9,937 research outputs found

    Bandit Problems with Side Observations

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    An extension of the traditional two-armed bandit problem is considered, in which the decision maker has access to some side information before deciding which arm to pull. At each time t, before making a selection, the decision maker is able to observe a random variable X_t that provides some information on the rewards to be obtained. The focus is on finding uniformly good rules (that minimize the growth rate of the inferior sampling time) and on quantifying how much the additional information helps. Various settings are considered and for each setting, lower bounds on the achievable inferior sampling time are developed and asymptotically optimal adaptive schemes achieving these lower bounds are constructed.Comment: 16 pages, 3 figures. To be published in the IEEE Transactions on Automatic Contro

    Learning Contextual Bandits in a Non-stationary Environment

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    Multi-armed bandit algorithms have become a reference solution for handling the explore/exploit dilemma in recommender systems, and many other important real-world problems, such as display advertisement. However, such algorithms usually assume a stationary reward distribution, which hardly holds in practice as users' preferences are dynamic. This inevitably costs a recommender system consistent suboptimal performance. In this paper, we consider the situation where the underlying distribution of reward remains unchanged over (possibly short) epochs and shifts at unknown time instants. In accordance, we propose a contextual bandit algorithm that detects possible changes of environment based on its reward estimation confidence and updates its arm selection strategy respectively. Rigorous upper regret bound analysis of the proposed algorithm demonstrates its learning effectiveness in such a non-trivial environment. Extensive empirical evaluations on both synthetic and real-world datasets for recommendation confirm its practical utility in a changing environment.Comment: 10 pages, 13 figures, To appear on ACM Special Interest Group on Information Retrieval (SIGIR) 201

    Explore no more: Improved high-probability regret bounds for non-stochastic bandits

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    This work addresses the problem of regret minimization in non-stochastic multi-armed bandit problems, focusing on performance guarantees that hold with high probability. Such results are rather scarce in the literature since proving them requires a large deal of technical effort and significant modifications to the standard, more intuitive algorithms that come only with guarantees that hold on expectation. One of these modifications is forcing the learner to sample arms from the uniform distribution at least Ω(T)\Omega(\sqrt{T}) times over TT rounds, which can adversely affect performance if many of the arms are suboptimal. While it is widely conjectured that this property is essential for proving high-probability regret bounds, we show in this paper that it is possible to achieve such strong results without this undesirable exploration component. Our result relies on a simple and intuitive loss-estimation strategy called Implicit eXploration (IX) that allows a remarkably clean analysis. To demonstrate the flexibility of our technique, we derive several improved high-probability bounds for various extensions of the standard multi-armed bandit framework. Finally, we conduct a simple experiment that illustrates the robustness of our implicit exploration technique.Comment: To appear at NIPS 201
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