# Occupancy-based Quantile Risk Control

arXiv: https://arxiv.org/abs/2609.03104 · HTML: https://mlsanity.com/paper/2609.03104/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 60 references that are in the map.
- First posted on arXiv 2 Sep 2026.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [GoEmotions: A Dataset of Fine-Grained Emotions](https://mlsanity.com/paper/2005.00547/) (2020)
- [PraNet: Parallel Reverse Attention Network for Polyp Segmentation](https://mlsanity.com/paper/2006.11392/) (2020)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Testing for Outliers with Conformal p-values](https://mlsanity.com/paper/2104.08279/) (2021)
- [TResNet: High Performance GPU-Dedicated Architecture](https://mlsanity.com/paper/2003.13630/) (2020)
- [Selection by Prediction with Conformal p-values](https://mlsanity.com/paper/2210.01408/) (2022)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [Learning Bounds for Risk-sensitive Learning](https://mlsanity.com/paper/2006.08138/) (2020)
- [Fast yet Safe: Early-Exiting with Risk Control](https://mlsanity.com/paper/2405.20915/) (2024)
- [Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problems](https://mlsanity.com/paper/2305.10124/) (2023)
- [SConU: Selective Conformal Uncertainty in Large Language Models](https://mlsanity.com/paper/2504.14154/) (2025)
- [Transductive conformal inference with adaptive scores](https://mlsanity.com/paper/2310.18108/) (2023)
- [COIN: Uncertainty-Guarding Selective Question Answering for Foundation Models with Provable Risk Guarantees](https://mlsanity.com/paper/2506.20178/) (2025)
- [Conformal Semantic Image Segmentation: Post-hoc Quantification of Predictive Uncertainty](https://mlsanity.com/paper/2405.05145/) (2024)
- [Conformal Linguistic Calibration: Trading-off between Factuality and Specificity](https://mlsanity.com/paper/2502.19110/) (2025)
- [Quantile Risk Control: A Flexible Framework for Bounding the Probability of High-Loss Predictions](https://mlsanity.com/paper/2212.13629/) (2022)
- [Conformal Risk Training: End-to-End Optimization of Conformal Risk Control](https://mlsanity.com/paper/2510.08748/) (2025)
- [Conformal Tail Risk Control for Large Language Model Alignment](https://mlsanity.com/paper/2502.20285/) (2025)
- [Supervised Learning with General Risk Functionals](https://mlsanity.com/paper/2206.13648/) (2022)
- [Quantile Learn-Then-Test: Quantile-Based Risk Control for Hyperparameter Optimization](https://mlsanity.com/paper/2407.17358/) (2024)

## Abstract (arXiv)

Conformal risk control is an emerging framework for the safe deployment of machine learning models with finite-sample guarantees. To accommodate a broader class of risk notions, quantile risk control extends this framework to quantile-based risk measures. However, existing methods either suffer from excessive conservatism or lack rigorous finite-sample guarantees. To address these limitations, we introduce Occupancy-based Quantile Risk Control (OQRC), a novel method that provides tight risk control bounds with finite-sample validity. Our key idea is to formulate risk control as a finite-occupancy problem by partitioning the loss space with the ordered calibration losses. Specifically, we estimate the distribution of test losses across the resulting bins and upper-bound the risk by the maximum loss attained within each bin. We then select the parameter λ such that this upper bound does not exceed a predefined threshold α with high probability 1-δ. Theoretically, we establish a finite-sample guarantee showing that OQRC yields tight risk control bounds that converge to the optimal bounds at a provable rate of O_ p(n-1/2). Extensive experiments demonstrate the effectiveness of our method, reducing the risk gap by up to 78.64% on common benchmarks.