# Optimal Confidence Intervals via Moderate Deviations Theory

arXiv: https://arxiv.org/abs/2305.14496 · HTML: https://mlsanity.com/paper/2305.14496/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 73 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 11 of 11)

- [Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems](https://mlsanity.com/paper/2005.01643/) (2020)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Doubly Robust Policy Evaluation and Optimization](https://mlsanity.com/paper/1503.02834/) (2015)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [From Data to Decisions: Distributionally Robust Optimization is Optimal](https://mlsanity.com/paper/1704.04118/) (2017)
- [Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimization](https://mlsanity.com/paper/1605.09349/) (2016)
- [A Pareto Dominance Principle for Data-Driven Optimization](https://mlsanity.com/paper/2010.06606/) (2020)
- [Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions](https://mlsanity.com/paper/2109.06911/) (2021)
- [Statistical Limit Theorems in Distributionally Robust Optimization](https://mlsanity.com/paper/2303.14867/) (2023)

## Built on by (most cited first, 1 of 1)

- [Towards Optimal Offline Reinforcement Learning](https://mlsanity.com/paper/2503.12283/) (2025)

## Abstract (arXiv)

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.