Optimal Spend Rate Estimation and Pacing for Ad Campaigns with Budgets

Abstract

Online ad platforms offer budget management tools for advertisers that aim to maximize the number of conversions given a budget constraint. As the volume of impressions, conversion rates and prices vary over time, these budget management systems learn a spend plan (to find the optimal distribution of budget over time) and run a pacing algorithm which follows the spend plan.This paper considers two models for impressions and competition that varies with time: a) an episodic model which exhibits stationarity in each episode, but each episode can be arbitrarily different from the next, and b) a model where the distributions of prices and values change slowly over time. We present the first learning theoretic guarantees on both the accuracy of spend plans and the resulting end-to-end budget management system. We present four main results: 1) for the episodic setting we give sample complexity bounds for the spend rate prediction problem: given n samples from each episode, with high probability we havewhere ρe is the optimal spend rate for the episode, ρe is the estimate from our algorithm, 2) we extend the algorithm of Balseiro and Gur [12] to operate on varying, approximate spend rates and show that the resulting combined system of optimal spend rate estimation and online pacing algorithm for episodic settings has regret that vanishes in number of historic samples n and the number of rounds T , 3) for non-episodic but slowly-changing distributions we show that the same approach approximates the optimal bidding strategy up to a factor dependent on the rate-of-change of the distributions and 4) we provide experiments showing that our algorithm outperforms both static spend plans and non-pacing across a wide variety of settings.

Robust Budget Pacing with a Single Sample

“…Zhou et al (2008) also study the adversarial setting and provide a pacing-based algorithm that achieves a differently-parameterized competitive ratio which scales as the logarithm of the ratio of the highest-to-lowest return-oninvestment, and show that it is optimal. Kumar et al (2022) study an episodic setting and provide a density-estimation-based algorithm for learning the target expenditures for each episode. Gaitonde et al (2022) study the performance of the algorithm of Balseiro & Gur (2019) for the different objective of value maximization, and against the different benchmark comprised of pacing multipliers which spend the same amount B/T at each time period.…”

“…Given the inherent non-stationarities that exist over time, in the volume of traffic, in the demographic of users that visit, the rates of conversion etc., an advertiser's own value and that of the competing advertisers' values are also non-stationary. To deal with this non-stationarity, budget management systems compute a target expenditure plan (Facebook-Guide; Kumar et al, 2022). The latter is a function of time that specifies the recommended amount of spend at each point of time.…”

Delivery Optimized Discovery in Behavioral User Segmentation under Budget Constraint

“…The problem of advertising (message) delivery under budget constraint occupies an early prominent role in search [18,22]. Optimization of message spend rate with budget is well attended [8,23]. An area of research emphasis is budget pacing, whereby a given budget from a firm is dynamically allocated over a time horizon, based on anticipated traffic with specified characteristics, as exemplified by the empirical and theoretical contributions [12,13,16,30,34], to name a few.…”