# Auto-bidding under Return-on-Spend Constraints with Uncertainty Quantification

arXiv: https://arxiv.org/abs/2509.16324 · HTML: https://mlsanity.com/paper/2509.16324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 19 of 19)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [The Best of Many Worlds: Dual Mirror Descent for Online Allocation Problems](https://mlsanity.com/paper/2011.10124/) (2020)
- [Dual Mirror Descent for Online Allocation Problems](https://mlsanity.com/paper/2002.10421/) (2020)
- [A Unifying Framework for Online Optimization with Long-Term Constraints](https://mlsanity.com/paper/2209.07454/) (2022)
- [Online learning in repeated auctions](https://mlsanity.com/paper/1511.05720/) (2015)
- [Learning to Bid Without Knowing your Value](https://mlsanity.com/paper/1711.01333/) (2017)
- [AuctionNet: A Novel Benchmark for Decision-Making in Large-Scale Games](https://mlsanity.com/paper/2412.10798/) (2024)
- [Auto-bidding and Auctions in Online Advertising: A Survey](https://mlsanity.com/paper/2408.07685/) (2024)
- [Robust Auction Design in the Auto-bidding World](https://mlsanity.com/paper/2111.02468/) (2021)
- [Field-aware Calibration: A Simple and Empirically Strong Method for Reliable Probabilistic Predictions](https://mlsanity.com/paper/1905.10713/) (2019)
- [Online Bidding Algorithms for Return-on-Spend Constrained Advertisers](https://mlsanity.com/paper/2208.13713/) (2022)
- [Beyond Primal-Dual Methods in Bandits with Stochastic and Adversarial Constraints](https://mlsanity.com/paper/2405.16118/) (2024)
- [No-Regret Algorithms in non-Truthful Auctions with Budget and ROI Constraints](https://mlsanity.com/paper/2404.09832/) (2024)
- [Posterior Probability Matters: Doubly-Adaptive Calibration for Neural Predictions in Online Advertising](https://mlsanity.com/paper/2205.07295/) (2022)
- [Efficient Algorithms for Stochastic Repeated Second-price Auctions](https://mlsanity.com/paper/2011.05072/) (2020)
- [Deep Ensemble Shape Calibration: Multi-Field Post-hoc Calibration in Online Advertising](https://mlsanity.com/paper/2401.09507/) (2024)
- [Online Bidding under RoS Constraints without Knowing the Value](https://mlsanity.com/paper/2503.03195/) (2025)
- [Online Auction Design Using Distribution-Free Uncertainty Quantification with Applications to E-Commerce](https://mlsanity.com/paper/2405.07038/) (2024)

## Abstract (arXiv)

Auto-bidding systems are widely used in advertising to automatically determine bid values under constraints such as total budget and Return-on-Spend (RoS) targets. Existing works often assume that the value of an ad impression, such as the conversion rate, is known. This paper considers the more realistic scenario where the true value is unknown. We propose a novel method that uses conformal prediction to quantify the uncertainty of these values based on machine learning methods trained on historical bidding data with contextual features, without assuming the data are i.i.d. This approach is compatible with current industry systems that use machine learning to predict values. Building on prediction intervals, we introduce an adjusted value estimator derived from machine learning predictions, and show that it provides performance guarantees without requiring knowledge of the true value. We apply this method to enhance existing auto-bidding algorithms with budget and RoS constraints, and establish theoretical guarantees for achieving high reward while keeping RoS violations low. Empirical results on both simulated and real-world industrial datasets demonstrate that our approach improves performance while maintaining computational efficiency.