Optimal Bidding, Allocation, and Budget Spending for a Demand-Side Platform With Generic Auctions
为需求侧平台开发了一个优化模型，通过放宽预算约束和适应任意拍卖类型，在非凸优化问题中利用Fenchel对偶理论实现高效求解，帮助平台在盈利与预算支出间取得更好平衡。
We develop a practical optimization model for the management of a demand-side platform (DSP), which is applicable in static planning situations where the DSP acquires valuable impressions for high-volume advertiser clients in a real-time bidding environment. We propose a highly flexible model for the DSP to maximize its profit while maintaining acceptable levels of budget spending for its advertisers. Our model achieves flexibility and improved performance primarily through two different aspects: (i) we replace standard budget constraints with a more general budget utilization proxy function over budget spending levels, and (ii) we can accommodate arbitrary auction types by directly modeling the interactions between the DSP and the auctions. Our proposed formulation leads to a non-convex optimization problem due to the joint optimization over both impression allocation and bid price decisions. Using Fenchel duality theory, we obtain a convex dual problem that can be efficiently solved with subgradient based algorithms and from which a primal solution may be recovered efficiently. Under a natural and intuitive “increasing marginal cost” condition, as well as under a more general condition, we show that there is zero duality gap between the dual problem and the original non-convex primal problem. Under the same conditions, we also demonstrate convergence of our algorithm to an optimal solution of the non-convex formulation as the dual problem is solved to near optimality. We conduct experiments on both synthetic data as well as data from a real DSP, and our results demonstrate how our algorithm allows the DSP to better trade off between profitability and budget spending as compared to a widely used “greedy” heuristic approach.