Optimal Real-time Bidding Policies for Contract Fulfillment in Second Price Auctions

TL;DR

This paper develops optimal real-time bidding strategies for fulfilling contractual obligations in second-price auctions, using control theory to convert the problem into a convex optimization task and providing algorithms for dynamic updates.

Contribution

It introduces a novel approach applying Pontryagin maximum principle to optimize bidding policies for contract fulfillment in real-time auctions, including dynamic updating algorithms.

Findings

Optimal bidding policies derived using Pontryagin maximum principle.

Convex optimization formulation enables efficient solution.

Algorithms for real-time plan updates demonstrated with real data.

Abstract

We study a real-time bidding problem resulting from a set of contractual obligations stipulating that a firm win a specified number of heterogeneous impressions or ad placements over a defined duration in a real-time auction. The contracts specify item targeting criteria (which may be overlapping), and a supply requirement. Using the Pontryagin maximum principle, we show that the resulting continuous time and time inhomogeneous planning problem can be reduced into a finite dimensional convex optimization problem and solved to optimality. In addition, we provide algorithms to update the bidding plan over time via a receding horizon. Finally, we provide numerical results based on real data and show a connection to production-transportation problems.