Stochastic Online Convex Optimization. Application to probabilistic time series forecasting

Olivier Wintenberger (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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.

Mots clés: Stochastic online optimization; time series prediction; probabilistic forecasting; Sequential learning

Domaines: Machine Learning [stat.ML]; Statistiques [math.ST]

Olivier Wintenberger. Stochastic Online Convex Optimization. Application to probabilistic time series forecasting. 2023. ⟨hal-03125863v4⟩