Calibration with many checking rules
Mathematics of Operations Research
Prediction, Learning, and Games
Prediction, Learning, and Games
Non-asymptotic calibration and resolution
Theoretical Computer Science
Strategies for Prediction Under Imperfect Monitoring
Mathematics of Operations Research
Internal Regret with Partial Monitoring: Calibration-Based Optimal Algorithms
The Journal of Machine Learning Research
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A calibrated strategy can be obtained by performing a strategy that has no internal regret in some auxiliary game. Such a strategy can be constructed explicitly with the use of Blackwell's approachability theorem, in an other auxiliary game. We establish the converse: a strategy that approaches a convex B-set can be derived from the construction of a calibrated strategy. We develop these tools in the framework of a game with partial monitoring, where players do not observe the actions of their opponents but receive random signals, to define a notion of internal regret and construct strategies that have no such regret.