Browsing by Subject "Bounded regret"

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Open Access
Combinatorial multi-armed bandit problem with probabilistically triggered arms: a case with bounded regret
(IEEE, 2017-11) Sarıtaç, A. Ömer; Tekin, Cem
In this paper, we study the combinatorial multi-armed bandit problem (CMAB) with probabilistically triggered arms (PTAs). Under the assumption that the arm triggering probabilities (ATPs) are positive for all arms, we prove that a simple greedy policy, named greedy CMAB (G-CMAB), achieves bounded regret. This improves the result in previous work, which shows that the regret is O (log T) under no such assumption on the ATPs. Then, we numerically show that G-CMAB achieves bounded regret in a real-world movie recommendation problem, where the action corresponds to recommending a set of movies, arms correspond to the edges between movies and users, and the goal is to maximize the total number of users that are attracted by at least one movie. In addition to this problem, our results directly apply to the online influence maximization (OIM) problem studied in numerous prior works.
Open Access
Global bandits
(Institute of Electrical and Electronics Engineers, 2018) Atan, O.; Tekin, Cem; Schaar, M. V. D.
Multiarmed bandits (MABs) model sequential decision-making problems, in which a learner sequentially chooses arms with unknown reward distributions in order to maximize its cumulative reward. Most of the prior works on MAB assume that the reward distributions of each arm are independent. But in a wide variety of decision problems - from drug dosage to dynamic pricing - the expected rewards of different arms are correlated, so that selecting one arm provides information about the expected rewards of other arms as well. We propose and analyze a class of models of such decision problems, which we call global bandits (GB). In the case in which rewards of all arms are deterministic functions of a single unknown parameter, we construct a greedy policy that achieves bounded regret, with a bound that depends on the single true parameter of the problem. Hence, this policy selects suboptimal arms only finitely many times with probability one. For this case, we also obtain a bound on regret that is independent of the true parameter; this bound is sublinear, with an exponent that depends on the informativeness of the arms. We also propose a variant of the greedy policy that achieves O(√T) worst case and O(1) parameter-dependent regret. Finally, we perform experiments on dynamic pricing and show that the proposed algorithms achieve significant gains with respect to the well-known benchmarks.