# Profit Maximization for Online Advertising Demand-Side Platforms

## TL;DR

This paper presents a novel optimization model and algorithm for demand-side platforms to maximize profit in real-time bidding environments, effectively balancing impression allocation and bid pricing.

## Contribution

It introduces a tractable convex dual formulation for profit maximization in DSPs, enabling efficient solution via subgradient methods and a two-phase optimization approach.

## Key findings

- Outperforms baseline methods in synthetic experiments
- Efficiently solves a nonconvex profit maximization problem
- Provides a practical approach for DSP profit optimization

## Abstract

We develop an optimization model and corresponding algorithm for the management of a demand-side platform (DSP), whereby the DSP aims to maximize its own profit while acquiring valuable impressions for its advertiser clients. We formulate the problem of profit maximization for a DSP interacting with ad exchanges in a real-time bidding environment in a cost-per-click/cost-per-action pricing model. Our proposed formulation leads to a nonconvex optimization problem due to the joint optimization over both impression allocation and bid price decisions. We use Lagrangian relaxation to develop a tractable convex dual problem, which, due to the properties of second-price auctions, may be solved efficiently with subgradient methods. We propose a two-phase solution procedure, whereby in the first phase we solve the convex dual problem using a subgradient algorithm, and in the second phase we use the previously computed dual solution to set bid prices and then solve a linear optimization problem to obtain the allocation probability variables. On several synthetic examples, we demonstrate that our proposed solution approach leads to superior performance over a baseline method that is used in practice.