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We develop a novel optimization model to maximize the profit of a Demand-SidePlatform (DSP) while ensuring that the budget utilization preferences of theDSP's advertiser clients are adequately met. Our model is highly flexible andcan be applied in a Real-Time Bidding environment (RTB) with arbitrary auctiontypes, e.g., both first and second price auctions. Our proposed formulationleads to a non-convex optimization problem due to the joint optimization overboth impression allocation and bid price decisions. Using Fenchel dualitytheory, we construct a dual problem that is convex and can be solvedefficiently to obtain feasible bidding prices and allocation variables that canbe deployed in a RTB setting. With a few minimal additional assumptions on theproperties of the auctions, we demonstrate theoretically that ourcomputationally efficient procedure based on convex optimization principles isguaranteed to deliver a globally optimal solution. We conduct experiments usingdata from a real DSP to validate our theoretical findings and to demonstratethat our method successfully trades off between DSP profitability and budgetutilization in a simulated online environment.

Optimal Bidding, Allocation and Budget Spending for a Demand Side Platform Under Many Auction Types