Objective Variables for Probabilistic Revenue Maximization in Second-Price Auctions with Reserve

TL;DR

This paper introduces a probabilistic framework using objective variables and EM algorithm to learn optimal reserve prices in second-price auctions, improving profitability and scalability over previous methods.

Contribution

It develops a novel objective variable framework for probabilistic modeling and decision-making in auction reserve pricing, enabling flexible prediction methods.

Findings

Outperforms previous methods in profit maximization

Scalable to large datasets with various prediction models

Effective on both simulated and real auction data

Abstract

Many online companies sell advertisement space in second-price auctions with reserve. In this paper, we develop a probabilistic method to learn a profitable strategy to set the reserve price. We use historical auction data with features to fit a predictor of the best reserve price. This problem is delicate - the structure of the auction is such that a reserve price set too high is much worse than a reserve price set too low. To address this we develop objective variables, a new framework for combining probabilistic modeling with optimal decision-making. Objective variables are "hallucinated observations" that transform the revenue maximization task into a regularized maximum likelihood estimation problem, which we solve with an EM algorithm. This framework enables a variety of prediction mechanisms to set the reserve price. As examples, we study objective variable methods with regression, kernelized regression, and neural networks on simulated and real data. Our methods outperform previous approaches both in terms of scalability and profit.