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Personalized Interpolation: Achieving Efficient Conversion Estimation with Flexible Optimization Windows

Xin Zhang, Weiliang Li, Rui Li, Zihang Fu, Tongyi Tang, Zhengyu Zhang, Wen-Yen Chen, Nima Noorshams, Nirav Jasapara, Xiaowen Ding, Ellie Wen, Xue Feng

TL;DR

The paper tackles the challenge of predicting conversions under advertiser-specific, flexible optimization windows by proposing Personalized Interpolation, which estimates the conversion probability for any intermediate window $T_f$ from predictions at two endpoints: a short window $T_s$ and a long window $T_l$. By modelling the CDF of conversion time and introducing an interpolation factor $\alpha$, the method interpolates between endpoint predictions using three designs (linear, rational, exponential) and can be layered on top of existing black-box models with no additional training cost. Extensive experiments on real ads data show that the interpolation approach achieves competitive or superior predictive accuracy (measured by normalized entropy) compared to production baselines and near the theoretical upper bound, while requiring far less training and infrastructure than dedicated multi-head models. The results indicate significant practical impact for deploying flexible, advertiser-tailored optimization windows in large-scale systems. The framework thus enables accurate, efficient conversion optimization across diverse delay distributions without sacrificing system stability or scalability.

Abstract

Optimizing conversions is crucial in modern online advertising systems, enabling advertisers to deliver relevant products to users and drive business outcomes. However, accurately predicting conversion events remains challenging due to variable time delays between user interactions (e.g., impressions or clicks) and the actual conversions. These delays vary substantially across advertisers and products, necessitating flexible optimization windows tailored to specific conversion behaviors. To address this, we propose a novel \textit{Personalized Interpolation} method that extends existing models based on fixed conversion windows to support flexible advertiser-specific optimization windows. Our method enables accurate conversion estimation across diverse delay distributions without increasing system complexity. We evaluate the effectiveness of the proposed approach through extensive experiments using a real-world ads conversion model. Our results show that this method achieves both high prediction accuracy and improved efficiency compared to existing solutions. This study demonstrates the potential of our Personalized Interpolation method to improve conversion optimization and support a wider range of advertising strategies in large-scale online advertising systems.

Personalized Interpolation: Achieving Efficient Conversion Estimation with Flexible Optimization Windows

TL;DR

The paper tackles the challenge of predicting conversions under advertiser-specific, flexible optimization windows by proposing Personalized Interpolation, which estimates the conversion probability for any intermediate window from predictions at two endpoints: a short window and a long window . By modelling the CDF of conversion time and introducing an interpolation factor , the method interpolates between endpoint predictions using three designs (linear, rational, exponential) and can be layered on top of existing black-box models with no additional training cost. Extensive experiments on real ads data show that the interpolation approach achieves competitive or superior predictive accuracy (measured by normalized entropy) compared to production baselines and near the theoretical upper bound, while requiring far less training and infrastructure than dedicated multi-head models. The results indicate significant practical impact for deploying flexible, advertiser-tailored optimization windows in large-scale systems. The framework thus enables accurate, efficient conversion optimization across diverse delay distributions without sacrificing system stability or scalability.

Abstract

Optimizing conversions is crucial in modern online advertising systems, enabling advertisers to deliver relevant products to users and drive business outcomes. However, accurately predicting conversion events remains challenging due to variable time delays between user interactions (e.g., impressions or clicks) and the actual conversions. These delays vary substantially across advertisers and products, necessitating flexible optimization windows tailored to specific conversion behaviors. To address this, we propose a novel \textit{Personalized Interpolation} method that extends existing models based on fixed conversion windows to support flexible advertiser-specific optimization windows. Our method enables accurate conversion estimation across diverse delay distributions without increasing system complexity. We evaluate the effectiveness of the proposed approach through extensive experiments using a real-world ads conversion model. Our results show that this method achieves both high prediction accuracy and improved efficiency compared to existing solutions. This study demonstrates the potential of our Personalized Interpolation method to improve conversion optimization and support a wider range of advertising strategies in large-scale online advertising systems.
Paper Structure (16 sections, 1 theorem, 6 equations, 8 figures, 2 tables)

This paper contains 16 sections, 1 theorem, 6 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Problem Statement
  4. Preliminary for Long Optimization Window
  5. Problem Formulation of FOW and its Challenges
  6. Methodology
  7. Framework of Personalized Interpolation
  8. Design of Interpolations Factor
  9. Integration with Black-Box Models
  10. Experiment
  11. Experiment Setup
  12. Performance Comparison
  13. Comparison with Existing methods
  14. Performance Check with Recurring Training
  15. Ablation Study on Hyperparameters
  16. ...and 1 more sections

Key Result

Proposition 1

Assume predictions are available for two optimization windows $T_s$ and $T_l$, and we seek to estimate the conversion probability for a new window $T_f \in [T_s, T_l]$. Then, the interpolation framework in Eq. Eq. linear_combination implies: where $\mathbb{P}(\tau \in (T_s, T_f] \mid \tau >T_s)$ denotes the conditional probability of a conversion occurring in the interval $(T_s, T_f]$ given that

Figures (8)

  • Figure 1: Illustration of varying conversion cycles from user interaction with ad impressions to final conversion events. The length of these cycles differs depending on the product type or conversion goal (e.g., form submission, game level achievement, or purchase). As a result, advertisers are motivated to optimize for different conversion windows tailored to their specific objectives.
  • Figure 2: Illustration of the interpolation framework on the conversion CDF. Given the conversion probabilities $\mathbb{P}(\tau \le T_s|e)$ and $\mathbb{P}(\tau \le T_l|e)$, the probability at an intermediate window $\mathbb{P}(\tau \le T_f|e)$ (black dot) can be approximated via a linear combination of the two endpoints (red dot).
  • Figure 3: Illustration and comparison of the three proposed interpolation functions under the setting $T_s = 1$ and $T_l = 7$.
  • Figure 4: Model and system architecture of the SOW/LOW multi-task multi-label framework integrated with the flexible optimization window (FOW) interpolation layer.
  • Figure 5: Conversion data analysis on real impression data collected from 2023-12-27 to 2024-02-04. The left panel shows the average conversion rates with three different interpolation estimations, while the right panel presents the corresponding calibration scores. For all three interpolation methods, the hyper-parameter $\beta$ values are set as listed in Table \ref{['tab:beta_setup']}.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Proposition 1