The work was focused on new algorithms for stochastic optimization and minimum tracking in nonstationary setting. Simultaneous Perturbation Stochatic Approximation is a powerful technique for robust estimation of function’s gradient using randomly generated measurement points. We generalize these algorithms to a setting when a minimum point is stochastically or deterministically drifting in time. We analyze accuracy of this type of algorithms, robustness to arbitrary random perturbations, their errors after a finite number of estimation steps.

Collaborators

Oleg Granichin, Lev Gurevich, Vsevolod Vlasov

Papers

Kosaty, D. and Vakhitov, A. and Granichin, O. and Yuchi, M. Stochastic Fast Gradient for Tracking, Proceedings of the 2019 American Control Conference, 2019, pp. 1476–1481 pdf bib

Vakhitov, A. Finite difference and simultaneous perturbation stochastic approximation with fixed step sizes in case of multiplicative noises, 2014 European Control Conference (ECC), 2014, pp. 1613–1618 pdf bib

Minin, I. and Vakhitov, A. Randomized smoothing for near-convex functions in context of image processing, 2012 American Control Conference (ACC), 2012, pp. 833–838 pdf bib

Vakhitov, A. and Vlasov, V. and Granichin, O. Adaptive control of SISO plant with time-varying coefficients based on random test perturbation, Proceedings of the 2010 American Control Conference, 2010, pp. 4004–4009 pdf bib

Granichin, O. and Gurevich, L. and Vakhitov, A. Discrete-time minimum tracking based on stochastic approximation algorithm with randomized differences, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009, pp. 5763–5767 pdf bib

Vakhitov, A. and Granichin, O. and Sysoev, S. A randomized stochastic optimization algorithm: Its estimation accuracy, Automation and remote control, 2006, pp. 589–597 pdf bib