Sequential Adversarial Hypothesis Testing

TL;DR

This paper investigates sequential adversarial hypothesis testing where an adversary influences data generation within convex distribution sets, and characterizes the limits of error exponents under various constraints.

Contribution

It provides a characterization of the achievable error exponents in sequential adversarial hypothesis testing with convex distribution sets.

Findings

Characterized the closure of achievable error exponent pairs.

Analyzed the impact of observation and error constraints on testing performance.

Abstract

We study the adversarial binary hypothesis testing problem in the sequential setting. Associated with each hypothesis is a closed, convex set of distributions. Given the hypothesis, each observation is generated according to a distribution chosen (from the set associated with the hypothesis) by an adversary who has access to past observations. In the sequential setting, the number of observations the detector uses to arrive at a decision is variable; this extra freedom improves the asymptotic performance of the test. We characterize the closure of the set of achievable pairs of error exponents. We also study the problem under constraints on the number of observations used and the probability of error incurred.