Sparse Covers for Sums of Indicators

TL;DR

This paper constructs a compact, efficiently computable cover for Poisson Binomial distributions, enabling improved approximation algorithms and equilibrium computations in anonymous games.

Contribution

It introduces a proper $ ext{epsilon}$-cover for Poisson Binomial distributions with a size bound and polynomial-time computability, advancing approximation methods.

Findings

Proper epsilon-cover size is polynomial in n and quasi-polynomial in 1/epsilon.

The cover can be computed efficiently in polynomial time.

Implications include improved algorithms for approximate Nash equilibria.

Abstract

For all $n, \epsilon >0$, we show that the set of Poisson Binomial distributions on $n$ variables admits a proper $\epsilon$-cover in total variation distance of size $n^2+n \cdot (1/\epsilon)^{O(\log^2 (1/\epsilon))}$, which can also be computed in polynomial time. We discuss the implications of our construction for approximation algorithms and the computation of approximate Nash equilibria in anonymous games.