Titre :

Variance-Aware Regret Bounds for Undiscounted Reinforcement Learning in MDPs

Auteur(s) :

Talebi, Mohammad [Auteur]
Sequential Learning [SEQUEL]
KTH School of Electrical Engineering
Maillard, Odalric Ambrym [Auteur]
Sequential Learning [SEQUEL]

Titre de la revue :

Journal of Machine Learning Research

Pagination :

1-36

Éditeur :

Microtome Publishing

Date de publication :

2018-04-01

ISSN :

1532-4435

Mot(s)-clé(s) en anglais :

Undiscounted Reinforcement Learning
Markov Decision Processes
Bellman Optimality
Regret Minimization
Concentration Inequalities

Discipline(s) HAL :

Statistiques [stat]/Machine Learning [stat.ML]
Mathématiques [math]/Statistiques [math.ST]

Résumé en anglais : [en]

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, ...
Lire la suite >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 O S s,a V s,a T for this algorithm for ergodic MDPs, where S denotes the number of states and where V s,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 O(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.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

BANDITS MANCHOTS POUR SIGNAUX NON-STATIONNAIRES ET STRUCTURES

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL