Chasing ghosts: Competing with stateful policies

Uriel Feige, Tomer Koren, Moshe Tennenholtz

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider sequential decision making in a setting where regret is measured with respect to a set of stateful reference policies, and feedback is limited to observing the rewards of the actions performed (the so called 'bandit' setting). If either the reference policies are stateless rather than stateful, or the feedback includes the rewards of all actions (the so called 'expert' setting), previous work shows that the optimal regret grows like (T) in terms of the number of decision rounds T. The difficulty in our setting is that the decision maker unavoidably loses track of the internal states of the reference policies, and thus cannot reliably attribute rewards observed in a certain round to any of the reference policies. In fact, in this setting it is impossible for the algorithm to estimate which policy gives the highest (or even approximately highest) total reward. Nevertheless, we design an algorithm that achieves expected regret that is sublinear in T, of the form O(T/log1/4T). Our algorithm is based on a certain local repetition lemma that may be of independent interest. We also show that no algorithm can guarantee expected regret better than O(T/log3/2T).

Original languageEnglish
Title of host publicationProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
PublisherIEEE Computer Society
Pages100-109
Number of pages10
ISBN (Electronic)9781479965175
DOIs
StatePublished - 7 Dec 2014
Externally publishedYes
Event55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014 - Philadelphia, United States
Duration: 18 Oct 201421 Oct 2014

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014
Country/TerritoryUnited States
CityPhiladelphia
Period18/10/1421/10/14

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