Will Ma Assistant Professor Decision, Risk, and Operations (DRO) division Graduate School of Business, Columbia University Email: wm2428 (at) gsb (dot) columbia (dot) edu Office: Kravis 951

Hi! I am an assistant professor in the Decision, Risk, and Operations division at Columbia Business School. Prior to July 2019, I was a postdoctoral researcher at Google Research. In July 2018, I received my Ph.D. from the MIT Operations Research Center.

I spent 2013-2015 as a co-founder of Lunarch Studios, the start-up that designed the strategy game Prismata. During those years, I had also been a research intern at Google, and a trading intern at Jane Street Capital.

I completed my undergraduate degree in 2010 from the University of Waterloo, majoring in Pure Mathematics and Combinatorics/Optimization. During that time, I competed in many international poker tournaments. In 2011 I founded the annual poker class at MIT, which can be accessed on MIT OpenCourseWare.

Research

Broadly speaking, I am interested in designing data-driven algorithms and analyzing their performance, usually in online decision-making settings. Specific topics from my recent focus include prophet inequalities and viewing assortment optimization through the lens of mechanism design.

My research is motivated by applications in revenue management, such as product recommendation, online and sequential assortment optimization, and selling reusable resources. I am also interested in supply chain management, especially pertaining to e-commerce fulfillment and rationing during shortages.

Below is a list of my available papers, sorted by topic. Please see my CV for a list of papers sorted by publication status.

Assortment Optimization and Mechanism Design

• When is Assortment Optimization Optimal?

  Management Science, 2022 (Articles in Advance)

  *One-page abstract forthcoming in the Proceedings of the 23rd ACM conference on Economics and Computation (EC), 2022

  *2nd Place, Rothkopf Junior Researcher Paper Prize for Auctions and Market Design, 2021

  *Selected for spotlight presentation in the INFORMS Revenue Management and Pricing Conference, 2022

  *Selected for presentation in the INFORMS Market Design Workshop at EC, 2021

  *Selected for presentation in the MSOM Service SIG, 2021

  *Selected for oral presentation in the Market Innovation Workshop, 2021

• Revenue-Optimal Deterministic Auctions for Multiple Buyers with Ordinal Preferences over Fixed-Price Items

  ACM Transactions on Economics and Computation (TEAC), Forthcoming

  *Invited submission from the Proceedings of the 16th Conference on Web and Internet Economics (WINE), 2020

• Separation between Second Price Auctions with Personalized Reserves and the Revenue Optimal Auction with Balasubramanian Sivan

  Operations Research Letters, 2020

Prophet Inequalities

• Tight Guarantees for Multi-unit Prophet Inequalities and Online Stochastic Knapsack with Jiashuo Jiang, Jiawei Zhang

  *Preliminary version appeared in the Proceedings of the 33rd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2022

  *Jiashuo Jiang was a Finalist for the Jeff McGill Student Paper Award for Revenue Management and Pricing, 2021

• Improved Guarantees for Offline Stochastic Matching via new Ordered Contention Resolution Schemes with Brian Brubach, Nathaniel Grammel, Aravind Srinivasan

  *Preliminary version appeared in the Proceedings of the 35th Conference on Neural Information Processing Systems (NeurIPS), 2021

• Tight Guarantees for Static Threshold Policies in the Prophet Secretary Problem with Nick Arnosti

  Operations Research, Major Revision

  *One-page abstract forthcoming in the Proceedings of the 23rd ACM conference on Economics and Computation (EC), 2022

Online and Stochastic Matching

• Follow Your Star: New Frameworks for Online Stochastic Matching with Known and Unknown Patience with Brian Brubach, Nathaniel Grammel, Aravind Srinivasan

  Operations Research, Major Revision

  *Preliminary version appeared in the Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS), 2021

• Algorithms for Online Matching, Assortment, and Pricing with Tight Weight-dependent Competitive Ratios with David Simchi-Levi

  Operations Research, 2020

  *One-page abstract, Tight Weight-dependent Competitive Ratios for Online Edge-weighted Bipartite Matching and Beyond, appeared in the Proceedings of the 20th ACM conference on Economics and Computation (EC), 2019

  *Finalist, George E. Nicholson Student Paper Competition, 2017

Online and Stochastic Knapsack

• A Competitive Analysis of Online Knapsack Problems with Unit Density with David Simchi-Levi, Jinglong Zhao

  *Jinglong Zhao earned an Honorable Mention in the POMS Hong Kong Student Paper Competition, 2020

• Improvements and Generalizations of Stochastic Knapsack and Markovian Bandits Approximation Algorithms

  Mathematics of Operations Research, 2018

  *Preliminary version, Improvements and Generalizations of Stochastic Knapsack and Multi-armed Bandit Approximation Algorithms, appeared in the Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2014

  *Honorable Mention, INFORMS Optimization Society Student Paper Competition, 2017

• See also Tight Guarantees for Multi-unit Prophet Inequalities and Online Stochastic Knapsack under "Prophet Inequalities" above.

