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Addressing Distribution Shift in RTB Markets via Exponential Tilting

Minji Kim, Seong Jin Lee, Bumsik Kim

TL;DR

The paper addresses distribution shifts in Real-Time Bidding (RTB) markets, where selection bias causes training on winning bids to misrepresent the broader bid population. It applies ExTRA, an exponential tilt reweighting method, to learn weights $w(x,i)=\exp(\theta_i^\top T(x)+\alpha_i)$ that align the source and target distributions using KL divergence, without requiring target labels. Key contributions include formalizing ExTRA in the RTB context with anchor-set identifiability, demonstrating weight estimation on simulated RTB data, and showing that higher weights are assigned to the rare positive class $U=1$ and to regions with larger feature means, thereby improving population-level risk estimation. The work enables target-domain evaluation and potential transfer in dynamic RTB environments and highlights future directions for the design of $T(X)$ and broader distribution-shift validation.

Abstract

In machine learning applications, distribution shifts between training and target environments can lead to significant drops in model performance. This study investigates the impact of such shifts on binary classification models within the Real-Time Bidding (RTB) market context, where selection bias contributes to these shifts. To address this challenge, we apply the Exponential Tilt Reweighting Alignment (ExTRA) algorithm, proposed by Maity et al. (2023). This algorithm estimates importance weights for the empirical risk by considering both covariate and label distributions, without requiring target label information, by assuming a specific weight structure. The goal of this study is to estimate weights that correct for the distribution shifts in RTB model and to evaluate the efficiency of the proposed model using simulated real-world data.

Addressing Distribution Shift in RTB Markets via Exponential Tilting

TL;DR

The paper addresses distribution shifts in Real-Time Bidding (RTB) markets, where selection bias causes training on winning bids to misrepresent the broader bid population. It applies ExTRA, an exponential tilt reweighting method, to learn weights that align the source and target distributions using KL divergence, without requiring target labels. Key contributions include formalizing ExTRA in the RTB context with anchor-set identifiability, demonstrating weight estimation on simulated RTB data, and showing that higher weights are assigned to the rare positive class and to regions with larger feature means, thereby improving population-level risk estimation. The work enables target-domain evaluation and potential transfer in dynamic RTB environments and highlights future directions for the design of and broader distribution-shift validation.

Abstract

In machine learning applications, distribution shifts between training and target environments can lead to significant drops in model performance. This study investigates the impact of such shifts on binary classification models within the Real-Time Bidding (RTB) market context, where selection bias contributes to these shifts. To address this challenge, we apply the Exponential Tilt Reweighting Alignment (ExTRA) algorithm, proposed by Maity et al. (2023). This algorithm estimates importance weights for the empirical risk by considering both covariate and label distributions, without requiring target label information, by assuming a specific weight structure. The goal of this study is to estimate weights that correct for the distribution shifts in RTB model and to evaluate the efficiency of the proposed model using simulated real-world data.
Paper Structure (5 sections, 2 theorems, 15 equations, 3 figures, 1 algorithm)

This paper contains 5 sections, 2 theorems, 15 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Real-Time Bidding market model
  3. The Exponential Tilt Model
  4. Simulated Real Data Analysis
  5. Conclusion

Key Result

Lemma 1

If there are anchor sets ${\mathop{\mathrm{\mathcal{S}}}\limits}_i$ for all $K$ classes in the source domain, and $T(\mathop{\mathrm{\mathcal{S}}}\limits_i)$ is $p$-dimensional, then there is at most one set of $\theta_i$'s and $\alpha_i$'s that satisfies eq eq:q_iden.

Figures (3)

  • Figure 1: Illustration of distribution shift: (Left) covariate shift and (Right) sample selection bias.
  • Figure 2: Illustration of selection bias in binary classification
  • Figure 3: Distribution shifts and fitted weights in the RTB dataset: (Top) Distribution of the source and target datasets, (Middle) Distribution of the source dataset conditioned on utility, and (Bottom) Distribution of the fitted weights for the source dataset.

Theorems & Definitions (3)

  • Definition 1: anchor set
  • Lemma 1: Proposition 4.2 of maity2023understanding
  • Lemma 2