Research

Research Papers

1. Decision-Focused Optimal Transport

   Suhan Liu, Mo Liu To be submitted. [arXiv]

   • "STOP" using L2 norm for optimal transport
   • "STOP" using Wasserstein distance — we need a decision-focused divergence.
   • "STOP" using $\frac{\mu+\nu}{2}$ as the average of two probability measures — we need a decision-focused average.

   We propose a new metric, termed decision-focused divergence, to quantify the distance between two distributions.

   • The estimation error bound is independent of the dimension of the distributions.
   • In the newsvendor problem, the decision-focused divergence is zero whenever the critical quantiles coincide, even if the distributions differ.
   • For any random vector $X$ and random variable $Y$, the decision-focused divergence between $X$ and $X \times Y$ is zero.
2. Decision-Focused Bias Correction for Fluid Approximation

   Can Er, Mo Liu. To be submitted. [arXiv]

   • "STOP" using fluid approximation for capacity planning — we need decision-corrected arrival rates

   This paper revisits fluid approximations in queueing systems and multi-product newsvendor problems from a capacity-sizing perspective.

   • Fluid approximation can be biased with respect to decision-making.
   • Should one plug in a time-varying arrival rate to replace the original demand arrival distribution when designing capacity for multi-server systems? (Short answer: No.)
   • Does a decision-corrected fluid approximation always exist? (Short answer: No.)
   • Does a (vectorized) point prediction always exist for multi-product multi-customer newsvendor problems? (Short answer: No.)
   • We provide necessary and sufficient conditions for the existence of the decision-corrected arrival rate.
3. Decision-Focused Sequential Experiment Design: A Directional Uncertainty-Guided Approach

   Beichen Wan, Mo Liu, Paul Grigas, Zuo-Jun Max Shen. Working paper. [arXiv] Preliminary version at [NeurIPS 2025 Workshop] [Poster]

   • "STOP" quantifying prediction uncertainty for data collection — we need decision-focused uncertainty quantification

   Traditional uncertainty quantification is often decision-blind. We introduce a directional uncertainty measure that aligns with downstream optimization problem.

   • Simply quantifying prediction uncertainty can be decision-blind.
   • The proposed criterion is computationally tractable and does not require solving optimization oracles.
   • Under certain distributions, it yields smaller sample complexity than decision-blind designs.
   • We establish strong consistency and convergence guarantees.
4. Marginal Value of One Data Point in Assortment Personalization

   Mo Liu, Junyu Cao, Zuo-Jun Max Shen. Resubmitted to Management Science. [SSRN] [Slides]

   • "STOP" assuming more (i.i.d.) data leads to higher revenue — better prediction can worsen decisions

   We study the marginal value of adding a single data point in personalized assortment optimization.

   • The marginal revenue contribution of a new customer can be negative.
   • By evaluating marginal contributions, we identify informative customers and reduce the training set size by about 80% while maintaining similar revenue.

1. Active Learning For Contextual Linear Optimization: A Margin-Based Approach

   Mo Liu, Paul Grigas, Heyuan Liu, Zuo-Jun Max Shen. Major Revision at Management Science. [arXiv] [Slides]

   • How to identify informative samples for decision-making.
   • Best Student Paper Nominee at INFORMS Workshop on Data Science 2023.
   • Second Place Poster Prize at [YinzOR 2023](https://yinzor.cmuinforms.org/).
2. Learning from Click Transition Data: Effectiveness of Greedy Pricing Policy under Dynamic Product Availability

   Mo Liu, Junyu Cao, Zuo-Jun Max Shen. Major Revision at Management Science. [SSRN]

   • Finalist at 2023 INFORMS Service Science Student Competition.
   • Fan Favorite Flash Talk at [YinzOR 2023](https://yinzor.cmuinforms.org/).
3. Inventory Management with LLM: Automated Decision-Making for Order Timing and Quantity

   Mo Liu, Yumo Bai, Meng Qi, Zuo-Jun Max Shen. Major Revision at Service Science. [SSRN]

4. A Re-solving Heuristic for Dynamic Assortment Optimization with Knapsack Constraints

   Xi Chen, Mo Liu, Yining Wang, Yuan Zhou. Accepted by Production and Operations Management. [arXiv]