On the Fair Comparison of Optimization Algorithms in Different Machines

TL;DR

This paper proposes a statistical methodology to fairly compare optimization algorithms executed on different machines by estimating runtimes and adjusting significance tests, addressing challenges when code or resources are limited.

Contribution

It introduces a model to estimate algorithm runtimes across different machines and an adapted sign test to ensure fair performance comparisons without running algorithms on the same hardware.

Findings

The runtime estimation model can be tuned for low error probability.

The adapted sign test maintains statistical validity across different hardware.

Method enables fair comparison without re-running algorithms on identical machines.

Abstract

An experimental comparison of two or more optimization algorithms requires the same computational resources to be assigned to each algorithm. When a maximum runtime is set as the stopping criterion, all algorithms need to be executed in the same machine if they are to use the same resources. Unfortunately, the implementation code of the algorithms is not always available, which means that running the algorithms to be compared in the same machine is not always possible. And even if they are available, some optimization algorithms might be costly to run, such as training large neural-networks in the cloud. In this paper, we consider the following problem: how do we compare the performance of a new optimization algorithm B with a known algorithm A in the literature if we only have the results (the objective values) and the runtime in each instance of algorithm A? Particularly, we present a methodology that enables a statistical analysis of the performance of algorithms executed in different machines. The proposed methodology has two parts. First, we propose a model that, given the runtime of an algorithm in a machine, estimates the runtime of the same algorithm in another machine. This model can be adjusted so that the probability of estimating a runtime longer than what it should be is arbitrarily low. Second, we introduce an adaptation of the one-sided sign test that uses a modified p-value and takes into account that probability. Such adaptation avoids increasing the probability of type I error associated with executing algorithms A and B in different machines.