# Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency

arXiv: https://arxiv.org/abs/2301.06240 · HTML: https://mlsanity.com/paper/2301.06240/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 65 references that are in the map.
- First posted on arXiv 16 Jan 2023.

## Builds on (most cited first, 21 of 21)

- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Double Reinforcement Learning for Efficient Off-Policy Evaluation in Markov Decision Processes](https://mlsanity.com/paper/1908.08526/) (2019)
- [Optimal and Adaptive Off-policy Evaluation in Contextual Bandits](https://mlsanity.com/paper/1612.01205/) (2016)
- [Provable Benefits of Actor-Critic Methods for Offline Reinforcement Learning](https://mlsanity.com/paper/2108.08812/) (2021)
- [Batch Value-function Approximation with Only Realizability](https://mlsanity.com/paper/2008.04990/) (2020)
- [Asymptotically Efficient Off-Policy Evaluation for Tabular Reinforcement Learning](https://mlsanity.com/paper/2001.10742/) (2020)
- [Optimally tackling covariate shift in RKHS-based nonparametric regression](https://mlsanity.com/paper/2205.02986/) (2022)
- [Balanced Policy Evaluation and Learning](https://mlsanity.com/paper/1705.07384/) (2017)
- [Generalized Optimal Matching Methods for Causal Inference](https://mlsanity.com/paper/1612.08321/) (2016)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [Augmented Minimax Linear Estimation](https://mlsanity.com/paper/1712.00038/) (2017)
- [Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments](https://mlsanity.com/paper/2012.10315/) (2020)
- [Optimal policy evaluation using kernel-based temporal difference methods](https://mlsanity.com/paper/2109.12002/) (2021)
- [Near-optimal inference in adaptive linear regression](https://mlsanity.com/paper/2107.02266/) (2021)
- [Robust Inference Using Inverse Probability Weighting](https://mlsanity.com/paper/1810.11397/) (2018)
- [Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness](https://mlsanity.com/paper/1712.04594/) (2017)
- [Minimax Linear Estimation of the Retargeted Mean](https://mlsanity.com/paper/1901.10296/) (2019)
- [Off-policy estimation of linear functionals: Non-asymptotic theory for semi-parametric efficiency](https://mlsanity.com/paper/2209.13075/) (2022)
- [Minimax Optimal Nonparametric Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/2002.06471/) (2020)
- [Minimax Off-Policy Evaluation for Multi-Armed Bandits](https://mlsanity.com/paper/2101.07781/) (2021)
- [A New Central Limit Theorem for the Augmented IPW Estimator: Variance Inflation, Cross-Fit Covariance and Beyond](https://mlsanity.com/paper/2205.10198/) (2022)

## Built on by (most cited first, 6 of 6)

- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Pseudo-Labeling for Kernel Ridge Regression under Covariate Shift](https://mlsanity.com/paper/2302.10160/) (2023)
- [Proportional Response: Contextual Bandits for Simple and Cumulative Regret Minimization](https://mlsanity.com/paper/2307.02108/) (2023)
- [K-Nearest-Neighbor Resampling for Off-Policy Evaluation in Stochastic Control](https://mlsanity.com/paper/2306.04836/) (2023)
- [Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression](https://mlsanity.com/paper/2604.13410/) (2026)
- [Optimal and Structure-Adaptive CATE Estimation with Kernel Ridge Regression](https://mlsanity.com/paper/2602.18958/) (2026)

## Abstract (arXiv)

We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how well the observational data covers the directions of interest. When it is violated, the classical semi-parametric efficiency bound can easily become infinite, so that the instance-optimal risk depends on the function class used to model the regression function. For any convex and symmetric function class F, we derive a non-asymptotic local minimax bound on the mean-squared error in estimating a broad class of linear functionals. This lower bound refines the classical semi-parametric one, and makes connections to moduli of continuity in functional estimation. When F is a reproducing kernel Hilbert space, we prove that this lower bound can be achieved up to a constant factor by analyzing a computationally simple regression estimator. We apply our general results to various families of examples, thereby uncovering a spectrum of rates that interpolate between the classical theories of semi-parametric efficiency (with √n-consistency) and the slower minimax rates associated with non-parametric function estimation.