Memory Constrained Adversarial Hypothesis Testing

2026-05-12

AI Summary

This work investigates adversarial binary hypothesis testing under memory constraints, where an adversary dynamically selects distributions based on past samples and the system’s current state. The detector is modeled as a time-invariant stochastic finite-state machine (FSM) with S internal states. By integrating minimax analysis with information-theoretic techniques, the study establishes matching upper and lower bounds—tight in a canonical class of problems—on the minimax error probability as a function of the number of states S. These bounds reveal an exponential decay of the error probability with S, precisely characterizing the fundamental trade-off between available memory resources and achievable detection 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.

Problem

• adversarial hypothesis testing
• memory constraints
• finite state machine
• minimax error probability
• binary hypothesis testing

Innovation

• adversarial hypothesis testing
• memory constraints
• finite state machine
• minimax error probability
• distributional uncertainty