Conjugate Natural Selection

TL;DR

This paper establishes that Fisher-Rao natural gradient descent (FR-NGD) optimally approximates the replicator equation, linking evolutionary dynamics and Bayesian inference, with practical demonstrations on optimization and system identification tasks.

Contribution

It introduces the concept of conjugate natural selection, showing FR-NGD as an optimal approximation of evolutionary and Bayesian processes, enabling new approaches in evolutionary computation.

Findings

FR-NGD approximates the replicator equation optimally

FR-NGD provides the best approximation for continuous Bayesian inference

Demonstrated effectiveness on non-convex optimization and system identification

Abstract

We prove that Fisher-Rao natural gradient descent (FR-NGD) optimally approximates the continuous time replicator equation (an essential model of evolutionary dynamics), and term this correspondence "conjugate natural selection". This correspondence promises alternative approaches for evolutionary computation over continuous or high-dimensional hypothesis spaces. As a special case, FR-NGD also provides the optimal approximation of continuous Bayesian inference when hypotheses compete on the basis of predicting actual observations. In this case, the method avoids the need to compute prior probabilities. We demonstrate our findings on a non-convex optimization problem and a system identification task for a stochastic process with time-varying parameters.