[Paper Review] Constructing a maximum utility slate of on-line advertisements

S. Sathiya Keerthi, John A. Tomlin|ArXiv.org|Jun 9, 2007

Consumer Market Behavior and Pricing8 references3 citations

TL;DR

This paper proposes a fast dynamic programming algorithm to construct an optimal slate of online advertisements that maximizes utility under budget constraints and fixed auction rankings. By modeling the problem as a longest-path network optimization, it efficiently computes the best ad order in under 25 microseconds per query, enabling real-time deployment in sponsored search systems.

ABSTRACT

We present an algorithm for constructing an optimal slate of sponsored search advertisements which respects the ordering that is the outcome of a generalized second price auction, but which must also accommodate complicating factors such as overall budget constraints. The algorithm is easily fast enough to use on the fly for typical problem sizes, or as a subroutine in an overall optimization.

Motivation & Objective

• To address the challenge of constructing an optimal ad slate when bidders face budget constraints, which reduces the desirability of showing certain ads.
• To extend the generalized second-price (GSP) auction outcome by incorporating utility factors that reflect budget limits, ad fatigue, or CTR components.
• To develop a computationally efficient algorithm that respects GSP ranking order while optimizing for maximum utility under practical constraints.
• To enable real-time or repeated use of the algorithm in online advertising systems by ensuring sub-millisecond performance.

Proposed method

• Formulate the ad slate selection as a longest-path problem in a directed acyclic network, where nodes represent ads in positions and edges represent transitions between ads.
• Define edge costs as the product of the ad's utility factor, click-through rate (CTR), and the second-price bid, capturing expected utility per placement.
• Use backward recursion with dynamic programming to compute the optimal marginal revenue-to-go, starting from the last position and working backward.
• Introduce dummy bidders with zero utility and minimum bid to standardize slate size to exactly m positions, simplifying the DP recursion.
• Incorporate a mask vector to exclude certain ads from consideration based on business rules, such as budget limits or ad fatigue.
• Extend the framework to hybrid objectives by combining first-price and second-price values in a weighted utility function, allowing flexible optimization criteria.

Experimental results

Research questions

• RQ1 How can we optimally select and order a slate of online ads to maximize utility when bidders are constrained by budgets?
• RQ2 Can we maintain the GSP auction ranking order while still achieving higher overall utility through strategic ad selection?
• RQ3 What is the computational complexity of solving the maximum utility slate problem under budget and position constraints?
• RQ4 How can we efficiently integrate additional factors like ad fatigue or CTR decomposition into the utility function?
• RQ5 To what extent can the algorithm be scaled for real-time use in production online advertising systems?

Key findings

• The proposed dynamic programming algorithm runs in O(n²m) time and is fast enough for real-time use, with an average execution time of 25 microseconds per query on a standard 2.8 GHz Xeon processor.
• The algorithm achieves optimal slate selection by modeling the problem as a longest-path network problem, ensuring global optimality under the given constraints.
• The inclusion of a mask vector allows selective exclusion of ads based on business rules without disrupting the ranking or optimization process.
• The framework supports hybrid utility objectives by combining first-price and second-price values, enabling flexible optimization for revenue, clicks, or other metrics.
• The method is robust and efficient even with small m (≤12) and moderate n (≤100), making it suitable for deployment in live advertising systems.
• The algorithm can be used as a subroutine in column generation frameworks, as demonstrated in companion work on budget-constrained ad allocation.