[Archimedes Talks Series] A Multi-Dimensional Online Contention Resolution Scheme for Revenue Maximization

Title: A Multi-Dimensional Online Contention Resolution Scheme for Revenue Maximization 

Speaker: Dimitris Christou, PhD Student at UT Austin 

Abstract: We study multi-buyer multi-item sequential item pricing mechanisms for online revenue maximization with the goal of approximating a natural fractional relaxation – the ex ante optimal revenue. We assume that buyers’ values are subadditive but make no assumptions on the value distributions. While the optimal revenue, and therefore also the ex ante benchmark, is inapproximable by any simple mechanism in this context, previous work has shown that a weaker benchmark that optimizes over so-called “buy-many” mechanisms can be approximated. Approximations are known, in particular, for settings with either a single buyer or many unit-demand buyers. We extend these results to the much broader setting of many subadditive buyers. We show that the ex ante buy-many revenue can be approximated via sequential item pricings to within an $O(log^2 m)$ factor, where m is the number of items. We also show that a logarithmic dependence on m is necessary. Our approximation is achieved through the construction of a new multi-dimensional Online Contention Resolution Scheme (OCRS), that provides an online rounding of the optimal ex ante solution.  

Bio: Dimitris Christou is a 3rd year Computer Science PhD student at UT Austin. He is fortunate to be advised by Prof. Shuchi Chawla. Prior to joining UT Austin, he received a Diploma in Electrical and Computer Engineering from the National Technical University of Athens, supervised by Prof. Dimitris Fotakis. During that time, he completed two research internships offered by the LIP6 Research Institute at Sorbonne University, France. His research interests lie in the intersection of Online Algorithms, Economics and Data-Driven algorithmic design. His previous work resolves open questions for online decision making, server problems, multistage optimisation and learning-augmented algorithms. His current work focuses on problems in the intersection of Online Decision Making and Economics, such as the Pandora’s Box problem and Online Revenue Maximization.