Improving Group Testing via Gradient Descent

TL;DR

This paper introduces a gradient descent-based optimization method for designing group testing strategies with non-identical priors, fixing the decoder and number of tests to improve accuracy over traditional methods.

Contribution

It formulates a non-convex optimization problem for test design in group testing and applies gradient descent with informed initialization to enhance performance.

Findings

Significant performance improvements over traditional group testing methods.

Effective optimization of test designs using gradient descent.

Applicable to non-identical, independent priors in group testing.

Abstract

We study the problem of group testing with non-identical, independent priors. So far, the pooling strategies that have been proposed in the literature take the following approach: a hand-crafted test design along with a decoding strategy is proposed, and guarantees are provided on how many tests are sufficient in order to identify all infections in a population. In this paper, we take a different, yet perhaps more practical, approach: we fix the decoder and the number of tests, and we ask, given these, what is the best test design one could use? We explore this question for the Definite Non-Defectives (DND) decoder. We formulate a (non-convex) optimization problem, where the objective function is the expected number of errors for a particular design. We find approximate solutions via gradient descent, which we further optimize with informed initialization. We illustrate through simulations that our method can achieve significant performance improvement over traditional approaches.