arXiv subjects

Farzin Ahmadi

Publications and source records attributed to Farzin Ahmadi.

6 recordsLinked to original sources

arXiv2026

From Non-Identifiability to Goal-Integrated Decision-Making in Parametric Inverse Optimization

Inverse optimization seeks to recover unknown objective parameters from observed decisions, yet fundamental questions about when recovery is possible have received limited formal treatment. This paper develops a comprehensive theoretical framework for inverse optimization in parametric convex models. We first establish that non-identifiability is the generic case: even with normalization and multiple observations, the parameter set compatible with data is generically multi-dimensional, and regularization does not resolve this. We derive necessary and sufficient conditions for identifiability. Motivated by these negative results, we introduce the Inverse Learning (IL) framework, which shifts the inferential target from the unknown parameter to the latent optimal solution, achieving a complexity reduction that is independent of the number of observations. IL explicitly characterizes the full set of compatible parameters rather than returning an arbitrary element. To address the tension between observational fidelity and constraint adherence, we formalize the Observation-Constraint Tradeoff and develop Goal-Integrated Inverse Learning models that enable structured navigation of this spectrum with guaranteed monotonicity. Numerical experiments demonstrate superior solution accuracy, higher parameter recovery rates, and significant computational speedups. We apply the framework to personalized dietary recommendations using NHANES data, proof-of-concept demonstrating improved glycemic control in a prospective feasibility study.

math.OC↗

arXiv2024

Improving Observed Decisions Quality using Inverse Optimization: A Radiation Therapy Treatment Planning Application

In many applied optimization settings, parameters that define the constraints may not guarantee the best possible solution, and superior solutions might exist that are infeasible for the given parameter values. Removing such constraints, re-optimizing, and evaluating the new solution may be insufficient, as the optimizer's preferences in selecting the existing solutions might be lost. To address this issue, we present an inverse optimization-based model that takes an observed solution as input and aims to improve upon it by projecting onto desired hyperplanes or expanding the feasible set while balancing the distance to the observed decision to preserve the optimizer's preferences. We demonstrate the applicability of the model in the context of radiation therapy treatment planning, an essential component of cancer treatment. Radiation therapy treatment planning is typically guided by expert-driven guidelines that define the optimization problem but remain mostly general. Our model provides an automated framework that learns new plans from available plans based on given clinical criteria, optimizing the desired effect without compromising the remaining constraints. The proposed approach is applied to a cohort of four prostate cancer patients, and the results demonstrate improvements in dose-volume histograms while maintaining comparable target coverage to clinically acceptable plans. By optimizing the parameters of the treatment planning problem and exploring the Pareto frontier, our methodology uncovers previously unattainable solutions that enhance organ-at-risk sparing without sacrificing target coverage. The framework's ability to handle multiple organs-at-risk and various dose-volume constraints highlights its flexibility and potential for application to diverse radiation therapy treatment planning scenarios.

math.OC↗

arXiv2023

Inverse Learning: Solving Partially Known Models Using Inverse Optimization

We consider the problem of learning optimal solutions of a partially known linear optimization problem and recovering its underlying cost function where a set of past decisions and the feasible set are known. We develop a new framework, denoted as Inverse Learning, that extends the inverse optimization literature to (1) learn the optimal solution of the underlying problem, (2) integrate additional information on constraints and their importance, and (3) control the balance between mimicking past behaviors and reaching new goals and rules for the learned solution. We pose inverse learning as an optimization problem that maps given (feasible and infeasible) observations to a single optimal solution with minimum perturbation, hence, not only recovering the missing cost vector but also providing an optimal solution simultaneously. The framework provides insights into an essential tradeoff in recovering linear optimization problems with regard to preserving observed behaviors and binding constraints of the known feasible set at optimality. We propose a series of mixed integer linear programming models to capture the effects of this tradeoff and validate it using a two-dimensional example. We then demonstrate the framework's applicability to a diet recommendation problem for a population of hypertension and prediabetic patients. The goal is to balance dietary constraints to achieve the necessary nutritional goals with the dietary habits of the users to encourage adherence to the diet. Results indicate that our models recommend daily food intakes that preserve the original data trends while providing a range of options to patients and providers based on the tradeoff.

