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تسجيل مستخدم جديدThompson Sampling for Contextual Bandits with Linear Payoffs
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Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better empirical performance compared to the state-of-the-art methods. However, many questions regarding its theoretical performance remained open. In this paper, we design and analyze a generalization of Thompson Sampling algorithm for the stochastic contextual multi-armed bandit problem with linear payoff functions, when the contexts are provided by an adaptive adversary. This is among the most important and widely studi
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We consider the linear contextual bandit problem with resource consumption, in addition to reward generation. In each round, the outcome of pulling an arm is a reward as well as a vector of resource consumptions. The expected values of these outcomes
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decision space, our algorithm makes decision according to posterior distribution only in the neighborhood of the arm that has the highest empirical mean estimate. We theoretically prove that, for Bernoulli rewards, the regret of our algorithm reaches the lower bound of unimodal bandits, thus it is asymptotically optimal. For Gaussian rewards, the regret of our algorithm is $mathcal{O}(log T)$, which is far better than standard Thompson Sampling algorithms. Extensive experiments demonstrate the effectiveness of the proposed algorithm on both synthetic data sets and the real-world applications.
Recent advances in contextual bandit optimization and reinforcement learning have garnered interest in applying these methods to real-world sequential decision making problems. Real-world applications frequently have constraints with respect to a cur
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ristic have recently been proposed. However, finite-time analysis of constrained TS is challenging; as a result, only O(sqrt{T}) bounds on the cumulative reward loss (i.e., the regret) are available. In this paper, we describe LinConTS, a TS-based algorithm for bandits that place a linear constraint on the probability of earning a reward in every round. We show that for LinConTS, the regret as well as the cumulative constraint violations are upper bounded by O(log T) for the suboptimal arms. We develop a proof technique that relies on careful analysis of the dual problem and combine it with recent theoretical work on unconstrained TS. Through numerical experiments on two real-world datasets, we demonstrate that LinConTS outperforms an asymptotically optimal upper confidence bound (UCB) scheme in terms of simultaneously minimizing the regret and the violation.
Thompson Sampling is one of the oldest heuristics for multi-armed bandit problems. It is a randomized algorithm based on Bayesian ideas, and has recently generated significant interest after several studies demonstrated it to have better empirical pe
rformance compared to the state of the art methods. In this paper, we provide a novel regret analysis for Thompson Sampling that simultaneously proves both the optimal problem-dependent bound of $(1+epsilon)sum_i frac{ln T}{Delta_i}+O(frac{N}{epsilon^2})$ and the first near-optimal problem-independent bound of $O(sqrt{NTln T})$ on the expected regret of this algorithm. Our near-optimal problem-independent bound solves a COLT 2012 open problem of Chapelle and Li. The optimal problem-dependent regret bound for this problem was first proven recently by Kaufmann et al. [ALT 2012]. Our novel martingale-based analysis techniques are conceptually simple, easily extend to distributions other than the Beta distribution, and also extend to the more general contextual bandits setting [Manuscript, Agrawal and Goyal, 2012].
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