Memory Constrained Adversarial Hypothesis Testing

TL;DR

This paper investigates the limits of adversarial binary hypothesis testing using memory-constrained finite state machines, providing bounds on error probabilities based on the number of states.

Contribution

It introduces bounds on the minimax error probability for adversarial hypothesis testing with finite state machine constraints, matching in certain cases.

Findings

Bounds on error probability scale exponentially with the number of states.

Upper and lower bounds match for a class of problems.

The analysis characterizes the trade-off between memory size and testing performance.

Abstract

We study adversarial binary hypothesis testing under memory constraints. The test is a time-invariant randomized finite state machine (FSM) with S states. Associated with each hypothesis is a set of distributions. Given the hypothesis, the distribution of each sample is chosen from the set associated with the hypothesis by an adversary who has access to past samples and the history of states of the FSM so far. We obtain upper and lower bounds on the minimax asymptotic probability of error as a function of S. The bounds have the same exponential behaviour in S and match for a class of problems.