Random sampling with a reservoir
ACM Transactions on Mathematical Software (TOMS)
Asymptotically efficient adaptive control in stochastic regression models
Advances in Applied Mathematics
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
The Nonstochastic Multiarmed Bandit Problem
SIAM Journal on Computing
Adaptive routing with end-to-end feedback: distributed learning and geometric approaches
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Online convex optimization in the bandit setting: gradient descent without a gradient
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Robbing the bandit: less regret in online geometric optimization against an adaptive adversary
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Prediction, Learning, and Games
Prediction, Learning, and Games
Improved second-order bounds for prediction with expert advice
Machine Learning
Sharp dichotomies for regret minimization in metric spaces
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Better Algorithms for Benign Bandits
The Journal of Machine Learning Research
Ranked bandits in metric spaces: learning diverse rankings over large document collections
The Journal of Machine Learning Research
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The online multi-armed bandit problem and its generalizations are repeated decision making problems, where the goal is to select one of several possible decisions in every round, and incur a cost associated with the decision, in such a way that the total cost incurred over all iterations is close to the cost of the best fixed decision in hindsight. The difference in these costs is known as the regret of the algorithm. The term bandit refers to the setting where one only obtains the cost of the decision used in a given iteration and no other information. Perhaps the most general form of this problem is the non-stochastic bandit linear optimization problem, where the set of decisions is a convex set in some Euclidean space, and the cost functions are linear. Only recently an efficient algorithm attaining Õ (√T) regret was discovered in this setting. In this paper we propose a new algorithm for the bandit linear optimization problem which obtains a regret bound of Õ (√Q), where Q is the total variation in the cost functions. This regret bound, previously conjectured to hold in the full information case, shows that it is possible to incur much less regret in a slowly changing environment even in the bandit setting. Our algorithm is efficient and applies several new ideas to bandit optimization such as reservoir sampling.