Single timescale stochastic approximation for stochastic Nash games in cognitive radio systems

Jayash Koshal, Angelia Nedich, Uday V. Shanbhagy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

In the face of increasing demand for wireless services, the design of spectrum assignment policies has gained enormous relevance. We consider one such instance in cognitive radio systems where recent efforts have focused on the application of game-theoretic approaches. Much of this work has been restricted to deterministic regimes and this paper considers a stochastic generalizations. The corresponding problems are seen to be stochastic Nash games over continuous strategy sets. Notably, the gradient map of player utilities is seen to be a monotone mapping over the cartesian product of strategy sets, leading to a monotone stochastic variational inequality. We consider the application of projection-based stochastic approximation schemes. However, such techniques are characterized by a key shortcoming in that the mappings were required to be be strongly monotone. Standard extensions of stochastic approximation schemes for merely monotone mappings rely on obtaining a sequence of increasingly exact solutions, a natively two-timescale scheme. However, obtaining solutions with increasing accuracy remains a challenging task in a simulation-based setting. Accordingly, we consider the development of single timescale techniques for computing equilibria when the associated gradient map does not admit strong monotonicity. We develop convergence theory for distributed single-timescale stochastic approximation schemes, namely stochastic iterative proximal point method which requires exactly one projection step at every step. Finally we apply this framework to the design of cognitive radio systems in uncertain regimes under temperature-interference constraints.

Original languageEnglish (US)
Title of host publication17th DSP 2011 International Conference on Digital Signal Processing, Proceedings
DOIs
StatePublished - 2011
Externally publishedYes
Event17th International Conference on Digital Signal Processing, DSP 2011 - Corfu, Greece
Duration: Jul 6 2011Jul 8 2011

Other

Other17th International Conference on Digital Signal Processing, DSP 2011
CountryGreece
CityCorfu
Period7/6/117/8/11

Fingerprint

Radio systems
Cognitive radio
Radio interference
Temperature

Keywords

  • Cognitive Radio
  • Communication
  • Game theory
  • Stochastic approximation
  • Variational Inequality

ASJC Scopus subject areas

  • Signal Processing

Cite this

Koshal, J., Nedich, A., & Shanbhagy, U. V. (2011). Single timescale stochastic approximation for stochastic Nash games in cognitive radio systems. In 17th DSP 2011 International Conference on Digital Signal Processing, Proceedings [6004914] https://doi.org/10.1109/ICDSP.2011.6004914

Single timescale stochastic approximation for stochastic Nash games in cognitive radio systems. / Koshal, Jayash; Nedich, Angelia; Shanbhagy, Uday V.

17th DSP 2011 International Conference on Digital Signal Processing, Proceedings. 2011. 6004914.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Koshal, J, Nedich, A & Shanbhagy, UV 2011, Single timescale stochastic approximation for stochastic Nash games in cognitive radio systems. in 17th DSP 2011 International Conference on Digital Signal Processing, Proceedings., 6004914, 17th International Conference on Digital Signal Processing, DSP 2011, Corfu, Greece, 7/6/11. https://doi.org/10.1109/ICDSP.2011.6004914
Koshal J, Nedich A, Shanbhagy UV. Single timescale stochastic approximation for stochastic Nash games in cognitive radio systems. In 17th DSP 2011 International Conference on Digital Signal Processing, Proceedings. 2011. 6004914 https://doi.org/10.1109/ICDSP.2011.6004914
Koshal, Jayash ; Nedich, Angelia ; Shanbhagy, Uday V. / Single timescale stochastic approximation for stochastic Nash games in cognitive radio systems. 17th DSP 2011 International Conference on Digital Signal Processing, Proceedings. 2011.
@inproceedings{bd2c1fa9d9f145339a558aee4c9b8b35,
title = "Single timescale stochastic approximation for stochastic Nash games in cognitive radio systems",
abstract = "In the face of increasing demand for wireless services, the design of spectrum assignment policies has gained enormous relevance. We consider one such instance in cognitive radio systems where recent efforts have focused on the application of game-theoretic approaches. Much of this work has been restricted to deterministic regimes and this paper considers a stochastic generalizations. The corresponding problems are seen to be stochastic Nash games over continuous strategy sets. Notably, the gradient map of player utilities is seen to be a monotone mapping over the cartesian product of strategy sets, leading to a monotone stochastic variational inequality. We consider the application of projection-based stochastic approximation schemes. However, such techniques are characterized by a key shortcoming in that the mappings were required to be be strongly monotone. Standard extensions of stochastic approximation schemes for merely monotone mappings rely on obtaining a sequence of increasingly exact solutions, a natively two-timescale scheme. However, obtaining solutions with increasing accuracy remains a challenging task in a simulation-based setting. Accordingly, we consider the development of single timescale techniques for computing equilibria when the associated gradient map does not admit strong monotonicity. We develop convergence theory for distributed single-timescale stochastic approximation schemes, namely stochastic iterative proximal point method which requires exactly one projection step at every step. Finally we apply this framework to the design of cognitive radio systems in uncertain regimes under temperature-interference constraints.",
keywords = "Cognitive Radio, Communication, Game theory, Stochastic approximation, Variational Inequality",
author = "Jayash Koshal and Angelia Nedich and Shanbhagy, {Uday V.}",
year = "2011",
doi = "10.1109/ICDSP.2011.6004914",
language = "English (US)",
isbn = "9781457702747",
booktitle = "17th DSP 2011 International Conference on Digital Signal Processing, Proceedings",

