# Identifying Cognitive Radars -- Inverse Reinforcement Learning using Revealed Preferences

arXiv: https://arxiv.org/abs/1912.00331 · HTML: https://mlsanity.com/paper/1912.00331/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Inverse reinforcement learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 2 of its 41 references that are in the map.
- First posted on arXiv 1 Dec 2019.

## Placed in

- Offline RL and imitation learning from data / [Inverse reinforcement learning](https://mlsanity.com/offlinerl/inverse-reinforcement-learning/)

## Builds on (most cited first, 2 of 2)

- [Partially Observed Markov Decision Processes. Problem Sets and Internet Supplement](https://mlsanity.com/paper/1604.08127/) (2016)
- [How to Calibrate your Adversary's Capabilities? Inverse Filtering for Counter-Autonomous Systems](https://mlsanity.com/paper/1905.07230/) (2019)

## Built on by (most cited first, 13 of 13)

- [Inverse Extended Kalman Filter -- Part I: Fundamentals](https://mlsanity.com/paper/2201.01539/) (2022)
- [Meta-Cognition. An Inverse-Inverse Reinforcement Learning Approach for Cognitive Radars](https://mlsanity.com/paper/2205.01794/) (2022)
- [Counter-Adversarial Learning with Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2210.00359/) (2022)
- [Identifying Coordination in a Cognitive Radar Network -- A Multi-Objective Inverse Reinforcement Learning Approach](https://mlsanity.com/paper/2211.06967/) (2022)
- [Necessary and Sufficient Conditions for Inverse Reinforcement Learning of Bayesian Stopping Time Problems](https://mlsanity.com/paper/2007.03481/) (2020)
- [Inverse Cubature and Quadrature Kalman filters](https://mlsanity.com/paper/2303.10322/) (2023)
- [Uncovering Utility Functions from Observed Outcomes](https://mlsanity.com/paper/2503.13432/) (2025)
- [How can a Radar Mask its Cognition?](https://mlsanity.com/paper/2210.11444/) (2022)
- [Inverse Unscented Kalman Filter](https://mlsanity.com/paper/2304.01698/) (2023)
- [Inverse Particle Filter](https://mlsanity.com/paper/2407.16623/) (2024)
- [Distributionally Robust Inverse Reinforcement Learning for Identifying Multi-Agent Coordinated Sensing](https://mlsanity.com/paper/2409.14542/) (2024)
- [Multi-Agent Inverse Reinforcement Learning for Identifying Pareto-Efficient Coordination -- A Distributionally Robust Approach](https://mlsanity.com/paper/2509.08956/) (2025)
- [Masking Radar Cognition under Adversarial Surveillance: A Distributional Privacy Framework](https://mlsanity.com/paper/2609.07428/) (2026)

## Abstract (arXiv)

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.