# Stochastic Online Optimization using Kalman Recursion

arXiv: https://arxiv.org/abs/2002.03636 · HTML: https://mlsanity.com/paper/2002.03636/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 6 of 6)

- [Adaptive Probabilistic Forecasting of Electricity (Net-)Load](https://mlsanity.com/paper/2301.10090/) (2023)
- [Non asymptotic analysis of Adaptive stochastic gradient algorithms and applications](https://mlsanity.com/paper/2303.01370/) (2023)
- [KOALA: A Kalman Optimization Algorithm with Loss Adaptivity](https://mlsanity.com/paper/2107.03331/) (2021)
- [Adaptive time series forecasting with markovian variance switching](https://mlsanity.com/paper/2402.14684/) (2024)
- [MODL: Multilearner Online Deep Learning](https://mlsanity.com/paper/2405.18281/) (2024)
- [An hybrid stochastic Newton algorithm for logistic regression](https://mlsanity.com/paper/2512.01790/) (2025)

## Abstract (arXiv)

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.