The Nonstochastic Multiarmed Bandit Problem
SIAM Journal on Computing
Prediction, Learning, and Games
Prediction, Learning, and Games
From External to Internal Regret
The Journal of Machine Learning Research
Strategies for Prediction Under Imperfect Monitoring
Mathematics of Operations Research
Calibration and internal no-regret with random signals
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
Near-optimal Regret Bounds for Reinforcement Learning
The Journal of Machine Learning Research
Minimizing regret with label efficient prediction
IEEE Transactions on Information Theory
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We provide consistent random algorithms for sequential decision under partial monitoring, when the decision maker does not observe the outcomes but receives instead random feedback signals. Those algorithms have no internal regret in the sense that, on the set of stages where the decision maker chose his action according to a given law, the average payoff could not have been improved in average by using any other fixed law. They are based on a generalization of calibration, no longer defined in terms of a Voronoï diagram but instead of a Laguerre diagram (a more general concept). This allows us to bound, for the first time in this general framework, the expected average internal, as well as the usual external, regret at stage n by O(n-1/3), which is known to be optimal.