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Robustness Properties in Fictitious-Play-Type Algorithms

Research output: Contribution to journalJournal article

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Robustness Properties in Fictitious-Play-Type Algorithms. / Swenson, Brian; Kar, Soummya; Xavier, João; Leslie, David S.

In: SIAM Journal on Control and Optimization, Vol. 55, 24.10.2017, p. 3295-3318.

Research output: Contribution to journalJournal article

Harvard

Swenson, B, Kar, S, Xavier, J & Leslie, DS 2017, 'Robustness Properties in Fictitious-Play-Type Algorithms' SIAM Journal on Control and Optimization, vol. 55, pp. 3295-3318. https://doi.org/10.1137/16M1093227

APA

Swenson, B., Kar, S., Xavier, J., & Leslie, D. S. (2017). Robustness Properties in Fictitious-Play-Type Algorithms. SIAM Journal on Control and Optimization, 55, 3295-3318. https://doi.org/10.1137/16M1093227

Vancouver

Swenson B, Kar S, Xavier J, Leslie DS. Robustness Properties in Fictitious-Play-Type Algorithms. SIAM Journal on Control and Optimization. 2017 Oct 24;55:3295-3318. https://doi.org/10.1137/16M1093227

Author

Swenson, Brian ; Kar, Soummya ; Xavier, João ; Leslie, David S. / Robustness Properties in Fictitious-Play-Type Algorithms. In: SIAM Journal on Control and Optimization. 2017 ; Vol. 55. pp. 3295-3318.

Bibtex

@article{092cb6fd39af43b1be13ddc5adcd47fa,
title = "Robustness Properties in Fictitious-Play-Type Algorithms",
abstract = "Fictitious play (FP) is a canonical game-theoretic learning algorithm which has been deployed extensively in decentralized control scenarios. However standard treatments of FP, and of many other game-theoretic models, assume rather idealistic conditions which rarely hold in realistic control scenarios. This paper considers a broad class of best response learning algorithms, that we refer to as FP-type algorithms. In such an algorithm, given some (possibly limited) information about the history of actions, each individual forecasts the future play and chooses a (myopic) best action given their forecast. We provide a unifed analysis of the behavior of FP-type algorithms under an important class of perturbations, thus demonstrating robustness to deviations from the idealistic operating conditions that have been previously assumed. This robustness result is then used to derive convergence results for two control-relevant relaxations of standard game-theoretic applications: distributed (network-based) implementation without full observability and asynchronous deployment (including in continuous time). In each case the results follow as a direct consequence of the main robustness result.",
keywords = "math.OC, 93A14, 93A15, 91A06, 91A26, 91A80",
author = "Brian Swenson and Soummya Kar and Jo{\~a}o Xavier and Leslie, {David S.}",
year = "2017",
month = "10",
day = "24",
doi = "10.1137/16M1093227",
language = "English",
volume = "55",
pages = "3295--3318",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",

}

RIS

TY - JOUR

T1 - Robustness Properties in Fictitious-Play-Type Algorithms

AU - Swenson, Brian

AU - Kar, Soummya

AU - Xavier, João

AU - Leslie, David S.

PY - 2017/10/24

Y1 - 2017/10/24

N2 - Fictitious play (FP) is a canonical game-theoretic learning algorithm which has been deployed extensively in decentralized control scenarios. However standard treatments of FP, and of many other game-theoretic models, assume rather idealistic conditions which rarely hold in realistic control scenarios. This paper considers a broad class of best response learning algorithms, that we refer to as FP-type algorithms. In such an algorithm, given some (possibly limited) information about the history of actions, each individual forecasts the future play and chooses a (myopic) best action given their forecast. We provide a unifed analysis of the behavior of FP-type algorithms under an important class of perturbations, thus demonstrating robustness to deviations from the idealistic operating conditions that have been previously assumed. This robustness result is then used to derive convergence results for two control-relevant relaxations of standard game-theoretic applications: distributed (network-based) implementation without full observability and asynchronous deployment (including in continuous time). In each case the results follow as a direct consequence of the main robustness result.

AB - Fictitious play (FP) is a canonical game-theoretic learning algorithm which has been deployed extensively in decentralized control scenarios. However standard treatments of FP, and of many other game-theoretic models, assume rather idealistic conditions which rarely hold in realistic control scenarios. This paper considers a broad class of best response learning algorithms, that we refer to as FP-type algorithms. In such an algorithm, given some (possibly limited) information about the history of actions, each individual forecasts the future play and chooses a (myopic) best action given their forecast. We provide a unifed analysis of the behavior of FP-type algorithms under an important class of perturbations, thus demonstrating robustness to deviations from the idealistic operating conditions that have been previously assumed. This robustness result is then used to derive convergence results for two control-relevant relaxations of standard game-theoretic applications: distributed (network-based) implementation without full observability and asynchronous deployment (including in continuous time). In each case the results follow as a direct consequence of the main robustness result.

KW - math.OC

KW - 93A14, 93A15, 91A06, 91A26, 91A80

U2 - 10.1137/16M1093227

DO - 10.1137/16M1093227

M3 - Journal article

VL - 55

SP - 3295

EP - 3318

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

ER -