Model-free Posterior Sampling via Learning Rate Randomization

Daniil Tiapkin · Denis Belomestny · Daniele Calandriello · Eric Moulines · Remi Munos · Alexey Naumov · Pierre Perrault · Michal Valko · Pierre Ménard

Great Hall & Hall B1+B2 (level 1) #1301
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Wed 13 Dec 8:45 a.m. PST — 10:45 a.m. PST

Abstract: In this paper, we introduce Randomized Q-learning (RandQL), a novel randomized model-free algorithm for regret minimization in episodic Markov Decision Processes (MDPs). To the best of our knowledge, RandQL is the first tractable model-free posterior sampling-based algorithm. We analyze the performance of RandQL in both tabular and non-tabular metric space settings. In tabular MDPs, RandQL achieves a regret bound of order $\widetilde{\mathcal{O}}(\sqrt{H^{5}SAT})$, where $H$ is the planning horizon, $S$ is the number of states, $A$ is the number of actions, and $T$ is the number of episodes. For a metric state-action space, RandQL enjoys a regret bound of order $\widetilde{\mathcal{O}}(H^{5/2} T^{(d_z+1)/(d_z+2)})$, where $d_z$ denotes the zooming dimension. Notably, RandQL achieves optimistic exploration without using bonuses, relying instead on a novel idea of learning rate randomization. Our empirical study shows that RandQL outperforms existing approaches on baseline exploration environments.

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