Abstract: 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.