Ordinal Optimisation for the Gaussian Copula Model

TL;DR

This paper develops a method to estimate success probabilities in ordinal optimisation over continuous spaces using Gaussian copula models, providing theoretical bounds and practical guarantees.

Contribution

It introduces a novel approach to compute success probabilities assuming Gaussian copula models, with proven bounds and demonstrated practical utility.

Findings

Derived a lower bound on success probability under Gaussian copula assumptions

Showed the lower bound approximates actual success probabilities well

Demonstrated high success probability guarantees in practical scenarios

Abstract

We present results on the estimation and evaluation of success probabilities for ordinal optimisation over uncountable sets (such as subsets of $\mathbb{R}^{d}$). Our formulation invokes an assumption of a Gaussian copula model, and we show that the success probability can be equivalently computed by assuming a special case of additive noise. We formally prove a lower bound on the success probability under the Gaussian copula model, and numerical experiments demonstrate that the lower bound yields a reasonable approximation to the actual success probability. Lastly, we showcase the utility of our results by guaranteeing high success probabilities with ordinal optimisation.