The Continuum-Armed Bandit Problem
SIAM Journal on Control and Optimization
Finite-time Analysis of the Multiarmed Bandit Problem
Machine Learning
Minimizing regret with label efficient prediction
IEEE Transactions on Information Theory
Multi-armed bandits in metric spaces
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Online Regret Bounds for Markov Decision Processes with Deterministic Transitions
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Algorithms and Bounds for Rollout Sampling Approximate Policy Iteration
Recent Advances in Reinforcement Learning
Experiments with Adaptive Transfer Rate in Reinforcement Learning
Knowledge Acquisition: Approaches, Algorithms and Applications
Online regret bounds for Markov decision processes with deterministic transitions
Theoretical Computer Science
Combining active learning and reactive control for robot grasping
Robotics and Autonomous Systems
Sharp dichotomies for regret minimization in metric spaces
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The Journal of Machine Learning Research
Lipschitz bandits without the Lipschitz constant
ALT'11 Proceedings of the 22nd international conference on Algorithmic learning theory
Dynamic pricing with limited supply
Proceedings of the 13th ACM Conference on Electronic Commerce
Dynamic Pricing Under a General Parametric Choice Model
Operations Research
Truthful incentives in crowdsourcing tasks using regret minimization mechanisms
Proceedings of the 22nd international conference on World Wide Web
Ranked bandits in metric spaces: learning diverse rankings over large document collections
The Journal of Machine Learning Research
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Considering one-dimensional continuum-armed bandit problems, we propose an improvement of an algorithm of Kleinberg and a new set of conditions which give rise to improved rates. In particular, we introduce a novel assumption that is complementary to the previous smoothness conditions, while at the same time smoothness of the mean payoff function is required only at the maxima. Under these new assumptions new bounds on the expected regret are derived. In particular, we show that apart from logarithmic factors, the expected regret scales with the square-root of the number of trials, provided that the mean payoff function has finitely many maxima and its second derivatives are continuous and non-vanishing at the maxima. This improves a previous result of Cope by weakening the assumptions on the function. We also derive matching lower bounds. To complement the bounds on the expected regret, we provide high probability bounds which exhibit similar scaling.