The Power of Flexible Budgets in Adwords

2026-10-01

AI Summary

This study addresses the efficiency and competitive optimization of flexible budget allocation in search advertising. By generalizing the D-day AdWords problem, it leverages online algorithm theory and competitive analysis to demonstrate that conventional algorithms fail to effectively exploit budget flexibility. Consequently, novel algorithms are designed that converge to the optimal competitive ratio, with the structure of optimal solutions precisely characterized under high-traffic scenarios. The proposed approach achieves spending efficiency close to the theoretical upper bound, validating that flexible budgets can attain optimal performance equivalent to less constrained environments under specific conditions. Ultimately, this work provides a rigorous theoretical foundation for daily ad delivery strategies in high-traffic settings.

Abstract

Search advertising platforms routinely spend beyond an advertiser's average daily budget on high-traffic days, so long as total spending over the month stays within the monthly budget. Motivated by this practice, we study a $D$-day generalization of the Adwords problem (Mehta et al. 2007), where each advertiser $i$ has a nominal (average) daily budget $B_i$ and a total horizon (monthly) budget $DB_i$. Given a flexibility parameter $δ$, the platform may spend at most $δB_i$ on advertiser $i$ on any single day, subject to the horizon spending limit of $DB_i$. We quantify the power of $δ$-flexible budgets by benchmarking against the inflexible offline optimum, which may spend at most $B_i$ on advertiser $i$ on each day. We show that no amount of flexibility helps direct generalizations of the classical algorithm of Mehta et al. (2007). By contrast, for every fixed $δ$, we design an algorithm whose competitive ratio converges to $1-e^{-δ}$ as $D\to\infty$, and we show that this is asymptotically optimal. Perhaps surprisingly, this matches the optimal competitive ratio in a more permissive setting where the algorithm receives a fresh spending limit of $δB_i$ each day and may spend up to $δD B_i$ over the horizon. Along the way, we characterize the exact optimal competitive ratio for every pair $(D,δ)$ on high-traffic instances, where the offline benchmark exhausts every advertiser's budget on every day.

Problem

• Adwords problem
• flexible budgets
• competitive ratio
• search advertising
• online allocation

Innovation

• Adwords problem
• flexible budgets
• competitive ratio
• online algorithms
• search advertising