The predict-then-optimize framework is fundamental in practical stochastic decision-making problems: first predict unknown parameters of an optimization model, then solve the problem using the predicted values. A natural loss function in this setting is defined by measuring the decision error induced by the predicted parameters, which was named the Smart Predict-then-Optimize (SPO) loss by Elmachtoub and Grigas [2021]. Since the SPO loss is typically nonconvex and possibly discontinuous, Elmachtoub and Grigas [2021] introduced a convex surrogate, called the SPO+ loss, that importantly accounts for the underlying structure of the optimization model. In this paper, we greatly expand upon the consistency results for the SPO+ loss provided by Elmachtoub and Grigas [2021]. We develop risk bounds and uniform calibration results for the SPO+ loss relative to the SPO loss, which provide a quantitative way to transfer the excess surrogate risk to excess true risk. By combining our risk bounds with generalization bounds, we show that the empirical minimizer of the SPO+ loss achieves low excess true risk with high probability. We first demonstrate these results in the case when the feasible region of the underlying optimization problem is a polyhedron, and then we show that the results can be strengthened substantially when the feasible region is a level set of a strongly convex function. We perform experiments to empirically demonstrate the strength of the SPO+ surrogate, as compared to standard $\ell_1$ and squared $\ell_2$ prediction error losses, on portfolio allocation and cost-sensitive multi-class classification problems.

Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively transforming the stochastic optimization problem into a deterministic one. This two-stage framework is built on the assumption that more accurate predictions result in solutions that are closer to the actual optimal solution. However, providing evidence for this assumption in the context of complex, constrained optimization problems is challenging and often overlooked in the literature. Simulating predictions of machine learning models offers a way to (experimentally) analyze how prediction error impacts solution quality without the need to train real models. Complementing an algorithm from the literature for simulating binary classification, we introduce a new algorithm for simulating predictions of multiclass classifiers. We conduct a computational study to evaluate the performance of these algorithms, and show that classifier performance can be simulated with reasonable accuracy, although some variability is observed. Additionally, we apply these algorithms to assess the performance of a Predict-Then-Optimize algorithm for a machine scheduling problem. The experiments demonstrate that the relationship between prediction error and how close solutions are to the actual optimum is non-trivial, highlighting important considerations for the design and evaluation of decision-making systems based on machine learning predictions.

Recently, using Large Language Models (LLMs) to generate optimization models from natural language descriptions has became increasingly popular. However, a major open question is how to validate that the generated models are correct and satisfy the requirements defined in the natural language description. In this work, we propose a novel agent-based method for automatic validation of optimization models that builds upon and extends methods from software testing to address optimization modeling . This method consists of several agents that initially generate a problem-level testing API, then generate tests utilizing this API, and, lastly, generate mutations specific to the optimization model (a well-known software testing technique assessing the fault detection power of the test suite). In this work, we detail this validation framework and show, through experiments, the high quality of validation provided by this agent ensemble in terms of the well-known software testing measure called mutation coverage.

However, generally designed schematic iterations may hard to investigate complex data distributions in real-world applications. Recently, training deep propagations (i.e., networks) has gained promising

This paper introduces SOLID (Synergizing Optimization and Large Language Models for Intelligent Decision-Making), a novel framework that integrates mathematical optimization with the contextual capabilities of large language models (LLMs). SOLID facilitates iterative collaboration between optimization and LLMs agents through dual prices and deviation penalties. This interaction improves the quality of the decisions while maintaining modularity and data privacy. The framework retains theoretical convergence guarantees under convexity assumptions, providing insight into the design of LLMs prompt. To evaluate SOLID, we applied it to a stock portfolio investment case with historical prices and financial news as inputs. Empirical results demonstrate convergence under various scenarios and indicate improved annualized returns compared to a baseline optimizer-only method, validating the synergy of the two agents. SOLID offers a promising framework for advancing automated and intelligent decision-making across diverse domains.

Recent advances in large language models (LLMs) have accelerated research on automated optimization modeling. While real-world decision-making is inherently uncertain, most existing work has focused on deterministic optimization with known parameters, leaving the application of LLMs in uncertain settings largely unexplored. To that end, we propose the DAOpt framework including a new dataset OptU, a multi-agent decision-making module, and a simulation environment for evaluating LLMs with a focus on out-of-sample feasibility and robustness. Additionally, we enhance LLMs' modeling capabilities by incorporating few-shot learning with domain knowledge from stochastic and robust optimization.

However, generally designed schematic iterations may hard to investigate complex data distributions in real-world applications. Recently, training deep propagations (i.e., networks) has gained promising

Tianyi Lin and Chenyou Fan contributed equally to this work.

Fruits and vegetables form a vital component of the global economy; however, their distribution poses complex logistical challenges due to high perishability, supply fluctuations, strict quality and safety standards, and environmental sensitivity. In this paper, we propose an adaptive optimization model that accounts for delays, travel time, and associated temperature changes impacting produce shelf life, and compare it against traditional approaches such as Robust Optimization, Distributionally Robust Optimization, and Stochastic Programming. Additionally, we conduct a series of computational experiments using Internet of Things (IoT) sensor data to evaluate the performance of our proposed model. Our study demonstrates that the proposed adaptive model achieves a higher shelf life, extending it by over 18\% compared to traditional optimization models, by dynamically mitigating temperature deviations through a temperature feedback mechanism. The promising results demonstrate the potential of this approach to improve both the freshness and efficiency of logistics systems an aspect often neglected in previous works.

Visual navigation is a fundamental problem in embodied AI, yet practical deployments demand long-horizon planning capabilities to address multi-objective tasks. A major bottleneck is data scarcity: policies learned from limited data often overfit and fail to generalize OOD. Existing neural network-based agents typically increase architectural complexity that paradoxically become counterproductive in the small-sample regime. This paper introduce NeuRO, a integrated learning-to-optimize framework that tightly couples perception networks with downstream task-level robust optimization. Specifically, NeuRO addresses core difficulties in this integration: (i) it transforms noisy visual predictions under data scarcity into convex uncertainty sets using Partially Input Convex Neural Networks (PICNNs) with conformal calibration, which directly parameterize the optimization constraints; and (ii) it reformulates planning under partial observability as a robust optimization problem, enabling uncertainty-aware policies that transfer across environments. Extensive experiments on both unordered and sequential multi-object navigation tasks demonstrate that NeuRO establishes SoTA performance, particularly in generalization to unseen environments. Our work thus presents a significant advancement for developing robust, generalizable autonomous agents.