Stochastic Online Optimization using Kalman Recursion


Séminaire Données et Aléatoire Théorie & Applications

13/01/2022 - 14:00 Joseph de Vilmarest (LPSM, Sorbonne Université - EDF) Salle 106

We present an analysis of the Extended Kalman Filter (EKF) in a degenerate setting called static. It has been remarked that in this setting the EKF can be seen as a gradient algorithm. Therefore, we study the static EKF as an online optimization algorithm to enrich the link between bayesian statistics and optimization.
We propose a two-phase analysis. First, for Generalized Linear Models, we obtain high probability bounds on the cumulative excess risk, under the assumption that after some time the algorithm is trapped in a small region around the optimum. Second, we prove that « local » assumption for linear and logistic regressions, slightly modifying the algorithm in the logistic setting.
This is a joint work with Olivier Wintenberger.

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