# Counterfactual Online Conformal Prediction Under Adaptive Logging

arXiv: https://arxiv.org/abs/2609.30811 · HTML: https://mlsanity.com/paper/2609.30811/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 38 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 28 of 28)

- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference of Counterfactuals and Individual Treatment Effects](https://mlsanity.com/paper/2006.06138/) (2020)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Optimal and Adaptive Off-policy Evaluation in Contextual Bandits](https://mlsanity.com/paper/1612.01205/) (2016)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Hypothesis testing with e-values](https://mlsanity.com/paper/2410.23614/) (2024)
- [Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictions](https://mlsanity.com/paper/2310.05921/) (2023)
- [Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents](https://mlsanity.com/paper/2502.02561/) (2025)
- [E-Values Expand the Scope of Conformal Prediction](https://mlsanity.com/paper/2503.13050/) (2025)
- [Conformal Off-Policy Prediction in Contextual Bandits](https://mlsanity.com/paper/2206.04405/) (2022)
- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [Conformal e-prediction](https://mlsanity.com/paper/2001.05989/) (2020)
- [Conformal Off-policy Prediction](https://mlsanity.com/paper/2206.06711/) (2022)
- [The Relationship between No-Regret Learning and Online Conformal Prediction](https://mlsanity.com/paper/2502.10947/) (2025)
- [Error-quantified Conformal Inference for Time Series](https://mlsanity.com/paper/2502.00818/) (2025)
- [Stochastic Online Conformal Prediction with Semi-Bandit Feedback](https://mlsanity.com/paper/2405.13268/) (2024)
- [Optimal Model Selection for Conformalized Robust Optimization](https://mlsanity.com/paper/2507.04716/) (2025)
- [Calibrating Decision Robustness via Inverse Conformal Risk Control](https://mlsanity.com/paper/2510.07750/) (2025)
- [Online Conformal Prediction with Adversarial Semi-bandit Feedback via Regret Minimization](https://mlsanity.com/paper/2604.17984/) (2026)
- [Anytime-valid FDR control with the stopped e-BH procedure](https://mlsanity.com/paper/2502.08539/) (2025)
- [Conformal Prediction in The Loop: A Feedback-Based Uncertainty Model for Trajectory Optimization](https://mlsanity.com/paper/2510.16376/) (2025)
- [Online Selective Conformal Prediction: Errors and Solutions](https://mlsanity.com/paper/2503.16809/) (2025)
- [Conformal e-prediction in the presence of confounding](https://mlsanity.com/paper/2603.11134/) (2026)

## Abstract (arXiv)

Online conformal prediction can fail when predictions shape actions and actions determine which outcomes enter calibration. Standard adaptive methods may retain marginal coverage while systematically miscovering the counterfactual outcomes of rarely selected actions. This paper formalizes the failure through counterfactual coverage and introduces Propensity-Weighted Online Conformal Prediction, an inverse-propensity-weighted recursion that debiases calibration. A doubly robust variant further reduces nuisance bias to the product of outcome-model and propensity errors. Under positivity, the resulting coverage rate matches an information-theoretic lower bound up to logarithmic factors. Experiments on synthetic decision tasks, open bandit data, and financial rebalancing show that PW-OCP and DR-OCP improve counterfactual coverage and downstream regret without sacrificing prediction-set sharpness.