Core Concepts
The authors propose a novel Poisson relaxation approach to efficiently solve the Bidder Selection Problem (BSP) for position auctions, which outperforms previous complex PTAS algorithms in both theoretical guarantees and practical implementation.
Abstract
The Bidder Selection Problem (BSP) arises in online advertising, where an advertising platform has a large pool of potential advertisers but can only run a proper auction for a fraction of them due to strict computational constraints. The goal is to efficiently select a subset of k out of n bidders that maximizes the expected social welfare or revenue of the platform.
The authors first formulate the fractional relaxation of the BSP for position auctions, where the objective is a linear combination of the expected maximum values of the selected bidders. They then propose a novel Poisson relaxation of this fractional problem, which has the following key properties:
The Poisson relaxation is a continuous maximization problem with a concave objective that can be solved efficiently in polynomial time.
The Poisson relaxation converges to the actual social welfare of the fractional BSP at a rate of 1 - O(k^(-1/4)) as the problem size k grows.
The standard rounding of the fractional Poisson solution suffers only a small loss of O(k^(-1/2)), yielding a 1 - O(k^(-1/4))-approximation for the integral BSP.
The authors also implement their algorithm and conduct extensive numerical experiments, which show that it outperforms existing heuristics like Greedy in both running time and approximation quality, especially on medium and large-sized instances.
The theoretical and practical results demonstrate the effectiveness of the Poisson relaxation approach for the Bidder Selection Problem in position auctions.