# Online Decision Deferral under Budget Constraints

arXiv: https://arxiv.org/abs/2409.20489 · HTML: https://mlsanity.com/paper/2409.20489/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 30 Sep 2024.

## Builds on (most cited first, 20 of 20)

- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Bandits with Knapsacks](https://mlsanity.com/paper/1305.2545/) (2013)
- [The Algorithmic Automation Problem: Prediction, Triage, and Human Effort](https://mlsanity.com/paper/1903.12220/) (2019)
- [Bandits with concave rewards and convex knapsacks](https://mlsanity.com/paper/1402.5758/) (2014)
- [Linear Contextual Bandits with Knapsacks](https://mlsanity.com/paper/1507.06738/) (2015)
- [Differentiable Learning Under Triage](https://mlsanity.com/paper/2103.08902/) (2021)
- [Adversarial Bandits with Knapsacks](https://mlsanity.com/paper/1811.11881/) (2018)
- [Who Should Predict? Exact Algorithms For Learning to Defer to Humans](https://mlsanity.com/paper/2301.06197/) (2023)
- [Calibrated Learning to Defer with One-vs-All Classifiers](https://mlsanity.com/paper/2202.03673/) (2022)
- [Sample Efficient Learning of Predictors that Complement Humans](https://mlsanity.com/paper/2207.09584/) (2022)
- [Human-AI Collaboration with Bandit Feedback](https://mlsanity.com/paper/2105.10614/) (2021)
- [Non-stationary Bandits with Knapsacks](https://mlsanity.com/paper/2205.12427/) (2022)
- [An optimal algorithm for bandit convex optimization](https://mlsanity.com/paper/1603.04350/) (2016)
- [Learning-to-defer for sequential medical decision-making under uncertainty](https://mlsanity.com/paper/2109.06312/) (2021)
- [A Bandit Model for Human-Machine Decision Making with Private Information and Opacity](https://mlsanity.com/paper/2007.04800/) (2020)
- [A Second-Order Method for Stochastic Bandit Convex Optimisation](https://mlsanity.com/paper/2302.05371/) (2023)
- [ROI Maximization in Stochastic Online Decision-Making](https://mlsanity.com/paper/1905.11797/) (2019)
- [Contextual Bandits with Knapsacks for a Conversion Model](https://mlsanity.com/paper/2206.00314/) (2022)
- [A Dynamic Model of Performative Human-ML Collaboration: Theory and Empirical Evidence](https://mlsanity.com/paper/2405.13753/) (2024)

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

- [Budgeted Multiple-Expert Deferral](https://mlsanity.com/paper/2510.26706/) (2025)
- [Feel-Good Thompson Sampling for Contextual Bandits: a Markov Chain Monte Carlo Showdown](https://mlsanity.com/paper/2507.15290/) (2025)
- [Online Learning-to-Defer with Varying Experts](https://mlsanity.com/paper/2605.12340/) (2026)
- [Learning to Assign Prediction Tasks to Agents with Capacity Constraints](https://mlsanity.com/paper/2605.27999/) (2026)
- [PixSim: a calibrated open-source simulator of instant-payment fraud, recovery and interdiction under analyst capacity constraints](https://mlsanity.com/paper/2609.30684/) (2026)

## Abstract (arXiv)

Machine Learning (ML) models are increasingly used to support or substitute decision making. In applications where skilled experts are a limited resource, it is crucial to reduce their burden and automate decisions when the performance of an ML model is at least of equal quality. However, models are often pre-trained and fixed, while tasks arrive sequentially and their distribution may shift. In that case, the respective performance of the decision makers may change, and the deferral algorithm must remain adaptive. We propose a contextual bandit model of this online decision making problem. Our framework includes budget constraints and different types of partial feedback models. Beyond the theoretical guarantees of our algorithm, we propose efficient extensions that achieve remarkable performance on real-world datasets.