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arXiv · 2002.03636

Stochastic Online Optimization using Kalman Recursion

Joseph de Vilmarest·Olivier Wintenberger
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Abstract

We study the Extended Kalman Filter in constant dynamics, offering a bayesian perspective of stochastic optimization. We obtain high probability bounds on the cumulative excess risk in an unconstrained setting. In order to avoid any projection step we propose a two-phase analysis. First, for linear and logistic regressions, we prove that the algorithm enters a local phase where the estimate stays in a small region around the optimum. We provide explicit bounds with high probability on this convergence time. Second, for generalized linear regressions, we provide a martingale analysis of the excess risk in the local phase, improving existing ones in bounded stochastic optimization. The EKF appears as a parameter-free online algorithm with O(d^2) cost per iteration that optimally solves some unconstrained optimization problems.

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BibTeXRIS

Joseph de Vilmarest, Olivier Wintenberger. 2020-02-10. Stochastic Online Optimization using Kalman Recursion. https://arxiv.org/abs/2002.03636

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