Bundling

• Constructing Demand Curves from a Single Observation of Bundle Sales with David Simchi-Levi

  Operations Research, Major Revision

  *1st Place, INFORMS Data Mining Section Best Student Paper Competition---Applied Track, 2018

• Reaping the Benefits of Bundling under High Production Costs with David Simchi-Levi

  Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS), 2021

Other Revenue Management

• Bifurcating Constraints to Improve Approximation Ratios for Network Revenue Management with Reusable Resources with Jackie Baek

  Operations Research, 2022 (Articles in Advance)

  *One-page abstract, Prophet Inequalities on the Intersection of a Matroid and a Graph, appeared in the Proceedings of the 12th International Symposium on Algorithmic Game Theory (SAGT), 2019

• Inventory Balancing with Online Learning with Wang Chi Cheung, David Simchi-Levi, Xinshang Wang

  Management Science, 2022

• Dynamic Pricing (and Assortment) under a Static Calendar with David Simchi-Levi, Jinglong Zhao

  Management Science, 2021

• On Policies for Single-leg Revenue Management with Limited Demand Information with David Simchi-Levi, Chung-Piaw Teo

  Operations Research, 2021

• Assortment Planning for Recommendations at Checkout under Inventory Constraints with Xi Chen, David Simchi-Levi, Linwei Xin

  Mathematics of Operations Research, under 3rd Round Review

  *Covered in Chicago Booth Review, 2018

  *1st Place, Chinese Scholars Association for Management Science and Engineering (CSAMSE) Best Paper Award sponsored by Columbia Business School, 2017

  *2nd Place, POMS Hong Kong Student Paper Competition, 2017

• Multi-Stage and Multi-Customer Assortment Optimization With Inventory Constraints with Elaheh Fata, David Simchi-Levi

Operations Research, Major Revision

Optimization Theory

• Distributionally Robust Linear and Discrete Optimization with Marginals with Louis Chen, Karthik Natarajan, David Simchi-Levi, Zhenzhen Yan

  Operations Research, 2022 (Articles in Advance)

• The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification with Christian Tjandraatmadja, Ross Anderson, Joey Huchette, Krunal Patel, Juan Pablo Vielma

  Proceedings of the 34th Conference on Neural Information Processing Systems (NeurIPS), 2020

• Strong Mixed-Integer Programming Formulations for Trained Neural Networks with Ross Anderson, Joey Huchette, Christian Tjandraatmadja, Juan Pablo Vielma

  Math Programming, 2020

• Distributionally Robust Max Flows with Louis Chen, Jim Orlin, David Simchi-Levi

  Proceedings of the 3rd ACM-SIAM Symposium on Simplicity in Algorithms (SOSA), 2020

Fairness in Online Matching

• Fairness Maximization among Offline Agents in Online-Matching Markets with Pan Xu, Yifan Xu

  *One-page abstract appeared in the Proceedings of the 17th Conference on Web and Internet Economics (WINE), 2021

• Group-level Fairness Maximization in Online Bipartite Matching with Pan Xu, Yifan Xu

  *Preliminary version appeared in the Proceedings of the 21st International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS), 2022

Video Games

• Optimizing for Strategy Diversity in the Design of Video Games with Oussama Hanguir, Christopher Thomas Ryan

• Predicting User Choice in Video Games with Arjun Khandelwal, David Simchi-Levi, and in partnership with Prismata

  These are the presentation slides from Arjun's UROP at MIT.

Other

• A Geometric Approach to Combinatorial Fixed-point Theorems with Elyot Grant

  Proceedings of the 7th European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB), 2013

• The Approximability and Integrality Gap of Interval Stabbing and Independence Problems with Shalev Ben-David, Elyot Grant, Malcolm Sharpe

  Proceedings of the 24th Canadian Conference on Computational Geometry (CCCG), 2012

• Packing and Covering Triangles in Planar Graphs with Qing Cui, Penny Haxell

  Graphs and Combinatorics, 2009