arXiv subjects

Man Yiu Tsang

Publications and source records attributed to Man Yiu Tsang.

6 recordsLinked to original sources

arXiv2025

Contextual Quantile Minimization for Two-Stage Stochastic Programs

Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a random loss, in many applications, risk-averse decision-makers may be interested in minimizing a specific quantile as a more prudent alternative. In this paper, we propose a new risk-averse contextual stochastic optimization problem with a quantile objective for general two-stage problems. Given historical data on the model's random parameters and contextual information, we model the conditional quantile by replacing the conditional expectation in its variational characterization with a generic estimator. Under two sets of mild regularity conditions, we derive the asymptotic almost-sure convergence and convergence in probability of the optimal solution and the optimal value of the associated optimization problem to their true counterparts. Optimization problems with a quantile objective is usually non-convex, which are generally regarded as challenging to solve. To address the computational difficulties, we propose a new stochastic inexact constraint generation method with convergence guarantee. Finally, through numerical experiments on a single-server appointment scheduling problem, we study the computational performance of our proposed solution method as well as operational performance of our proposed methodology. Our results demonstrate the importance of incorporating useful contextual information and decision-maker's risk attitude into the optimization model.

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arXiv2025

A Unified Framework for Analyzing and Optimizing a Class of Convex Fairness Measures

We propose a new framework that unifies different fairness measures into a general, parameterized class of convex fairness measures suitable for optimization contexts. First, we propose a new class of order-based fairness measures, discuss their properties, and derive an axiomatic characterization for such measures. Then, we introduce the class of convex fairness measures, discuss their properties, and derive an equivalent dual representation of these measures as a robustified order-based fairness measure over their dual sets. Importantly, this dual representation renders a unified mathematical expression and an alternative geometric characterization for convex fairness measures through their dual sets. Moreover, it allows us to develop a unified framework for optimization problems with a convex fairness measure objective or constraint, including unified reformulations and solution methods. In addition, we provide stability results that quantify the impact of employing different convex fairness measures on the optimal value and solution of the resulting fairness-promoting optimization problem. Finally, we present numerical results demonstrating the computational efficiency of our unified framework over traditional ones and illustrating our stability results.

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arXiv2025

On the Trade-Off Between Distributional Belief and Ambiguity: Conservatism, Finite-Sample Guarantees, and Asymptotic Properties

We propose and analyze a new data-driven trade-off (TRO) approach for modeling uncertainty that serves as a middle ground between the optimistic approach, which adopts a distributional belief, and the pessimistic distributionally robust optimization approach, which hedges against distributional ambiguity. We equip the TRO model with a TRO ambiguity set characterized by a size parameter controlling the level of optimism and a shape parameter representing distributional ambiguity. We first show that constructing the TRO ambiguity set using a general star-shaped shape parameter with the empirical distribution as its star center is necessary and sufficient to guarantee the hierarchical structure of the sequence of TRO ambiguity sets. Then, we analyze the properties of the TRO model, including quantifying conservatism, quantifying bias and generalization error, and establishing asymptotic properties. Specifically, we show that the TRO model could generate a spectrum of decisions, ranging from optimistic to conservative decisions. Additionally, we show that it could produce an unbiased estimator of the true optimal value. Furthermore, we establish the almost-sure convergence of the optimal value and the set of optimal solutions of the TRO model to their true counterparts. We exemplify our theoretical results using an inventory control problem and a portfolio optimization problem.

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arXiv2024

Stochastic Optimization Approaches for an Operating Room and Anesthesiologist Scheduling Problem

We propose combined allocation, assignment, sequencing, and scheduling problems under uncertainty involving multiple operation rooms (ORs), anesthesiologists, and surgeries, as well as methodologies for solving such problems. Specifically, given sets of ORs, regular anesthesiologists, on-call anesthesiologists, and surgeries, our methodologies solve the following decision-making problems simultaneously: (1) an allocation problem that decides which ORs to open and which on-call anesthesiologists to call in, (2) an assignment problem that assigns an OR and an anesthesiologist to each surgery, and (3) a sequencing and scheduling problem that determines the order of surgeries and their scheduled start times in each OR. To address uncertainty of each surgery's duration, we propose and analyze stochastic programming (SP) and distributionally robust optimization (DRO) models with both risk-neutral and risk-averse objectives. We obtain near-optimal solutions of our SP models using sample average approximation and propose a computationally efficient column-and-constraint generation method to solve our DRO models. In addition, we derive symmetry-breaking constraints that improve the models' solvability. Using real-world, publicly available surgery data and a case study from a health system in New York, we conduct extensive computational experiments comparing the proposed methodologies empirically and theoretically, demonstrating where significant performance improvements can be gained. Additionally, we derive several managerial insights relevant to practice.

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arXiv2022

An inexact column-and-constraint generation method to solve two-stage robust optimization problems

We propose a new inexact column-and-constraint generation (i-C&CG) method to solve two-stage robust optimization problems. The method allows solutions to the master problems to be inexact, which is desirable when solving large-scale and/or challenging problems. It is equipped with a backtracking routine that controls the trade-off between bound improvement and inexactness. Importantly, this routine allows us to derive theoretical finite convergence guarantees for our i-C&CG method. Numerical experiments demonstrate computational advantages of our i-C&CG method over state-of-the-art column-and-constraint generation methods.

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arXiv2022

Adaptive Robust Online Portfolio Selection

The online portfolio selection (OLPS) problem differs from classical portfolio model problems, as it involves making sequential investment decisions. Many OLPS strategies described in the literature capture market movement based on various beliefs and are shown to be profitable. In this paper, we propose a robust optimization (RO)-based strategy that takes transaction costs into account. Moreover, unlike existing studies that calibrate model parameters from benchmark data sets, we develop a novel adaptive scheme that decides the parameters sequentially. With a wide range of parameters as input, our scheme captures market uptrend and protects against market downtrend while controlling trading frequency to avoid excessive transaction costs. We numerically demonstrate the advantages of our adaptive scheme against several benchmarks under various settings. Our adaptive scheme may also be useful in general sequential decision-making problems. Finally, we compare the performance of our strategy with that of existing OLPS strategies using both benchmark and newly collected data sets. Our strategy outperforms these existing OLPS strategies in terms of cumulative returns and competitive Sharpe ratios across diversified data sets, demonstrating its adaptability-driven superiority.

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