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

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.

💡 Research Summary

The paper tackles a fundamental gap in online advertising: most auto‑bidding algorithms assume that the value of each impression (e.g., conversion rate) is known at bidding time, while in practice these values must be predicted and are inherently uncertain. The authors propose a principled framework that quantifies this uncertainty using conformal prediction and integrates the resulting adjusted predictions into a budget‑ and Return‑on‑Spend (RoS)‑constrained bidding algorithm.

Key components of the approach

1. Uncertainty quantification via conformal prediction – Using a historical dataset of contextual features z and delayed true values v, a standard machine‑learning model μ̂(z) is first trained. The authors then apply split conformal prediction for non‑exchangeable data (Barber et al., 2022) to construct a one‑sided prediction interval C(z) that contains the true value with probability at least 1 − β. Unlike the usual absolute‑error nonconformity score, they use a signed score b_S(z,v)=v−μ̂(z) so that the interval directly yields an upper bound μ̂(z)+Δ(z). This upper bound is interpreted as a conservative estimate of the true value.

2. Adjusted predicted value – The upper bound μ̂(z)+Δ(z) is defined as the “adjusted predicted value” v̂_adj. By construction v̂_adj ≥ v with high probability, guaranteeing that any decision based on v̂_adj will not underestimate the true value.

3. Integration with online mirror descent – The adjusted value replaces the unknown true value in the online mirror‑descent (OMD) algorithm of Feng et al. (2020). At each auction t the algorithm solves
   b_t = argmax_{b≥0}