayesian policy is intractable. Our key insight is to compute a near-optimal value function by covering the continuous state-belief-action space with a finite set of representative samples and exploiting the Lipschitz continuity of the value function. We prove the near-optimality of our algorithm and analyze a number of schemes that boost the algorithm's efficiency. Finally, we empirically validate our approach on a number of discrete and continuous BAMDPs and show that the learned policy has consistently competitive performance against baseline approaches.