Optimal Learning via Moderate Deviations Theory
Type
conference lecture
Date Issued
2025-09-02
Author(s)
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 satisfy criteria regarding exponential accuracy, minimality, consistency, mischaracterization probability, and eventual uniformly most accurate (UMA) property. The confidence intervals suggested by this approach are expressed as solutions to robust optimization problems, where the uncertainty is expressed via the underlying moderate deviation rate function induced by the data-generating process. We demonstrate that for many models these optimization problems admit tractable reformulations as finite convex programs even when they are infinite-dimensional.
Language
English
Keywords
Interval estimation
Large deviations
Moderate deviations
Stochastic processes
Distributionally robust optimization
HSG Classification
contribution to scientific community
Refereed
No
Subject(s)
Division(s)
Contact Email Address
tobias.sutter@unisg.ch
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open.access
Name
RSS_talk_sutter.pdf
Size
521.03 KB
Format
Adobe PDF
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