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Some reinforcement learning methods suffer from high sample complexitycausing them to not be practical in real-world situations. $Q$-function reuse,a transfer learning method, is one way to reduce the sample complexity oflearning, potentially improving usefulness of existing algorithms. Prior workhas shown the empirical effectiveness of $Q$-function reuse for variousenvironments when applied to model-free algorithms. To the best of ourknowledge, there has been no theoretical work showing the regret of$Q$-function reuse when applied to the tabular, model-free setting. We aim tobridge the gap between theoretical and empirical work in $Q$-function reuse byproviding some theoretical insights on the effectiveness of $Q$-function reusewhen applied to the $Q$-learning with UCB-Hoeffding algorithm. Our maincontribution is showing that in a specific case if $Q$-function reuse isapplied to the $Q$-learning with UCB-Hoeffding algorithm it has a regret thatis independent of the state or action space. We also provide empirical resultssupporting our theoretical findings.

The Effect of Q-function Reuse on the Total Regret of Tabular, Model-Free, Reinforcement Learning