Efficient Bidder Selection for Position Auctions via Poisson Approximation

Grunnleggende konsepter

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.

Sammendrag

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.

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Viktige innsikter hentet fra

Bidder Selection Problem in Position Auctions: A Fast and Simple Algorithm via Poisson Approximation

by Nickolai Gra... klokken arxiv.org 04-30-2024

https://arxiv.org/pdf/2306.10648.pdf

Dypere Spørsmål

How can the proposed Poisson relaxation approach be extended to handle other constraints or objectives beyond the standard BSP formulation

The proposed Poisson relaxation approach can be extended to handle other constraints or objectives beyond the standard BSP formulation by adapting the Poisson approximation technique to suit the specific requirements of the new constraints or objectives. For example, if there are additional capacity constraints on the number of bidders that can be selected, the Poisson relaxation can be modified to incorporate these constraints into the optimization problem. This can be achieved by adjusting the threshold values or the set of bidders considered in the Poisson approximation to ensure that the constraints are satisfied while maximizing the objective function. Additionally, if there are multiple objectives to optimize simultaneously, the Poisson relaxation can be extended to include a multi-objective optimization framework where the different objectives are weighted and optimized accordingly.

What are the potential limitations or drawbacks of the Poisson approximation technique, and how can they be addressed in future work

While the Poisson approximation technique offers several advantages in solving the Bidder Selection Problem, there are potential limitations and drawbacks that should be considered. One limitation is the assumption of small probabilities for the Poisson approximation to be effective, which may not always hold true in practical scenarios. To address this limitation, future work could explore alternative approximation techniques that are more robust to variations in probabilities and thresholds. Additionally, the Poisson approximation may introduce errors in the optimization process, leading to suboptimal solutions. This can be mitigated by conducting sensitivity analyses and incorporating error bounds to ensure the reliability of the results. Furthermore, the computational complexity of the Poisson approximation approach may increase significantly with larger problem sizes, requiring efficient algorithms and optimization strategies to handle scalability issues.

Given the practical relevance of the BSP, how can the insights from this work be applied to improve the efficiency and performance of real-world advertising platforms

The insights from this work on the Bidder Selection Problem can be applied to improve the efficiency and performance of real-world advertising platforms in several ways. Firstly, the Poisson relaxation approach can be implemented in existing auction mechanisms to enhance the bidder selection process and optimize social welfare or revenue objectives. By incorporating the Poisson approximation technique, advertising platforms can efficiently select a subset of bidders while maximizing the expected outcome. Secondly, the findings from this research can inform the development of new algorithms and heuristics for bidder selection in position auctions, leading to improved decision-making and better allocation of ad slots. Additionally, the practical relevance of the BSP optimization can drive the adoption of advanced optimization techniques in advertising platforms to enhance competitiveness and profitability. Overall, leveraging the insights from this study can help advertising platforms streamline their auction processes, improve performance metrics, and achieve better outcomes in real-world scenarios.