Calibration and Internal no-Regret with Partial Monitoring

TL;DR

This paper explores the relationship between calibrated strategies and no internal regret strategies in partial monitoring games, providing methods to construct such strategies using approachability theory.

Contribution

It establishes a converse link between approachability of convex sets and calibrated strategies in the context of partial monitoring.

Findings

Strategies approaching convex B-sets can be derived from calibrated strategies.

The paper develops tools for constructing no internal regret strategies under partial monitoring.

It extends approachability and calibration concepts to games with incomplete information.

Abstract

Calibrated strategies can be obtained by performing strategies that have no internal regret in some auxiliary game. Such strategies 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.