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Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis
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Proposes parallel budget-controlled A/B testing via market segmentation and derives a debiased surrogate with plug-in estimator and asymptotic normality to correct interference bias among first-price pacing equilibria.
Problem
A/B tests in budget-constrained ad auction markets suffer interference between arms; budget splitting shrinks per-arm budgets and hurts statistics, and running parallel experiments across submarkets introduces residual cross-submarket interference bias.
Approach
Model cross-submarket leakage as supply contamination in a first-price pacing equilibrium (FPPE) and use a directional-derivative-based debiased surrogate that removes the first-order bias of pacing multipliers and revenue, with a plug-in estimator and asymptotic normality results.
Key results
- Debiased surrogate bias for pacing multipliers and revenue is much smaller than the contaminated limit quantities across alpha values.
- Coverage of the pacing multiplier CI is about 0.83-0.88 against a 95% nominal level across contamination levels (e.g., 0.877 at 1000/11000).
- Production Meta experiments: parallel design agrees in sign with budget-split design in 75% of 99 comparisons, rising to 79% after a guardrail metric.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Exclude experiments that violate the guardrail | Parallel budget-controlled A/B tests · Meta paired experiments, 1 day | sign consistency (%): 75.8 -> 81.0 | Helped |
| Exclude experiments that violate the guardrail | Parallel budget-controlled A/B tests · Meta paired experiments, 1 day | sign consistency (%): 73.7 -> 76.2 | Helped |
| Exclude experiments that violate the guardrail | Parallel budget-controlled A/B tests · Meta paired experiments, 6 days | sign consistency (%): 87.5 -> 100 | Helped |
| Exclude experiments that violate the guardrail | Parallel budget-controlled A/B tests · Meta paired experiments, 6 days | sign consistency (%): 68.8 -> 78.6 | Helped |
| Add the first-order debiasing correction | FPPE pacing multiplier estimate under supply contamination · Semi-synthetic experiments | normalized bias | Helped |
| Add the first-order debiasing correction | FPPE revenue estimate under supply contamination · Semi-synthetic experiments | normalized bias | Helped |
| Use the proposed variance estimator for pacing multipliers | Debiased pacing multiplier estimator · Semi-synthetic experiments | coverage: 0.877, 0.849, 0.852, 0.828, 0.826 | Hurt |
| Use the analytic revenue confidence interval instead of the bootstrap CI | Debiased revenue estimator · Semi-synthetic experiments | coverage: 1.0 vs 0.95; 1.0 vs 0.87; 1.0 vs 0.81; 1.0 vs 0.90; 1.0 vs 0.90 | Mixed |
Surprising findings
- Analytic revenue CIs over-cover (coverage 1.0) while parametric bootstrap CIs under-cover (0.81-0.95).
- Variance estimator can perform badly in either direction for finite markets.
Limitations
- Variance estimator under-estimates variance in finite markets, causing under-coverage for pacing multipliers.
- Assumes contamination level alpha is known and submarket structure is given.
- Assumes all advertisers use multiplicative pacing with single-item-per-impression first-price auctions.
Experimental setup
Datasets: historical Meta ad bidding data (semi-synthetic)
Benchmarks: semi-synthetic pacing equilibrium simulations (40 buyers, 10000 good items)
Metrics: normalized bias of pacing multipliers and revenue CI coverage CI width
Baselines: naive finite FPPE estimate under interference budget-split design
Builds on: first-price pacing equilibrium Eisenberg-Gale convex program budget-controlled A/B testing
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