Vladislav B. Tadic – Optimization Online

Convergence and Convergence Rate of Stochastic Gradient Search in the Case of Multiple and Non-Isolated Extrema

Published: 2009/07/07, Updated: 2009/07/17

Control Applications, Stochastic Programming convergence rate, lojasiewicz gradient inequality, machine learning, point-convergence, stochastic gradient search, system identification

The asymptotic behavior of stochastic gradient algorithms is studied. Relying on some results of differential geometry (Lojasiewicz gradient inequality), the almost sure point-convergence is demonstrated and relatively tight almost sure bounds on the convergence rate are derived. In sharp contrast to all existing result of this kind, the asymptotic results obtained here do not require … Read more

Convergence Rate of Stochastic Gradient Search in the Case of Multiple and Non-Isolated Minima

Published: 2009/04/27

Vladislav B. Tadic

Control Applications, Statistics, Stochastic Programming arma models, lojasiewicz inequalities, machine learning, rate of convergence, recursive prediction error, stochastic gradient algorithms, supervised learning, system identification, temporal-difference learning

The convergence rate of stochastic gradient search is analyzed in this paper. Using arguments based on differential geometry and Lojasiewicz inequalities, tight bounds on the convergence rate of general stochastic gradient algorithms are derived. As opposed to the existing results, the results presented in this paper allow the objective function to have multiple, non-isolated minima, … Read more