Stochastic Optimization and Adaptive Filtering

We are interested in synthesizing and analyzing stochastic approximation algorithms for distributed optimization and game-theoretic learning. How quickly can a constant step size stochastic approximation track a time varying parameter or more generally, the equilibria of a time varying game? Stochastic averaging theory is the main tool that we use to analyze such algorithms. One of our major results is that if the parameter jumps according to a Markov chain with slow transition matrix, then the asymptotic behavior of the stochastic approximation converges to a switched-Markovian ordinary differential equation or differential inclusion.

Related Papers

Stochastic Gradient Algorithms & Weak convergence; Reinforcement Learning

Global Games, Bayesian Nash equilibria, Revealed Preferences

  •  W. Hoiles, V. Krishnamurthy, A. Aprem, PAC Algorithms for Detecting Nash Equilibrium Play in Social Networks: From Twitter to Energy Markets, IEEE Access Journal, Vol.4, Nov., pp.8147–8161, 2016.
  • V. Krishnamurthy, Decentralized Activation in Sensor Networks Global Games and Adaptive Filtering Games, Digital Signal Processing, Vol.21, No.5, pp. 638{647, 2011.
  • V. Krishnamurthy, Decentralized Spectrum Access amongst Cognitive Agents – An Interacting Multivariate Global Games Approach, IEEE Transactions Signal Processing, Vol.57, No.10, pp.3999-4013, Oct.2009.
  • V. Krishnamurthy, Decentralized Activation in Dense Sensor Networks via Global Games, IEEE Transactions Signal Processing, Vol.56, No.10, pp.4936{4950, Oct.2008.