Bayes-CPACE: PAC Optimal Exploration in Continuous Space Bayes-Adaptive Markov Decision Processes
This addresses model uncertainty in reinforcement learning for continuous domains, offering a novel solution to a known bottleneck.
The paper tackles the problem of computing optimal policies in Bayes-Adaptive Markov Decision Processes (BAMDPs) with continuous state and action spaces, which is intractable, by developing a PAC optimal algorithm that uses finite sampling and Lipschitz continuity to achieve near-optimal value functions, with empirical validation showing competitive performance against baselines.
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.