Bayesian reinforcement learning (BRL) provides a principled framework for optimal exploration-exploitation tradeoff in reinforcement learning. We focus on model based BRL, which involves a compact formulation of the optimal tradeoff from the Bayesian perspective. However, it still remains a computational challenge to compute the Bayes-optimal policy. In this paper, we propose a novel approach to compute tighter value function bounds of the Bayes-optimal value function, which is crucial for improving the performance of many model-based BRL algorithms. We then present how our bounds can be integrated into real-time AO* heuristic search, and provide a theoretical analysis on the impact of improved bounds on the search efficiency. We also provide empirical results on standard BRL domains that demonstrate the effectiveness of our approach.
Bayesian planning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, planning optimally in the face of uncertainty is notoriously taxing, since the search space is enormous. In this paper we introduce a tractable, sample-based method for approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our approach avoids expensive applications of Bayes rule within the search tree by sampling models from current beliefs, and furthermore performs this sampling in a lazy manner. This enables it to outperform previous Bayesian model-based reinforcement learning algorithms by a significant margin on several well-known benchmark problems. As we show, our approach can even work in problems with an infinite state space that lie qualitatively out of reach of almost all previous work in Bayesian exploration.
Bayes-optimal behavior, while well-defined, is often difficult to achieve. Recent advances in the use of Monte-Carlo tree search (MCTS) have shown that it is possible to act near-optimally in Markov Decision Processes (MDPs) with very large or infinite state spaces. Bayes-optimal behavior in an unknown MDP is equivalent to optimal behavior in the known belief-space MDP, although the size of this belief-space MDP grows exponentially with the amount of history retained, and is potentially infinite. We show how an agent can use one particular MCTS algorithm, Forward Search Sparse Sampling (FSSS), in an efficient way to act nearly Bayes-optimally for all but a polynomial number of steps, assuming that FSSS can be used to act efficiently in any possible underlying MDP.
Bayesian reinforcement learning (BRL) provides a formal framework for optimal exploration-exploitation tradeoff in reinforcement learning. Unfortunately, it is generally intractable to find the Bayes-optimal behavior except for restricted cases. As a consequence, many BRL algorithms, model-based approaches in particular, rely on approximated models or real-time search methods. In this paper, we present potential-based shaping for improving the learning performance in model-based BRL. We propose a number of potential functions that are particularly well suited for BRL, and are domain-independent in the sense that they do not require any prior knowledge about the actual environment. By incorporating the potential function into real-time heuristic search, we show that we can significantly improve the learning performance in standard benchmark domains.
Bayesian reinforcement learning (BRL) provides a formal framework for optimal exploration-exploitation tradeoff in reinforcement learning. Unfortunately, it is generally intractable to find the Bayes-optimal behavior except for restricted cases. As a consequence, many BRL algorithms, model-based approaches in particular, rely on approximated models or real-time search methods.