# Off-Policy Evaluation with Policy-Dependent Optimization Response

arXiv: https://arxiv.org/abs/2202.12958 · HTML: https://mlsanity.com/paper/2202.12958/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 57 references that are in the map.
- First posted on arXiv 25 Feb 2022.

## Builds on (most cited first, 19 of 19)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Doubly Robust Policy Evaluation and Optimization](https://mlsanity.com/paper/1503.02834/) (2015)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Policy Evaluation and Optimization with Continuous Treatments](https://mlsanity.com/paper/1802.06037/) (2018)
- [Universal Off-Policy Evaluation](https://mlsanity.com/paper/2104.12820/) (2021)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [Interference, Bias, and Variance in Two-Sided Marketplace Experimentation: Guidance for Platforms](https://mlsanity.com/paper/2104.12222/) (2021)
- [Policy Learning with Observational Data](https://mlsanity.com/paper/1702.02896/) (2017)
- [Experimenting in Equilibrium](https://mlsanity.com/paper/1903.02124/) (2019)
- [Cost-Effective Incentive Allocation via Structured Counterfactual Inference](https://mlsanity.com/paper/1902.02495/) (2019)
- [Debiasing In-Sample Policy Performance for Small-Data, Large-Scale Optimization](https://mlsanity.com/paper/2107.12438/) (2021)
- [Spatio-Temporal Pricing for Ridesharing Platforms](https://mlsanity.com/paper/1801.04015/) (2018)
- [Median Optimal Treatment Regimes](https://mlsanity.com/paper/2103.01802/) (2021)
- [Learning Resource Allocation Policies from Observational Data with an Application to Homeless Services Delivery](https://mlsanity.com/paper/2201.10053/) (2022)
- [Bounding Optimality Gap in Stochastic Optimization via Bagging: Statistical Efficiency and Stability](https://mlsanity.com/paper/1810.02905/) (2018)

## Built on by (most cited first, 3 of 3)

- [Decision-Focused Learning with Directional Gradients](https://mlsanity.com/paper/2402.03256/) (2024)
- [Data-Driven Influence Functions for Optimization-Based Causal Inference](https://mlsanity.com/paper/2208.13701/) (2022)
- [When Can You Trust Offline Evaluation of Equal-Cost Top-k Allocation? A Controlled, Reproducible Benchmark and Practitioner's Guide](https://mlsanity.com/paper/2608.12489/) (2026)

## Abstract (arXiv)

The intersection of causal inference and machine learning for decision-making is rapidly expanding, but the default decision criterion remains an textitaverage of individual causal outcomes across a population. In practice, various operational restrictions ensure that a decision-maker's utility is not realized as an textitaverage but rather as an textitoutput of a downstream decision-making problem (such as matching, assignment, network flow, minimizing predictive risk). In this work, we develop a new framework for off-policy evaluation with textitpolicy-dependent linear optimization responses: causal outcomes introduce stochasticity in objective function coefficients. Under this framework, a decision-maker's utility depends on the policy-dependent optimization, which introduces a fundamental challenge of textitoptimization bias even for the case of policy evaluation. We construct unbiased estimators for the policy-dependent estimand by a perturbation method, and discuss asymptotic variance properties for a set of adjusted plug-in estimators. Lastly, attaining unbiased policy evaluation allows for policy optimization: we provide a general algorithm for optimizing causal interventions. We corroborate our theoretical results with numerical simulations.