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In this paper, we introduce Randomized Q-learning (RandQL), a novelrandomized model-free algorithm for regret minimization in episodic MarkovDecision Processes (MDPs). To the best of our knowledge, RandQL is the firsttractable model-free posterior sampling-based algorithm. We analyze theperformance of RandQL in both tabular and non-tabular metric space settings. Intabular 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 thenumber of episodes. For a metric state-action space, RandQL enjoys a regretbound 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 optimisticexploration without using bonuses, relying instead on a novel idea of learningrate randomization. Our empirical study shows that RandQL outperforms existingapproaches on baseline exploration environments.

Model-free Posterior Sampling via Learning Rate Randomization