Delay and cooperation in nonstochastic bandits

Nicolò Cesa-Bianchi, Claudio Gentile, Yishay Mansour, Alberto Minora

Research output: Contribution to journalConference articlepeer-review


We study networks of communicating learning agents that cooperate to solve a common nonstochastic bandit problem. Agents use an underlying communication network to get messages about actions selected by other agents, and drop messages that took more than d hops to arrive, where d is a delay parameter. We introduce EXP3-COOP, a cooperative version of the EXP3 algorithm and prove that with K actions and N agents the average per-agent regret after T rounds is at most of order q(d + 1 + KN α≤d)(T ln K), where α≤d is the independence number of the d-th power of the communication graph G. We then show that for any connected graph, for d = √K the regret bound is K1/4 √T, strictly better than the minimax regret √KT for noncooperating agents. More informed choices of d lead to bounds which are arbitrarily close to the full information minimax regret √T ln K when G is dense. When G has sparse components, we show that a variant of EXP3-COOP, allowing agents to choose their parameters according to their centrality in G, strictly improves the regret. Finally, as a by-product of our analysis, we provide the first characterization of the minimax regret for bandit learning with delay.

Original languageEnglish
Pages (from-to)605-622
Number of pages18
JournalJournal of Machine Learning Research
Issue numberJune
StatePublished - 6 Jun 2016
Event29th Conference on Learning Theory, COLT 2016 - New York, United States
Duration: 23 Jun 201626 Jun 2016


FundersFunder number
Bloom's Syndrome Foundation
Blavatnik Family Foundation
United States-Israel Binational Science Foundation
Israel Science Foundation
Israeli Centers for Research Excellence4/11


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