}

TY - GEN

T1 - Single timescale stochastic approximation for stochastic Nash games in cognitive radio systems

AU - Koshal, Jayash

AU - Nedich, Angelia

AU - Shanbhagy, Uday V.

PY - 2011

Y1 - 2011

N2 - In the face of increasing demand for wireless services, the design of spectrum assignment policies has gained enormous relevance. We consider one such instance in cognitive radio systems where recent efforts have focused on the application of game-theoretic approaches. Much of this work has been restricted to deterministic regimes and this paper considers a stochastic generalizations. The corresponding problems are seen to be stochastic Nash games over continuous strategy sets. Notably, the gradient map of player utilities is seen to be a monotone mapping over the cartesian product of strategy sets, leading to a monotone stochastic variational inequality. We consider the application of projection-based stochastic approximation schemes. However, such techniques are characterized by a key shortcoming in that the mappings were required to be be strongly monotone. Standard extensions of stochastic approximation schemes for merely monotone mappings rely on obtaining a sequence of increasingly exact solutions, a natively two-timescale scheme. However, obtaining solutions with increasing accuracy remains a challenging task in a simulation-based setting. Accordingly, we consider the development of single timescale techniques for computing equilibria when the associated gradient map does not admit strong monotonicity. We develop convergence theory for distributed single-timescale stochastic approximation schemes, namely stochastic iterative proximal point method which requires exactly one projection step at every step. Finally we apply this framework to the design of cognitive radio systems in uncertain regimes under temperature-interference constraints.

AB - In the face of increasing demand for wireless services, the design of spectrum assignment policies has gained enormous relevance. We consider one such instance in cognitive radio systems where recent efforts have focused on the application of game-theoretic approaches. Much of this work has been restricted to deterministic regimes and this paper considers a stochastic generalizations. The corresponding problems are seen to be stochastic Nash games over continuous strategy sets. Notably, the gradient map of player utilities is seen to be a monotone mapping over the cartesian product of strategy sets, leading to a monotone stochastic variational inequality. We consider the application of projection-based stochastic approximation schemes. However, such techniques are characterized by a key shortcoming in that the mappings were required to be be strongly monotone. Standard extensions of stochastic approximation schemes for merely monotone mappings rely on obtaining a sequence of increasingly exact solutions, a natively two-timescale scheme. However, obtaining solutions with increasing accuracy remains a challenging task in a simulation-based setting. Accordingly, we consider the development of single timescale techniques for computing equilibria when the associated gradient map does not admit strong monotonicity. We develop convergence theory for distributed single-timescale stochastic approximation schemes, namely stochastic iterative proximal point method which requires exactly one projection step at every step. Finally we apply this framework to the design of cognitive radio systems in uncertain regimes under temperature-interference constraints.

KW - Cognitive Radio

KW - Communication

KW - Game theory

KW - Stochastic approximation

KW - Variational Inequality

UR - http://www.scopus.com/inward/record.url?scp=80053139024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053139024&partnerID=8YFLogxK

U2 - 10.1109/ICDSP.2011.6004914

DO - 10.1109/ICDSP.2011.6004914

M3 - Conference contribution

SN - 9781457702747

BT - 17th DSP 2011 International Conference on Digital Signal Processing, Proceedings

ER -