Dueling Algorithms

TL;DR

This paper explores competitive scenarios in classic optimization problems modeled as zero-sum games, providing methods to find optimal strategies and analyzing how often these strategies outperform traditional algorithms.

Contribution

It introduces a framework for analyzing optimization problems as duels between players, leveraging combinatorial structures to find optimal strategies and bounds on their performance.

Findings

Developed techniques for minmax strategy computation in duels

Applied framework to ranking, hiring, compression, and binary search

Provided bounds on outperforming classic algorithms in duels

Abstract

We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two players, whose only goal is to outperform the opponent. Such games are typically exponentially large zero-sum games, but they often have a rich combinatorial structure. We provide general techniques by which such structure can be leveraged to find minmax-optimal and approximate minmax-optimal strategies. We give examples of ranking, hiring, compression, and binary search duels, among others. We give bounds on how often one can beat the classic optimization algorithms in such duels.