First-order regret bounds for combinatorial semi-bandits

Gergely Neu 1
1 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : We consider the problem of online combinatorial optimization under semi-bandit feedback, where a learner has to repeatedly pick actions from a combinatorial decision set in order to minimize the total losses associated with its decisions. After making each decision, the learner observes the losses associated with its action, but not other losses. For this problem, there are several learning algorithms that guarantee that the learner's expected regret grows as O(√ T) with the number of rounds T. In this paper, we propose an algorithm that improves this scaling to O(√ L * T), where L * T is the total loss of the best action. Our algorithm is among the first to achieve such guarantees in a partial-feedback scheme, and the first one to do so in a combinatorial setting.
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Submitted on : Tuesday, October 13, 2015 - 2:40:50 PM
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Gergely Neu. First-order regret bounds for combinatorial semi-bandits. Proceedings of the 28th Annual Conference on Learning Theory (COLT), Jul 2015, Paris, France. pp.1360-1375. ⟨hal-01215001⟩

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