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Research in reinforcement learning has produced algorithms for optimaldecision making under uncertainty that fall within two main types. The firstemploys a Bayesian framework, where optimality improves with increasedcomputational time. This is because the resulting planning task takes the formof a dynamic programming problem on a belief tree with an infinite number ofstates. The second type employs relatively simple algorithm which are shown tosuffer small regret within a distribution-free framework. This paper presents alower bound and a high probability upper bound on the optimal value functionfor the nodes in the Bayesian belief tree, which are analogous to similarbounds in POMDPs. The bounds are then used to create more efficient strategiesfor exploring the tree. The resulting algorithms are compared with thedistribution-free algorithm UCB1, as well as a simpler baseline algorithm onmulti-armed bandit problems.

Tree Exploration for Bayesian RL Exploration