Sequential Design for Ranking Response Surfaces

TL;DR

This paper develops sequential design methods using kriging surrogates to efficiently identify the minimal response surface among several options over a continuous domain, with applications in stochastic control.

Contribution

It introduces novel sequential design heuristics based on uncertainty reduction and classification complexity, connecting continuous input problems to multi-armed bandit frameworks.

Findings

Effective adaptive designs demonstrated on synthetic and real epidemic control data.

Sequential methods outperform non-adaptive sampling in identifying minimal responses.

Approaches successfully handle noisy, one-at-a-time sampling scenarios.

Abstract

We propose and analyze sequential design methods for the problem of ranking several response surfaces. Namely, given $L \ge 2$ response surfaces over a continuous input space $\cal X$, the aim is to efficiently find the index of the minimal response across the entire $\cal X$. The response surfaces are not known and have to be noisily sampled one-at-a-time. This setting is motivated by stochastic control applications and requires joint experimental design both in space and response-index dimensions. To generate sequential design heuristics we investigate stepwise uncertainty reduction approaches, as well as sampling based on posterior classification complexity. We also make connections between our continuous-input formulation and the discrete framework of pure regret in multi-armed bandits. To model the response surfaces we utilize kriging surrogates. Several numerical examples using both synthetic data and an epidemics control problem are provided to illustrate our approach and the efficacy of respective adaptive designs.