Stochastic Online Convex Optimization. Application to probabilistic time series forecasting
Machine Learning
2023-04-24 v3 Statistics Theory
Statistics Theory
Abstract
We introduce a general framework of stochastic online convex optimization to obtain fast-rate stochastic regret bounds. We prove that algorithms such as online newton steps and a scale-free 10 version of Bernstein online aggregation achieve best-known rates in unbounded stochastic settings. We apply our approach to calibrate parametric probabilistic forecasters of non-stationary sub-gaussian time series. Our fast-rate stochastic regret bounds are any-time valid. Our proofs combine self-bounded and Poissonnian inequalities for martingales and sub-gaussian random variables, respectively, under a stochastic exp-concavity assumption.
Cite
@article{arxiv.2102.00729,
title = {Stochastic Online Convex Optimization. Application to probabilistic time series forecasting},
author = {Olivier Wintenberger},
journal= {arXiv preprint arXiv:2102.00729},
year = {2023}
}