# Meta-Cognition. An Inverse-Inverse Reinforcement Learning Approach for Cognitive Radars

arXiv: https://arxiv.org/abs/2205.01794 · HTML: https://mlsanity.com/paper/2205.01794/

## Key facts

- Cited by 6 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 5 of its 41 references that are in the map.
- First posted on arXiv 3 May 2022.

## Placed in

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

## Builds on (most cited first, 5 of 5)

- [Face-Off: Adversarial Face Obfuscation](https://mlsanity.com/paper/2003.08861/) (2020)
- [Identifying Cognitive Radars -- Inverse Reinforcement Learning using Revealed Preferences](https://mlsanity.com/paper/1912.00331/) (2019)
- [How to Calibrate your Adversary's Capabilities? Inverse Filtering for Counter-Autonomous Systems](https://mlsanity.com/paper/1905.07230/) (2019)
- [Adversarial Radar Inference: Inverse Tracking, Identifying Cognition and Designing Smart Interference](https://mlsanity.com/paper/2008.01559/) (2020)
- [How can a Cognitive Radar Mask its Cognition?](https://mlsanity.com/paper/2110.08608/) (2021)

## Built on by (most cited first, 6 of 6)

- [Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems](https://mlsanity.com/paper/2208.06683/) (2022)
- [Inverse-Inverse Reinforcement Learning. How to Hide Strategy from an Adversarial Inverse Reinforcement Learner](https://mlsanity.com/paper/2205.10802/) (2022)
- [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)
- [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)

## Abstract (arXiv)

This paper considers meta-cognitive radars in an adversarial setting. A cognitive radar optimally adapts its waveform (response) in response to maneuvers (probes) of a possibly adversarial moving target. A meta-cognitive radar is aware of the adversarial nature of the target and seeks to mitigate the adversarial target. How should the meta-cognitive radar choose its responses to sufficiently confuse the adversary trying to estimate the radar's utility function? This paper abstracts the radar's meta-cognition problem in terms of the spectra (eigenvalues) of the state and observation noise covariance matrices, and embeds the algebraic Riccati equation into an economics-based utility maximization setup. This adversarial target is an inverse reinforcement learner. By observing a noisy sequence of radar's responses (waveforms), the adversarial target uses a statistical hypothesis test to detect if the radar is a utility maximizer. In turn, the meta-cognitive radar deliberately chooses sub-optimal responses that increasing its Type-I error probability of the adversary's detector. We call this counter-adversarial step taken by the meta-cognitive radar as inverse inverse reinforcement learning (I-IRL). We illustrate the meta-cognition results of this paper via simple numerical examples. Our approach for meta-cognition in this paper is based on revealed preference theory in micro-economics and inspired by results in differential privacy and adversarial obfuscation in machine learning.