
Tight Lower Bounds for Combinatorial MultiArmed Bandits
The Combinatorial MultiArmed Bandit problem is a sequential decisionma...
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An Armwise Randomization Approach to Combinatorial Linear Semibandits
Combinatorial linear semibandits (CLS) are widely applicable frameworks...
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Predictive Bandits
We introduce and study a new class of stochastic bandit problems, referr...
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Contextual Search via Intrinsic Volumes
We study the problem of contextual search, a multidimensional generaliza...
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Sequential Experimental Design for Transductive Linear Bandits
In this paper we introduce the transductive linear bandit problem: given...
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Efficient Linear Bandits through Matrix Sketching
We prove that two popular linear contextual bandit algorithms, OFUL and ...
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Matroid Bandits: Fast Combinatorial Optimization with Learning
A matroid is a notion of independence in combinatorial optimization whic...
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NearOptimal Regret Bounds for Contextual Combinatorial SemiBandits with Linear Payoff Functions
The contextual combinatorial semibandit problem with linear payoff functions is a decisionmaking problem in which a learner chooses a set of arms with the feature vectors in each round under given constraints so as to maximize the sum of rewards of arms. Several existing algorithms have regret bounds that are optimal with respect to the number of rounds T. However, there is a gap of Õ(max(√(d), √(k))) between the current best upper and lower bounds, where d is the dimension of the feature vectors, k is the number of the chosen arms in a round, and Õ(·) ignores the logarithmic factors. The dependence of k and d is of practical importance because k may be larger than T in realworld applications such as recommender systems. In this paper, we fill the gap by improving the upper and lower bounds. More precisely, we show that the C^2UCB algorithm proposed by Qin, Chen, and Zhu (2014) has the optimal regret bound Õ(d√(kT) + dk) for the partition matroid constraints. For general constraints, we propose an algorithm that modifies the reward estimates of arms in the C^2UCB algorithm and demonstrate that it enjoys the optimal regret bound for a more general problem that can take into account other objectives simultaneously. We also show that our technique would be applicable to related problems. Numerical experiments support our theoretical results and considerations.
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