Learning Multiple Markov Chains via Adaptive Allocation

Talebi, Mohammad; Maillard, Odalric Ambrym

Document type :

Communication dans un congrès avec actes

Title :

Learning Multiple Markov Chains via Adaptive Allocation

Author(s) :

Talebi, Mohammad [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Sequential Learning [SEQUEL]
Maillard, Odalric Ambrym [Auteur]

Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Sequential Learning [SEQUEL]

Conference title :

Advances in Neural Information Processing Systems 32 (NIPS 2019)

City :

Vancouver

Country :

Canada

Start date of the conference :

2019-12

HAL domain(s) :

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

English abstract : [en]

We study the problem of learning the transition matrices of a set of Markov chains from a single stream of observations on each chain. We assume that the Markov chains are ergodic but otherwise unknown. The learner can ...
Show more >We study the problem of learning the transition matrices of a set of Markov chains from a single stream of observations on each chain. We assume that the Markov chains are ergodic but otherwise unknown. The learner can sample Markov chains sequentially to observe their states. The goal of the learner is to sequentially select various chains to learn transition matrices uniformly well with respect to some loss function. We introduce a notion of loss that naturally extends the squared loss for learning distributions to the case of Markov chains, and further characterize the notion of being uniformly good in all problem instances. We present a novel learning algorithm that efficiently balances exploration and exploitation intrinsic to this problem, without any prior knowledge of the chains. We provide finite-sample PAC-type guarantees on the performance of the algorithm. Further, we show that our algorithm asymptotically attains an optimal loss.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

BANDITS MANCHOTS POUR SIGNAUX NON-STATIONNAIRES ET STRUCTURES

Collections :