Stochastic Online Convex Optimization; Application to probabilistic time series forecasting

Stochastic regret bounds for online algorithms are usually derived from an ''online to batch'' conversion. Inverting the reasoning, we start our analyze by a ''batch to online'' conversion that applies in any Stochastic Online Convex Optimization problem under stochastic exp-concavity condition. We obtain fast rate stochastic regret bounds with high probability for non-convex loss functions. Based on this approach, we provide prediction and probabilistic forecasting methods for non-stationary unbounded time series.