# Anytime-Valid Inference for Double/Debiased Machine Learning of Causal Parameters

arXiv: https://arxiv.org/abs/2408.09598 · HTML: https://mlsanity.com/paper/2408.09598/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 106 references that are in the map.
- First posted on arXiv 18 Aug 2024.

## Builds on (most cited first, 25 of 25)

- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [Time-uniform, nonparametric, nonasymptotic confidence sequences](https://mlsanity.com/paper/1810.08240/) (2018)
- [lil' UCB : An Optimal Exploration Algorithm for Multi-Armed Bandits](https://mlsanity.com/paper/1312.7308/) (2013)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Mixture Martingales Revisited with Applications to Sequential Tests and Confidence Intervals](https://mlsanity.com/paper/1811.11419/) (2018)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [A Theory on Adam Instability in Large-Scale Machine Learning](https://mlsanity.com/paper/2304.09871/) (2023)
- [The State of Applied Econometrics - Causality and Policy Evaluation](https://mlsanity.com/paper/1607.00699/) (2016)
- [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (2018)
- [How to avoid machine learning pitfalls: a guide for academic researchers](https://mlsanity.com/paper/2108.02497/) (2021)
- [Time-uniform central limit theory and asymptotic confidence sequences](https://mlsanity.com/paper/2103.06476/) (2021)
- [Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables](https://mlsanity.com/paper/1611.09925/) (2016)
- [Sequential Nonparametric Testing with the Law of the Iterated Logarithm](https://mlsanity.com/paper/1506.03486/) (2015)
- [Always Valid Inference: Bringing Sequential Analysis to A/B Testing](https://mlsanity.com/paper/1512.04922/) (2015)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [Visually Communicating and Teaching Intuition for Influence Functions](https://mlsanity.com/paper/1810.03260/) (2018)
- [Martingale Methods for Sequential Estimation of Convex Functionals and Divergences](https://mlsanity.com/paper/2103.09267/) (2021)
- [An Experimental Design for Anytime-Valid Causal Inference on Multi-Armed Bandits](https://mlsanity.com/paper/2311.05794/) (2023)
- [Rapid Regression Detection in Software Deployments through Sequential Testing](https://mlsanity.com/paper/2205.14762/) (2022)
- [Estimating Causal Effects with Double Machine Learning -- A Method Evaluation](https://mlsanity.com/paper/2403.14385/) (2024)
- [Anytime-Valid Inference for Multinomial Count Data](https://mlsanity.com/paper/2011.03567/) (2020)
- [Exact Anytime-valid Confidence Intervals for Contingency Tables and Beyond](https://mlsanity.com/paper/2203.09785/) (2022)
- [Forster-Warmuth Counterfactual Regression: A Unified Learning Approach](https://mlsanity.com/paper/2307.16798/) (2023)
- [Generic E-Variables for Exact Sequential k-Sample Tests that allow for Optional Stopping](https://mlsanity.com/paper/2106.02693/) (2021)

## Built on by (most cited first, 5 of 5)

- [Anytime-valid, Bayes-assisted, Prediction-Powered Inference](https://mlsanity.com/paper/2505.18000/) (2025)
- [Efficient Adaptive Experimentation with Noncompliance](https://mlsanity.com/paper/2505.17468/) (2025)
- [Online Data Collection for Efficient Semiparametric Inference](https://mlsanity.com/paper/2411.03195/) (2024)
- [What Do We Care About in Bandits with Noncompliance? BRACE: Bandits with Recommendations, Abstention, and Certified Effects](https://mlsanity.com/paper/2603.09532/) (2026)
- [Adaptive Experimentation for Censored Survival Outcomes](https://mlsanity.com/paper/2605.18459/) (2026)

## Abstract (arXiv)

Double (debiased) machine learning (DML) has seen widespread use in recent years for learning causal/structural parameters, in part due to its flexibility and adaptability to high-dimensional nuisance functions as well as its ability to avoid bias from regularization or overfitting. However, the classic double-debiased framework is only valid asymptotically for a predetermined sample size, thus lacking the flexibility of collecting more data if sharper inference is needed, or stopping data collection early if useful inferences can be made earlier than expected. This can be of particular concern in large scale experimental studies with huge financial costs or human lives at stake, as well as in observational studies where the length of confidence of intervals do not shrink to zero even with increasing sample size due to partial identifiability of a structural parameter. In this paper, we present time-uniform counterparts to the asymptotic DML results, enabling valid inference and confidence intervals for structural parameters to be constructed at any arbitrary (possibly data-dependent) stopping time. We provide conditions which are only slightly stronger than the standard DML conditions, but offer the stronger guarantee for anytime-valid inference. This facilitates the transformation of any existing DML method to provide anytime-valid guarantees with minimal modifications, making it highly adaptable and easy to use. We illustrate our procedure using two instances: a) local average treatment effect in online experiments with non-compliance, and b) partial identification of average treatment effect in observational studies with potential unmeasured confounding.