Robust autobidding for noisy conversion prediction models

TL;DR

The paper addresses robustness in autobidding under uncertainty in CTR and CVR predictions for display advertising auctions. It formulates a robust optimization framework that yields analytic bid formulas for CTR, CVR, and joint uncertainties, enabling efficient, closed-form bidding rules (RobustBid). The main contributions include deriving CTR-, CVR-, and joint-uncertainty bid formulas with explicit perturbation terms, and validating them on synthetic, iPinYou, and BAT datasets where RobustBid improves total conversion value (TCV) and reduces average CPC under perturbations. This work demonstrates the practical impact of robust optimization in bidding, offering a scalable solution that maintains performance in the presence of prediction errors.

Abstract

Managing millions of digital auctions is an essential task for modern advertising auction systems. The main approach to managing digital auctions is an autobidding approach, which depends on the Click-Through Rate and Conversion Rate values. While these quantities are estimated with ML models, their prediction uncertainty directly impacts advertisers' revenue and bidding strategies. To address this issue, we propose RobustBid, an efficient method for robust autobidding taking into account uncertainty in CTR and CVR predictions. Our approach leverages advanced, robust optimization techniques to prevent large errors in bids if the estimates of CTR/CVR are perturbed. We derive the analytical solution of the stated robust optimization problem, which leads to the runtime efficiency of the RobustBid method. The synthetic, iPinYou, and BAT benchmarks are used in our experimental evaluation of RobustBid. We compare our method with the non-robust baseline and the RiskBid algorithm in terms of total conversion volume (TCV) and average cost-per-click ($CPC_{avg}$) performance metrics. The experiments demonstrate that RobustBid provides bids that yield larger TCV and smaller $CPC_{avg}$ than competitors in the case of large perturbations in CTR/CVR predictions.

Figures (5)

• Figure 1: Experimental results with $CTR$ uncertainty and $CVR$ accurate estimate. The green dotted line represents the upper bound on the CPC constraint. Root mean squared deviation is specified in the gradient shading form. $\alpha$ is a risk-averse parameter, the larger $\alpha$ corresponds to less risky strategies.
• Figure 2: Heatmaps with comparison $TCV$ and $CPC_{avg}$ for Synthetic dataset. NonRobustBid metrics remain approximately the same, slightly decreasing at large values of $\varepsilon_a$ and $\varepsilon_b$. RobustBid performs better overall, with $TCV$ decreasing only at large $\varepsilon_a$, while maintaining lower $CPC_{avg}$.
• Figure 3: Heatmaps with comparison $TCV$ and $CPC_{avg}$ for iPinYou dataset. NonRobustBid metrics remain approximately the same across all $\varepsilon_a$ and $\varepsilon_b$. In contrast, RobustBid metrics show significant variation while demonstrating better performance overall.
• Figure 4: Heatmaps with comparison $TCV$ and $CPC_{avg}$ for BAT dataset. While $\varepsilon_a$ grows, NonRobustBid shows lower $TCV$ and higher $CPC_{avg}$. At the same time, RobustBid metrics are nearly independent of $\varepsilon_a$ and $\varepsilon_b$.
• Figure 5: Experimental results. The blue line indicates the value of the metrics on the non-robust solution of the problem, the red line - on the robust one. The green dotted line represents the CPC limit. Shades of red specify the root mean square error in the gradient shading form.

Theorems & Definitions (3)

• Lemma 1: The bid for the CTR uncertainty in MSE terms
• Lemma 2: The bid for the CVR uncertainty in MSE terms
• Lemma 3: The bid for the CTR and CVR uncertainty in MSE terms