# Policy Learning with Abstention

arXiv: https://arxiv.org/abs/2510.19672 · HTML: https://mlsanity.com/paper/2510.19672/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 48 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Builds on (most cited first, 17 of 17)

- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Safe Policy Improvement with Baseline Bootstrapping](https://mlsanity.com/paper/1712.06924/) (2017)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Safe Policy Improvement by Minimizing Robust Baseline Regret](https://mlsanity.com/paper/1607.03842/) (2016)
- [Online Learning with Abstention](https://mlsanity.com/paper/1703.03478/) (2017)
- [Fast Rates for Online Prediction with Abstention](https://mlsanity.com/paper/2001.10623/) (2020)
- [Safe Policy Improvement with an Estimated Baseline Policy](https://mlsanity.com/paper/1909.05236/) (2019)
- [Fast classification rates without standard margin assumptions](https://mlsanity.com/paper/1910.12756/) (2019)
- [Off-policy Confidence Sequences](https://mlsanity.com/paper/2102.09540/) (2021)
- [Consistent Algorithms for Multiclass Classification with a Reject Option](https://mlsanity.com/paper/1505.04137/) (2015)
- [A Regret-Variance Trade-Off in Online Learning](https://mlsanity.com/paper/2206.02656/) (2022)
- [Inference on Optimal Dynamic Policies via Softmax Approximation](https://mlsanity.com/paper/2303.04416/) (2023)
- [Bandits with Abstention under Expert Advice](https://mlsanity.com/paper/2402.14585/) (2024)
- [CSPI-MT: Calibrated Safe Policy Improvement with Multiple Testing for Threshold Policies](https://mlsanity.com/paper/2408.12004/) (2024)

## Abstract (arXiv)

Policy learning algorithms are widely used in areas such as personalized medicine and advertising to develop individualized treatment regimes. However, most methods force a decision even when predictions are uncertain, which is risky in high-stakes settings. We study policy learning with abstention, where a policy may defer to a safe default or an expert. When a policy abstains, it receives a small additive reward on top of the value of a random guess. We propose a two-stage learner that first identifies a set of near-optimal policies and then constructs an abstention rule from their disagreements. We establish fast O(1/n)-type regret guarantees when propensities are known, and extend these guarantees to the unknown-propensity case via a doubly robust (DR) objective. We further show that abstention is a versatile tool with direct applications to other core problems in policy learning: it yields improved guarantees under margin conditions without the common realizability assumption, connects to distributionally robust policy learning by hedging against small data shifts, and supports safe policy improvement by ensuring improvement over a baseline policy with high probability.