# Efficient Bias-Span-Constrained Exploration-Exploitation in Reinforcement Learning

1 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : We introduce SCAL, an algorithm designed to perform efficient exploration-exploitation in any unknown weakly-communicating Markov decision process (MDP) for which an upper bound $c$ on the span of the optimal bias function is known. For an MDP with $S$ states, $A$ actions and $\Gamma \leq S$ possible next states, we prove a regret bound of $\widetilde{O}(c\sqrt{\Gamma SAT})$, which significantly improves over existing algorithms (e.g., UCRL and PSRL), whose regret scales linearly with the MDP diameter $D$. In fact, the optimal bias span is finite and often much smaller than $D$ (e.g., $D=\infty$ in non-communicating MDPs). A similar result was originally derived by Bartlett and Tewari (2009) for REGAL.C, for which no tractable algorithm is available. In this paper, we relax the optimization problem at the core of REGAL.C, we carefully analyze its properties, and we provide the first computationally efficient algorithm to solve it. Finally, we report numerical simulations supporting our theoretical findings and showing how SCAL significantly outperforms UCRL in MDPs with large diameter and small span.
Document type :
Conference papers
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https://hal.inria.fr/hal-01941206
Contributor : Matteo Pirotta <>
Submitted on : Friday, November 30, 2018 - 6:24:07 PM
Last modification on : Friday, March 22, 2019 - 1:37:09 AM
Long-term archiving on : Friday, March 1, 2019 - 4:04:19 PM

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• HAL Id : hal-01941206, version 1

### Citation

Ronan Fruit, Matteo Pirotta, Alessandro Lazaric, Ronald Ortner. Efficient Bias-Span-Constrained Exploration-Exploitation in Reinforcement Learning. ICML 2018 - The 35th International Conference on Machine Learning, Jul 2018, Stockholm, Sweden. pp.1578-1586. ⟨hal-01941206⟩

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