HEC Paris2014-08-11 8:50 PM

A primal condition for approachability with partial monitoring

Abstract

In approachability with full monitoring there are two types of conditions that are known to be equivalent for convex sets: a primal and a dual condition. The primal one is of the form: a set C is approachable if and only all containing half-spaces are approachable in the one-shot game. The dual condition is of the form: a convex set C is approachable if and only if it intersects all payoff sets of a certain form. We consider approachability in games with partial monitoring. In previous works we provided a dual characterization of approachable convex sets and we also exhibited efficient strategies in the case where C is a polytope. In this paper we provide primal conditions on a convex set to be approachable with partial monitoring. They depend on a modified reward function and lead to approachability strategies based on modified payoff functions and that proceed by projections similarly to Blackwell's (1956) strategy. This is in contrast with previously studied strategies in this context that relied mostly on the signaling structure and aimed at estimating well the distributions of the signals received. Our results generalize classical results by Kohlberg and apply to games with arbitrary signaling structure as well as to arbitrary convex sets.

 

Author

S. MANNOR, V. PERCHET, G. STOLTZ

 

Departments

Economics & Decision Sciences, GREGHEC (CNRS)

 

Journal Information

Journal of Dynamics and Games, July 2014, vol. 1, n°3, pp.447-469

 

Full Article

http://arxiv.org/abs/1305.5399 

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HEC Paris

Founded in 1881 by the Paris Chamber of Commerce and Industry, HEC Paris specializes in education and research in management sciences. As a leading academic institution in Europe and worldwide, HEC Paris offers a complete and unique range of education programs for students and leaders.

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