Online Advertisement, Optimization and Stochastic Networks

In this paper, we propose a stochastic model to describe how search service providers charge client companies based on users’ queries for the keywords related to these companies’ ads by using certain advertisement assignment strategies. We formulate an optimization problem to maximize the long-term average revenue for the service provider under each client’s long-term average budget constraint, and design an online algorithm which captures the stochastic properties of users’ queries and click-through behaviors. We solve the optimization problem by making connections to scheduling problems in wireless networks, queueing theory and stochastic networks. Unlike prior models, we do not assume that the number of query arrivals is known. Due to the stochastic nature of the arrival process considered here, either temporary “free” service, i.e., service above the specified budget or under-utilization of the budget is unavoidable. We prove that our online algorithm can achieve a revenue that is within $O(\epsilon)$ of the optimal revenue while ensuring that the overdraft or underdraft is $O(1/\epsilon)$, where $\epsilon$ can be arbitrarily small. With a view towards practice, we can show that one can always operate strictly under the budget. In addition, we extend our results to a click-through rate maximization model, and also show how our algorithm can be modified to handle non-stationary query arrival processes and clients with short-term contracts. Our algorithm allows us to quantify the effect of errors in click-through rate estimation on the achieved revenue. We also show that in the long run, an expected overdraft level of $\Omega(\log(1/\epsilon))$ is unavoidable (a universal lower bound) under any stationary ad assignment algorithm which achieves a long-term average revenue within $O(\epsilon)$ of the offline optimum.

💡 Research Summary

The paper addresses the fundamental problem faced by search‑service providers: how to assign advertisements to user queries in a way that maximizes the provider’s long‑term average revenue while respecting each advertiser’s long‑term average budget. Unlike many earlier works that assume a known, deterministic query arrival rate or enforce hard budget caps, the authors model query arrivals as a stochastic process and treat click‑through rates (CTRs) as random variables that may be estimated with error.

The authors first formulate a constrained stochastic optimization problem. Let (r_{ij}) denote the expected revenue obtained when ad (j) is shown for a query that matches advertiser (i), and let (b_{ij}) denote the expected budget consumption (e.g., cost‑per‑click). The objective is to maximize
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