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Variance-Aware Regr...
Variance-Aware Regret Bounds for Undiscounted Reinforcement Learning in MDPs
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- Talebi Mazraeh Shahi, Mohammad Sadegh, 1982- (författare)
- KTH,Reglerteknik
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- Maillard, Odalric Ambrym (författare)
- INRIA Lille – Nord Europe, Villeneuve d’Ascq, France
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(creator_code:org_t)
- ML Research Press, 2018
- 2018
- Engelska.
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Ingår i: Proceedings of 29th International Conference on Algorithmic Learning Theory, ALT 2018. - : ML Research Press. ; , s. 770-805
- Relaterad länk:
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https://urn.kb.se/re...
Abstract
Ämnesord
Stäng
- The problem of reinforcement learning in an unknown and discrete Markov Decision Process (MDP) under the average-reward criterion is considered, when the learner interacts with the system in a single stream of observations, starting from an initial state without any reset. We revisit the minimax lower bound for that problem by making appear the local variance of the bias function in place of the diameter of the MDP. Furthermore, we provide a novel analysis of the KL-Ucrl algorithm establishing a high-probability regret bound scaling as Oe(q S Ps,a V?s,aT ) for this algorithm for ergodic MDPs, where S denotes the number of states and where Vs,a? is the variance of the bias function with respect to the next-state distribution following action a in state s. The resulting bound improves upon the best previously known regret bound Oe(DS√AT) for that algorithm, where A and D respectively denote the maximum number of actions (per state) and the diameter of MDP. We finally compare the leading terms of the two bounds in some benchmark MDPs indicating that the derived bound can provide an order of magnitude improvement in some cases. Our analysis leverages novel variations of the transportation lemma combined with Kullback-Leibler concentration inequalities, that we believe to be of independent interest.
Ämnesord
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
Nyckelord
- Bellman Optimality
- Concentration Inequalities
- Markov Decision Processes
- Regret Minimization
- Undiscounted Reinforcement Learning
Publikations- och innehållstyp
- ref (ämneskategori)
- kon (ämneskategori)