math.OC↗

arXiv2022

You Are What You Eat: A Preference-Aware Inverse Optimization Approach

A key challenge in the emerging field of precision nutrition entails providing diet recommendations that reflect both the (often unknown) dietary preferences of different patient groups and known dietary constraints specified by human experts. Motivated by this challenge, we develop a preference-aware constrained-inference approach in which the objective function of an optimization problem is not pre-specified and can differ across various segments. Among existing methods, clustering models from machine learning are not naturally suited for recovering the constrained optimization problems, whereas constrained inference models such as inverse optimization do not explicitly address non-homogeneity in given datasets. By harnessing the strengths of both clustering and inverse optimization techniques, we develop a novel approach that recovers the utility functions of a constrained optimization process across clusters while providing optimal diet recommendations as cluster representatives. Using a dataset of patients' daily food intakes, we show how our approach generalizes stand-alone clustering and inverse optimization approaches in terms of adherence to dietary guidelines and partitioning observations, respectively. The approach makes diet recommendations by incorporating both patient preferences and expert recommendations for healthier diets, leading to structural improvements in both patient partitioning and nutritional recommendations for each cluster. An appealing feature of our method is its ability to consider infeasible but informative observations for a given set of dietary constraints. The resulting recommendations correspond to a broader range of dietary options, even when they limit unhealthy choices.

math.OC↗

arXiv2020

Optimal Resource and Demand Redistribution for Healthcare Systems Under Stress from COVID-19

When facing an extreme stressor, such as the COVID-19 pandemic, healthcare systems typically respond reactively by creating surge capacity at facilities that are at or approaching their baseline capacity. However, creating individual capacity at each facility is not necessarily the optimal approach, and redistributing demand and critical resources between facilities can reduce the total required capacity. Data shows that this additional load was unevenly distributed between hospitals during the COVID-19 pandemic, requiring some to create surge capacity while nearby hospitals had unused capacity. Not only is this inefficient, but it also could lead to a decreased quality of care at over-capacity hospitals. In this work, we study the problem of finding optimal demand and resource transfers to minimize the required surge capacity and resource shortage during a period of heightened demand. We develop and analyze a series of linear and mixed-integer programming models that solve variants of the demand and resource redistribution problem. We additionally consider demand uncertainty and use robust optimization to ensure solution feasibility. We also incorporate a range of operational constraints and costs that decision-makers may need to consider when implementing such a scheme. Our models are validated retrospectively using COVID-19 hospitalization data from New Jersey, Texas, and Miami, yielding at least an 85% reduction in required surge capacity relative to the observed outcome of each case. Results show that such solutions are operationally feasible and sufficiently robust against demand uncertainty. In summary, this work provides decision-makers in healthcare systems with a practical and flexible tool to reduce the surge capacity necessary to properly care for patients in cases when some facilities are over capacity.

math.OC↗

arXiv2020

An Open-Source Dataset on Dietary Behaviors and DASH Eating Plan Optimization Constraints

Linear constrained optimization techniques have been applied to many real-world settings. In recent years, inferring the unknown parameters and functions inside an optimization model has also gained traction. This inference is often based on existing observations and/or known parameters. Consequently, such models require reliable, easily accessed, and easily interpreted examples to be evaluated. To facilitate research in such directions, we provide a modified dataset based on dietary behaviors of different groups of people, their demographics, and pre-existing conditions, among other factors. This data is gathered from the National Health and Nutrition Examination Survey (NHANES) and complemented with the nutritional data from the United States Department of Agriculture (USDA). We additionally provide tailored datasets for hypertension and pre-diabetic patients as groups of interest who may benefit from targetted diets such as the Dietary Approaches to Stop Hypertension (DASH) eating plan. The data is compiled and curated in such a way that it is suitable as input to linear optimization models. We hope that this data and its supplementary, open-accessed materials can accelerate and simplify interpretations and research on linear optimization and constrained inference models. The complete dataset can be found in the following repository: https://github.com/CSSEHealthcare/InverseLearning

math.OC↗