arXiv:2102.00729
Stochastic Online Convex Optimization. Application to probabilistic time series forecasting
원문 초록
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.
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