Robust Hypothesis Testing with Abstention

TL;DR

This paper investigates a robust binary hypothesis testing framework allowing abstention when adversarial corruption is suspected, and characterizes error trade-offs under various contamination models.

Contribution

It introduces a novel hypothesis testing approach that incorporates abstention to mitigate adversarial influence and provides theoretical error trade-off characterizations.

Findings

Error exponents are characterized for different contamination models.

Abstention improves robustness against adversarial corruption.

Trade-offs between error types are quantified.

Abstract

We study the binary hypothesis testing problem where an adversary may potentially corrupt a fraction of the samples. The detector is, however, permitted to abstain from making a decision if (and only if) the adversary is present. We consider a few natural "contamination models" and characterize for them the trade-off between the error exponents of the four types of errors -- errors of deciding in favour of the incorrect hypothesis when the adversary is present and errors of abstaining or deciding in favour of the wrong hypothesis when the adversary is absent, under the two hypotheses.