From Dirichlet to Rubin: Optimistic Exploration in RL without Bonuses. (arXiv:2205.07704v2 [stat.ML] UPDATED)

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular,
stage-dependent, episodic Markov decision process: a natural extension of the
Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our
method uses the quantile of a Q-value function posterior as upper confidence
bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound
of order $\widetilde{O}(\sqrt{H^3SAT})$ where $H$ is the length of one episode,
$S$ is the number of states, $A$ the number of actions, $T$ the …

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