Bayesian model-based reinforcement learning is a formally elegant approach to learning optimal behaviour under model uncertainty, trading off exploration and exploitation in an ideal way. Unfortunately, finding the resulting Bayes-optimal policies is notoriously taxing, since the search space becomes enormous. In this paper we introduce a tractable, sample-based method for approximate Bayes-optimal planning which exploits Monte-Carlo tree search. Our approach outperformed prior Bayesian model-based RL algorithms by a significant margin on several well-known benchmark problems -- because it avoids expensive applications of Bayes rule within the search tree by lazily sampling models from the current beliefs. We illustrate the advantages of our approach by showing it working in an infinite state space domain which is qualitatively out of reach of almost all previous work in Bayesian exploration.
Bayesian Exploration Bonus (BEB) solves the posterior mean MDP, but with an additional reward bonus that depends on visitation counts @cite_14 . Similarly, propose an algorithm with a different form of exploration bonus @cite_18 . These algorithms provide performance guarantees after a polynomial number of steps in the environment. However, behavior in the early steps of exploration is very sensitive to the precise exploration bonuses; and it turns out to be hard to translate sophisticated prior knowledge into the form of a bonus.
@cite_18 @cite_14
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We consider the exploration exploitation problem in reinforcement learning (RL). The Bayesian approach to model-based RL offers an elegant solution to this problem, by considering a distribution over possible models and acting to maximize expected reward; unfortunately, the Bayesian solution is intractable for all but very restricted cases. In this paper we present a simple algorithm, and prove that with high probability it is able to perform e-close to the true (intractable) optimal Bayesian policy after some small (polynomial in quantities describing the system) number of time steps. The algorithm and analysis are motivated by the so-called PAC-MDP approach, and extend such results into the setting of Bayesian RL. In this setting, we show that we can achieve lower sample complexity bounds than existing algorithms, while using an exploration strategy that is much greedier than the (extremely cautious) exploration of PAC-MDP algorithms. In environments with uncertain dynamics exploration is necessary to learn how to perform well. Existing reinforcement learning algorithms provide strong exploration guarantees, but they tend to rely on an ergodicity assumption. The essence of ergodicity is that any state is eventually reachable from any other state by following a suitable policy. This assumption allows for exploration algorithms that operate by simply favoring states that have rarely been visited before. For most physical systems this assumption is impractical as the systems would break before any reasonable exploration has taken place, i.e., most physical systems don't satisfy the ergodicity assumption. In this paper we address the need for safe exploration methods in Markov decision processes. We first propose a general formulation of safety through ergodicity. We show that imposing safety by restricting attention to the resulting set of guaranteed safe policies is NP-hard. We then present an efficient algorithm for guaranteed safe, but potentially suboptimal, exploration. At the core is an optimization formulation in which the constraints restrict attention to a subset of the guaranteed safe policies and the objective favors exploration policies. Our framework is compatible with the majority of previously proposed exploration methods, which rely on an exploration bonus. Our experiments, which include a Martian terrain exploration problem, show that our method is able to explore better than classical exploration methods. The explore exploit dilemma is one of the central challenges in Reinforcement Learning (RL). Bayesian RL solves the dilemma by providing the agent with information in the form of a prior distribution over environments; however, full Bayesian planning is intractable. Planning with the mean MDP is a common myopic approximation of Bayesian planning. We derive a novel reward bonus that is a function of the posterior distribution over environments, which, when added to the reward in planning with the mean MDP, results in an agent which explores efficiently and effectively. Although our method is similar to existing methods when given an uninformative or unstructured prior, unlike existing methods, our method can exploit structured priors. We prove that our method results in a polynomial sample complexity and empirically demonstrate its advantages in a structured exploration task. In the classic Bayesian restless multi-armed bandit (RMAB) problem, there are N arms, with rewards on all arms evolving at each time as Markov chains with known parameters. A player seeks to activate K ≥ 1 arms at each time in order to maximize the expected total reward obtained over multiple plays. RMAB is a challenging problem that is known to be PSPACE-hard in general. We consider in this work the even harder non-Bayesian RMAB, in which the parameters of the Markov chain are assumed to be unknown a priori. We develop an original approach to this problem that is applicable when the corresponding Bayesian problem has the structure that, depending on the known parameter values, the optimal solution is one of a prescribed finite set of policies. In such settings, we propose to learn the optimal policy for the non-Bayesian RMAB by employing a suitable meta-policy which treats each policy from this finite set as an arm in a different non-Bayesian multi-armed bandit problem for which a single-arm selection policy is optimal. We demonstrate this approach by developing a novel sensing policy for opportunistic spectrum access over unknown dynamic channels. We prove that our policy achieves near-logarithmic regret (the difference in expected reward compared to a model-aware genie), which leads to the same average reward that can be achieved by the optimal policy under a known model. This is the first such result in the literature for a non-Bayesian RMAB.