Mallesh Pai

Daniel Lee, Georgy Noarov, Mallesh Pai et al.

We introduce a simple but general online learning framework in which a learner plays against an adversary in a vector-valued game that changes every round. Even though the learner's objective is not convex-concave (and so the minimax theorem does not apply), we give a simple algorithm that can compete with the setting in which the adversary must announce their action first, with optimally diminishing regret. We demonstrate the power of our framework by using it to (re)derive optimal bounds and efficient algorithms across a variety of domains, ranging from multicalibration to a large set of no regret algorithms, to a variant of Blackwell's approachability theorem for polytopes with fast convergence rates. As a new application, we show how to ``(multi)calibeat'' an arbitrary collection of forecasters -- achieving an exponentially improved dependence on the number of models we are competing against, compared to prior work.

Mallesh Pai, Aaron Roth

This paper is a survey of recent work at the intersection of mechanism design and privacy. The connection is a natural one, but its study has been jump-started in recent years by the advent of differential privacy, which provides a rigorous, quantitative way of reasoning about the costs that an agent might experience because of the loss of his privacy. Here, we survey several facets of this study, and differential privacy plays a role in more than one way. Of course, it provides us a basis for modeling agent costs for privacy, which is essential if we are to attempt mechanism design in a setting in which agents have preferences for privacy. It also provides a toolkit for controlling those costs. However, perhaps more surprisingly, it provides a powerful toolkit for controlling the stability of mechanisms in general, which yields a set of tools for designing novel mechanisms even in economic settings completely unrelated to privacy.