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Online Causal Inference for Advertising in Real-Time Bidding Auctions

Caio Waisman, Harikesh S. Nair, Carlos Carrion

TL;DR

This work tackles causal inference for advertising in real-time bidding (RTB) auctions by linking the conditional average treatment effect $ATE(x)$ to the advertiser’s optimal bid $b^*(x)$ under second-price and first-price formats. It introduces Bidding Thompson Sampling (BITS), a Bayesian online algorithm that simultaneously learns $b^*(x)$ and $ATE(x)$ by solving a nonlinear contextual multi-armed bandit problem with auction payoffs, using MCMC-based posterior updates. The authors derive exact identifications between $ATE(x)$ and optimal bids in SPAs and FPAs (with FPAs requiring a bid-adjustment via the reverse-hazard of competing bids), along with an order-optimal regret bound for BITS. Empirical evaluation on the iPinYou RTB dataset shows that BITS substantially reduces experimentation costs while achieving accurate $ATE$ estimates, outperforming traditional A/B tests, ETC, and naive TS variants, with simpler variants sometimes offering near-equivalent performance. The results highlight the practical value of embedding economic structure into experimental design and point to broader applications where firm payoff and causal efficacy must be learned concurrently at scale.

Abstract

Real-time bidding (RTB) systems, which utilize auctions to allocate user impressions to competing advertisers, continue to enjoy success in digital advertising. Assessing the effectiveness of such advertising remains a challenge in research and practice. This paper proposes a new approach to perform causal inference on advertising bought through such mechanisms. Leveraging the economic structure of first- and second-price auctions, we first show that the effects of advertising are identified by the optimal bids. Hence, since these optimal bids are the only objects that need to be recovered, we introduce an adapted Thompson sampling (TS) algorithm to solve a multi-armed bandit problem that succeeds in recovering such bids and, consequently, the effects of advertising while minimizing the costs of experimentation. We derive a regret bound for our algorithm which is order optimal and use data from RTB auctions to show that it outperforms commonly used methods that estimate the effects of advertising.

Online Causal Inference for Advertising in Real-Time Bidding Auctions

TL;DR

This work tackles causal inference for advertising in real-time bidding (RTB) auctions by linking the conditional average treatment effect to the advertiser’s optimal bid under second-price and first-price formats. It introduces Bidding Thompson Sampling (BITS), a Bayesian online algorithm that simultaneously learns and by solving a nonlinear contextual multi-armed bandit problem with auction payoffs, using MCMC-based posterior updates. The authors derive exact identifications between and optimal bids in SPAs and FPAs (with FPAs requiring a bid-adjustment via the reverse-hazard of competing bids), along with an order-optimal regret bound for BITS. Empirical evaluation on the iPinYou RTB dataset shows that BITS substantially reduces experimentation costs while achieving accurate estimates, outperforming traditional A/B tests, ETC, and naive TS variants, with simpler variants sometimes offering near-equivalent performance. The results highlight the practical value of embedding economic structure into experimental design and point to broader applications where firm payoff and causal efficacy must be learned concurrently at scale.

Abstract

Real-time bidding (RTB) systems, which utilize auctions to allocate user impressions to competing advertisers, continue to enjoy success in digital advertising. Assessing the effectiveness of such advertising remains a challenge in research and practice. This paper proposes a new approach to perform causal inference on advertising bought through such mechanisms. Leveraging the economic structure of first- and second-price auctions, we first show that the effects of advertising are identified by the optimal bids. Hence, since these optimal bids are the only objects that need to be recovered, we introduce an adapted Thompson sampling (TS) algorithm to solve a multi-armed bandit problem that succeeds in recovering such bids and, consequently, the effects of advertising while minimizing the costs of experimentation. We derive a regret bound for our algorithm which is order optimal and use data from RTB auctions to show that it outperforms commonly used methods that estimate the effects of advertising.

Paper Structure

This paper contains 64 sections, 2 theorems, 21 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Online learning in ad auctions
  3. Experimentation in digital advertising
  4. Causal inference with multi-armed bandits
  5. Problem formulation
  6. Issue 1: The advertiser cannot randomize treatment directly
  7. Issue 2: Bid randomization alone is insufficient for identification
  8. Issue 3: High costs of experimentation
  9. Issue 4: Aligning the inference and economic goals
  10. Aligning the advertiser's objectives
  11. Novelty and implications
  12. Accomplishing the advertiser's objectives
  13. Data generating process
  14. Observed data
  15. Bidding Thompson Sampling (BITS) algorithm
  16. ...and 49 more sections

Key Result

Proposition 1

Optimal bid in SPAs Suppose that Assumptions ass:pv, ass:dens, ass:fin_means, and ass:pos_dens hold. If the auction is an SPA, then $b^*(x)= \max \left \{ 0, ATE(x) \right \}$.

Figures (6)

  • Figure 1: Evolution of cumulative regret for SPAs: contexts 4 and 7
  • Figure 2: MSEs for SPAs: contexts 4 and 7
  • Figure 3: Evolution of cumulative regret for FPAs: contexts 4 and 7
  • Figure 4: MSEs for FPAs: contexts 4 and 7
  • Figure E.1: Evolution of cumulative regret for SPAs
  • ...and 1 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • proof
  • proof