Poster
Regret Minimization for Reinforcement Learning by Evaluating the Optimal Bias Function
Zihan Zhang · Xiangyang Ji
East Exhibition Hall B, C #211
Keywords: [ Reinforcement Learning ] [ Reinforcement Learning and Planning ] [ Decision and Control; Reinforcement Learning and Planning ] [ Algorithms -> Online Learning; Reinforcement Learning and Planning ]
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Abstract
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Abstract:
We present an algorithm based on the \emph{Optimism in the Face of Uncertainty} (OFU) principle which is able to learn Reinforcement Learning (RL) modeled by Markov decision process (MDP) with finite state-action space efficiently.
By evaluating the state-pair difference of the optimal bias function h∗, the proposed algorithm achieves a regret bound of ˜O(√SAHT)\footnote{The symbol ˜O means O with log factors ignored. } for MDP with S states and A actions, in the case that an upper bound H on the span of h∗, i.e., sp(h∗) is known.
This result outperforms the best previous regret bounds ˜O(S√AHT)\citep{fruit2019improved} by a factor of √S.
Furthermore, this regret bound matches the lower bound of Ω(√SAHT)\citep{jaksch2010near} up to a logarithmic factor. As a consequence, we show that there is a near optimal regret bound of ˜O(√SADT) for MDPs with a finite diameter D compared to the lower bound of Ω(√SADT)\citep{jaksch2010near}.
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