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Bayesian Persuasion With State-Dependent Quadratic Cost Measures
- Source :
- IEEE Transactions on Automatic Control. 67:1241-1252
- Publication Year :
- 2022
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2022.
-
Abstract
- We address Bayesian persuasion between a sender and a receiver with state-dependent quadratic cost measures for general classes of distributions. The receiver seeks to make mean-square-error estimate of a state based on a signal sent by the sender while the sender signals strategically in order to control the receiver's estimate in a certain way. Such a scheme could model, e.g., deception and privacy, problems in multi-agent systems. Existing solution concepts are not viable since here the receiver has continuous action space. We show that for finite state spaces, optimal signaling strategies can be computed through an equivalent linear optimization problem over the cone of completely positive matrices. We then establish its strong duality to a copositive program. To exemplify the effectiveness of this equivalence result, we adopt sequential polyhedral approximation of completely-positive cones and analyze its performance numerically. We also quantify the approximation error for a quantized version of a continuous distribution and show that a semi-definite program relaxation of the equivalent problem could be a benchmark lower bound for the sender's cost for large state spaces.
- Subjects :
- FOS: Computer and information sciences
Mathematical optimization
Computer science
State (functional analysis)
Upper and lower bounds
Computer Science Applications
Quantization (physics)
Matrix (mathematics)
Computer Science - Computer Science and Game Theory
Optimization and Control (math.OC)
Control and Systems Engineering
Approximation error
FOS: Mathematics
Benchmark (computing)
Strong duality
Symmetric matrix
Relaxation (approximation)
Electrical and Electronic Engineering
Mathematics - Optimization and Control
Equivalence (measure theory)
Computer Science and Game Theory (cs.GT)
Subjects
Details
- ISSN :
- 23343303 and 00189286
- Volume :
- 67
- Database :
- OpenAIRE
- Journal :
- IEEE Transactions on Automatic Control
- Accession number :
- edsair.doi.dedup.....32dc877c9b490cc43157970d8b85b8c4