Identifying Cognitive Radars - Inverse Reinforcement Learning using Revealed Preferences

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...

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Veröffentlicht in:	IEEE transactions on signal processing Jg. 68; S. 1
Hauptverfasser:	Krishnamurthy, Vikram, Angley, Daniel, Evans, Rob, Moran, Bill
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.01.2020 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	adversarial signal processing Afriat's theorem algebraic Riccati equation Algorithms Bayes methods beam scheduling Cognitive radar Constraints Covariance matrix detection economics-based-rationality Eigenvalues Error detection identifying cognitive behavior inverse reinforcement learning Kalman filter tracker Learning (artificial intelligence) Machine learning Maximization Noise Optimization Probes Radar Radar detection Radar tracking revealed preferences Riccati equation spectral revealed preferences Statistical tests stochastic gradient algorithm waveform selection Waveforms
ISSN:	1053-587X, 1941-0476
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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.
AbstractList	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.
Author	Angley, Daniel Moran, Bill Evans, Rob Krishnamurthy, Vikram
Author_xml	– sequence: 1 givenname: Vikram surname: Krishnamurthy fullname: Krishnamurthy, Vikram email: vikramk@cornell.edu organization: Electrical and Computer Engineering, Cornell University, Ithaca, New York United States (e-mail: vikramk@cornell.edu) – sequence: 2 givenname: Daniel surname: Angley fullname: Angley, Daniel email: dangley@unimelb.edu.au organization: University of Melbourne, Melbourne, Victoria Australia (e-mail: dangley@unimelb.edu.au) – sequence: 3 givenname: Rob surname: Evans fullname: Evans, Rob email: robinje@unimelb.edu.au organization: Electrical and Electronic Engineering, the University of Melbourne, MELBOURNE, Victoria Australia (e-mail: robinje@unimelb.edu.au) – sequence: 4 givenname: Bill surname: Moran fullname: Moran, Bill email: wmoran@unimelb.edu.au organization: University of Melbourne, Parkville, Victoria Australia (e-mail: wmoran@unimelb.edu.au)
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SubjectTerms	adversarial signal processing Afriat's theorem algebraic Riccati equation Algorithms Bayes methods beam scheduling Cognitive radar Constraints Covariance matrix detection economics-based-rationality Eigenvalues Error detection identifying cognitive behavior inverse reinforcement learning Kalman filter tracker Learning (artificial intelligence) Machine learning Maximization Noise Optimization Probes Radar Radar detection Radar tracking revealed preferences Riccati equation spectral revealed preferences Statistical tests stochastic gradient algorithm waveform selection Waveforms
Title	Identifying Cognitive Radars - Inverse Reinforcement Learning using Revealed Preferences
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