# Deep Gamblers: Learning to Abstain with Portfolio Theory

arXiv: https://arxiv.org/abs/1907.00208 · HTML: https://mlsanity.com/paper/1907.00208/

## Key facts

- Cited by 71 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2019.

## Built on by (most cited first, 30 of 71)

- [MultiBench: Multiscale Benchmarks for Multimodal Representation Learning](https://mlsanity.com/paper/2107.07502/) (2021)
- [Machine Learning with a Reject Option: A survey](https://mlsanity.com/paper/2107.11277/) (2021)
- [Pixel-wise Energy-biased Abstention Learning for Anomaly Segmentation on Complex Urban Driving Scenes](https://mlsanity.com/paper/2111.12264/) (2021)
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- [Towards Unbiased and Accurate Deferral to Multiple Experts](https://mlsanity.com/paper/2102.13004/) (2021)
- [MaskTune: Mitigating Spurious Correlations by Forcing to Explore](https://mlsanity.com/paper/2210.00055/) (2022)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis](https://mlsanity.com/paper/2210.03736/) (2022)
- [Residual Pattern Learning for Pixel-wise Out-of-Distribution Detection in Semantic Segmentation](https://mlsanity.com/paper/2211.14512/) (2022)
- [A Call to Reflect on Evaluation Practices for Failure Detection in Image Classification](https://mlsanity.com/paper/2211.15259/) (2022)
- [Unmasking Anomalies in Road-Scene Segmentation](https://mlsanity.com/paper/2307.13316/) (2023)
- [Principled Approaches for Learning to Defer with Multiple Experts](https://mlsanity.com/paper/2310.14774/) (2023)
- [Overcoming Common Flaws in the Evaluation of Selective Classification Systems](https://mlsanity.com/paper/2407.01032/) (2024)
- [Predictor-Rejector Multi-Class Abstention: Theoretical Analysis and Algorithms](https://mlsanity.com/paper/2310.14772/) (2023)
- [Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention](https://mlsanity.com/paper/2310.14770/) (2023)
- [Consistency and Uncertainty: Identifying Unreliable Responses From Black-Box Vision-Language Models for Selective Visual Question Answering](https://mlsanity.com/paper/2404.10193/) (2024)
- [Towards Better Selective Classification](https://mlsanity.com/paper/2206.09034/) (2022)
- [Learning to Complete Code with Sketches](https://mlsanity.com/paper/2106.10158/) (2021)
- [Selective Prediction via Training Dynamics](https://mlsanity.com/paper/2205.13532/) (2022)
- [Self-Adaptive Training: Bridging Supervised and Self-Supervised Learning](https://mlsanity.com/paper/2101.08732/) (2021)
- [How to Fix a Broken Confidence Estimator: Evaluating Post-hoc Methods for Selective Classification with Deep Neural Networks](https://mlsanity.com/paper/2305.15508/) (2023)
- [Balanced Energy Regularization Loss for Out-of-distribution Detection](https://mlsanity.com/paper/2306.10485/) (2023)
- [Reinforcement Learning Under Algorithmic Triage](https://mlsanity.com/paper/2109.11328/) (2021)
- [AUC-based Selective Classification](https://mlsanity.com/paper/2210.10703/) (2022)
- [Selective Classification Under Distribution Shifts](https://mlsanity.com/paper/2405.05160/) (2024)
- [Designing Closed Human-in-the-loop Deferral Pipelines](https://mlsanity.com/paper/2202.04718/) (2022)
- [Towards Understanding Why Label Smoothing Degrades Selective Classification and How to Fix It](https://mlsanity.com/paper/2403.14715/) (2024)
- [R-U-SURE? Uncertainty-Aware Code Suggestions By Maximizing Utility Across Random User Intents](https://mlsanity.com/paper/2303.00732/) (2023)
- [WellDunn: On the Robustness and Explainability of Language Models and Large Language Models in Identifying Wellness Dimensions](https://mlsanity.com/paper/2406.12058/) (2024)
- [Affinity Uncertainty-based Hard Negative Mining in Graph Contrastive Learning](https://mlsanity.com/paper/2301.13340/) (2023)

## Abstract (arXiv)

We deal with the textitselective classification problem (supervised-learning problem with a rejection option), where we want to achieve the best performance at a certain level of coverage of the data. We transform the original m-class classification problem to (m+1)-class where the (m+1)-th class represents the model abstaining from making a prediction due to disconfidence. Inspired by portfolio theory, we propose a loss function for the selective classification problem based on the doubling rate of gambling. Minimizing this loss function corresponds naturally to maximizing the return of a textithorse race, where a player aims to balance between betting on an outcome (making a prediction) when confident and reserving one's winnings (abstaining) when not confident. This loss function allows us to train neural networks and characterize the disconfidence of prediction in an end-to-end fashion. In comparison with previous methods, our method requires almost no modification to the model inference algorithm or model architecture. Experiments show that our method can identify uncertainty in data points, and achieves strong results on SVHN and CIFAR10 at various coverages of the data.