Unimodal bandits: Regret lower bounds and optimal algorithms
2014 (English)In: 31st International Conference on Machine Learning, ICML 2014, 2014, 799-807 p.Conference paper (Refereed)
2014 We consider stochastic multi-armed bandits where the expected reward is a unimodal function over partially ordered arms. This important class of problems has been recently investigated in (Cope, 2009; Yu&Mannor, 2011). The set of arms is either discrete, in which case arms correspond to the vertices of a finite graph whose structure represents similarity in rewards, or continuous, in which case arms belong to a bounded interval. For discrete unimodal bandits, we derive asymptotic lower bounds for the regret achieved under any algorithm, and propose OSUB, an algorithm whose regret matches this lower bound. Our algorithm optimally exploits the unimodal structure of the problem, and surprisingly, its asymptotic regret does not depend on the number of arms. We also provide a regret upper bound for OSUB in non-stationary environments where the expected rewards smoothly evolve over time. The analytical results are supported by numerical experiments showing that OSUB performs significantly better than the state-of-the-art algorithms. For continuous sets of arms, we provide a brief discussion. We show that combining an appropriate discretization of the set of arms with the UCB algorithm yields an order-optimal regret, and in practice, outperforms recently proposed algorithms designed to exploit the unimodal structure.
Place, publisher, year, edition, pages
2014. 799-807 p.
Artificial intelligence, Learning systems, Stochastic systems, Analytical results, Discretizations, Multi armed bandit, Non-stationary environment, Numerical experiments, Optimal algorithm, State-of-the-art algorithms, Unimodal functions, Algorithms
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-168369ScopusID: 2-s2.0-84919789435ISBN: 9781634393973OAI: oai:DiVA.org:kth-168369DiVA: diva2:815975
31st International Conference on Machine Learning, ICML 2014, 21 June 2014 through 26 June 2014
QC 201506022015-06-022015-06-022015-06-02Bibliographically approved