ICML 2025

Optimistic Algorithms for
Adaptive Estimation of the Average Treatment Effect
Ojash Neopane 1 Aaditya Ramdas 1 2 Aarti Singh 1
Abstract
Estimation and inference for the Average Treat-
ment Effect (ATE) is a cornerstone of causal infer-
ence and often serves as the foundation for devel-
oping procedures for more complicated settings.
Although traditionally analyzed in a batch setting,
recent advances in martingale theory have paved
the way for adaptive methods that can enhance
the power of downstream inference. Despite these
advances, progress in understanding and develop-
ing adaptive algorithms remains in its early stages.
Existing work either focus on asymptotic analy-
ses that overlook exploration-exploitation trade-
offs relevant in finite-sample regimes or rely on
simpler but suboptimal estimators. In this work,
we address these limitations by studying adaptive
sampling procedures that take advantage of the
asymptotically optimal Augmented Inverse Prob-
ability Weighting (AIPW) estimator. Our analy-
sis uncovers challenges obscured by asymptotic
approaches and introduces a novel algorithmic
design principle reminiscent of optimism in multi-
armed bandits. This principled approach enables
our algorithm to achieve significant theoretical
and empirical gains compared to previous meth-
ods. Our findings mark a step forward in the ad-
vancement of adaptive causal inference methods
in theory and practice.
1. Introduction
The problem of estimating the average treatment effect
(ATE) is central to causal inference and has been extensively
studied. We have a precise understanding of the difficulty of
this problem in both asymptotic and nonasymptotic regimes.
1Machine Learning Department, Carnegie Mellon Uni-
versity
2Department of Statistics & Data Science, Carnegie
Mellon University.
Correspondence to:
Ojash Neopane
<oneopane@andrew.cmu.edu>.
Proceedings of the 42 nd International Conference on Machine
Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025
by the a...