Byzantine Fault-Tolerant Min-Max Optimization

TL;DR

This paper introduces the first algorithms for Byzantine fault-tolerant min-max optimization, addressing adversarial manipulation in both centralized and distributed settings, with bounds and approximations provided.

Contribution

It presents novel algorithms for Byzantine fault-tolerant min-max optimization, including bounds and an extension to distributed systems.

Findings

Proposed a simple Byzantine min-max optimization algorithm.

Provided bounds on the algorithm's output.

Extended the approach to distributed settings.

Abstract

In this paper, we consider a min-max optimization problem under adversarial manipulation, where there are $n$ cost functions, up to $f$ of which may be replaced by arbitrary faulty functions by an adversary. The goal is to minimize the maximum cost over $x$ among the $n$ functions despite the faulty functions. The problem formulation could naturally extend to Byzantine fault-tolerant distributed min-max optimization. We present a simple algorithm for Byzantine min-max optimization, and provide bounds on the output of the algorithm. We also present an approximate algorithm for this problem. We then extend the problem to a distributed setting and present a distributed algorithm. To the best of our knowledge, we are the first to consider this problem.