Optimal Learning via Moderate Deviations Theory

arXiv:2305.14496v3 Announce Type: replace
Abstract: This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming problem or various SDE models. More precisely, we develop a systematic construction of highly accurate confidence intervals by using a moderate deviation principle-based approach. It is shown that the proposed confidence intervals are statistically optimal in the sense that they …

abstract arxiv confidence construction function general interval loss math.oc math.pr math.st non-parametric paper parametric programming stat.ml stat.th stochastic theory type value via