Identifying Cognitive Radars -- Inverse Reinforcement Learning using Revealed Preferences

TL;DR

This paper develops methods to identify and test whether an enemy radar operates as a cognitive, utility-maximizing agent using inverse reinforcement learning and revealed preferences, with applications in strategic probing and detection.

Contribution

It introduces a novel framework combining inverse reinforcement learning and revealed preferences to detect and estimate the utility functions of cognitive radars from observed actions.

Findings

Formulated a spectral and Riccati equation-based approach for utility estimation.

Developed a statistical detector with a tight Type-II error bound for cognitive radar detection.

Proposed a stochastic optimization method for optimal probing of enemy radars.

Abstract

We consider an inverse reinforcement learning problem involving us versus an enemy radar equipped with a Bayesian tracker. By observing the emissions of the enemy radar,how can we identify if the radar is cognitive (constrained utility maximizer)? Given the observed sequence of actions taken by the enemy's radar, we consider three problems: (i) Are the enemy radar's actions (waveform choice, beam scheduling) consistent with constrained utility maximization? If so how can we estimate the cognitive radar's utility function that is consistent with its actions. We formulate and solve the problem in terms of the spectra (eigenvalues) of the state and observation noise covariance matrices, and the algebraic Riccati equation. (ii) How to construct a statistical test for detecting a cognitive radar (constrained utility maximization) when we observe the radar's actions in noise or the radar observes our probe signal in noise? We propose a statistical detector with a tight Type-II error bound. (iii) How can we optimally probe (interrogate) the enemy's radar by choosing our state to minimize the Type-II error of detecting if the radar is deploying an economic rational strategy, subject to a constraint on the Type-I detection error? We present a stochastic optimization algorithm to optimize our probe signal. The main analysis framework used in this paper is that of revealed preferences from microeconomics.