Lock in Feedback in Sequential Experiments

TL;DR

This paper introduces a new sequential experimentation method inspired by physics and engineering to efficiently find the maximum of an unknown function, demonstrating robustness to drifting maxima and low signal-to-noise ratios.

Contribution

The paper presents a novel feedback-based method and two algorithms for sequential experiments to locate function maxima, inspired by physical principles.

Findings

Effective in identifying maxima of unknown functions.

Robust to drifting maxima and low signal-to-noise ratios.

Validated through simulation studies.

Abstract

We often encounter situations in which an experimenter wants to find, by sequential experimentation, $x_{max} = \arg\max_{x} f(x)$, where $f(x)$ is a (possibly unknown) function of a well controllable variable $x$. Taking inspiration from physics and engineering, we have designed a new method to address this problem. In this paper, we first introduce the method in continuous time, and then present two algorithms for use in sequential experiments. Through a series of simulation studies, we show that the method is effective for finding maxima of unknown functions by experimentation, even when the maximum of the functions drifts or when the signal to noise ratio is low.