# Regret Bounds and Experimental Design for Estimate-then-Optimize

arXiv: https://arxiv.org/abs/2210.15576 · HTML: https://mlsanity.com/paper/2210.15576/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Builds on (most cited first, 6 of 6)

- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [Generalization Bounds in the Predict-then-Optimize Framework](https://mlsanity.com/paper/1905.11488/) (2019)
- [Fast Rates for Contextual Linear Optimization](https://mlsanity.com/paper/2011.03030/) (2020)

## Built on by (most cited first, 2 of 2)

- [Learning Choice Model Trees for Feature-Based Multi-Product Pricing: Exact Optimization and Field Evidence](https://mlsanity.com/paper/2609.16952/) (2026)
- [Decision-Focused Learning for Mean-Variance Portfolio Optimization via KKT-Based Reformulation](https://mlsanity.com/paper/2609.21427/) (2026)

## Abstract (arXiv)

In practical applications, data is used to make decisions in two steps: estimation and optimization. First, a machine learning model estimates parameters for a structural model relating decisions to outcomes. Second, a decision is chosen to optimize the structural model's predicted outcome as if its parameters were correctly estimated. Due to its flexibility and simple implementation, this ``estimate-then-optimize'' approach is often used for data-driven decision-making. Errors in the estimation step can lead estimate-then-optimize to sub-optimal decisions that result in regret, i.e., a difference in value between the decision made and the best decision available with knowledge of the structural model's parameters. We provide a novel bound on this regret for smooth and unconstrained optimization problems. Using this bound, in settings where estimated parameters are linear transformations of sub-Gaussian random vectors, we provide a general procedure for experimental design to minimize the regret resulting from estimate-then-optimize. We demonstrate our approach on simple examples and a pandemic control application.