CatCMA : Stochastic Optimization for Mixed-Category Problems

TL;DR

CatCMA is a novel stochastic optimization algorithm designed for mixed-category black-box problems, combining Gaussian and categorical distributions with natural gradient updates to improve scalability and robustness.

Contribution

It introduces a joint distribution approach with acceleration techniques for efficient high-dimensional mixed-variable optimization.

Findings

Outperforms state-of-the-art Bayesian optimization methods

Demonstrates robustness across various problem dimensions

Shows superior convergence and efficiency in numerical experiments

Abstract

Black-box optimization problems often require simultaneously optimizing different types of variables, such as continuous, integer, and categorical variables. Unlike integer variables, categorical variables do not necessarily have a meaningful order, and the discretization approach of continuous variables does not work well. Although several Bayesian optimization methods can deal with mixed-category black-box optimization (MC-BBO), they suffer from a lack of scalability to high-dimensional problems and internal computational cost. This paper proposes CatCMA, a stochastic optimization method for MC-BBO problems, which employs the joint probability distribution of multivariate Gaussian and categorical distributions as the search distribution. CatCMA updates the parameters of the joint probability distribution in the natural gradient direction. CatCMA also incorporates the acceleration techniques used in the covariance matrix adaptation evolution strategy (CMA-ES) and the stochastic natural gradient method, such as step-size adaptation and learning rate adaptation. In addition, we restrict the ranges of the categorical distribution parameters by margin to prevent premature convergence and analytically derive a promising margin setting. Numerical experiments show that the performance of CatCMA is superior and more robust to problem dimensions compared to state-of-the-art Bayesian optimization algorithms.