Stochastic Online Convex Optimization. Application to probabilistic time series forecasting
This provides improved theoretical guarantees for online learning algorithms in stochastic environments, with applications to time series forecasting, though it appears incremental as it builds on existing methods like online Newton steps.
The paper tackles the problem of obtaining fast-rate stochastic regret bounds in online convex optimization, proving that algorithms like online Newton steps achieve best-known rates in unbounded stochastic settings, and applies this to calibrate parametric probabilistic forecasters for non-stationary sub-gaussian time series with any-time valid bounds.
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.