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# Learning Exploration/Exploitation Strategies for Single Trajectory Reinforcement Learning

*Proceedings of the Tenth European Workshop on Reinforcement Learning*, PMLR 24:1-10, 2013.

#### Abstract

We consider the problem of learning high-performance Exploration/Exploitation (E/E) strategies for finite Markov Decision Processes (MDPs) when the MDP to be controlled is supposed to be drawn from a known probability distribution $p_\mathcal{M}(\cdot)$. The performance criterion is the sum of discounted rewards collected by the E/E strategy over an infinite length trajectory. We propose an approach for solving this problem that works by considering a rich set of candidate E/E strategies and by looking for the one that gives the best average performances on MDPs drawn according to $p_\mathcal{M}(\cdot)$. As candidate E/E strategies, we consider index-based strategies parametrized by small formulas combining variables that include the estimated reward function, the number of times each transition has occurred and the optimal value functions and the optimal value functions $\hat{V}$ and $\hat{Q}$ of the estimated MDP (obtained through value iteration). The search for the best formula is formalized as a multi-armed bandit problem, each arm being associated with a formula. We experimentally compare the performances of the approach with R-max as well as with $\epsilon$-Greedy strategies and the results are promising.