Session: AI Meets Optimization (Part 3)
Chair: Wotao Yin
Cluster: Optimization for Emerging Technologies (LLMs, Quantum Computing, ...)
Talk 1: OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling
Speaker: Zhonglin Xie
Abstract: Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language descriptions (NL). This data scarcity also contributes to the generalization difficulties experienced by learning-based methods. To address these challenges, we propose a scalable framework for synthesizing a high-quality dataset, named OptMATH. Starting from curated seed data with mathematical formulations (MF), this framework automatically generates problem data (PD) with controllable complexity. Then, a back-translation step is employed to obtain NL. To verify the correspondence between the NL and the PD, a forward modeling step followed by rejection sampling is used. The accepted pairs constitute the training part of OptMATH. Then a collection of rejected pairs is identified and further filtered. This collection serves as a new benchmark for optimization modeling, containing difficult instances whose lengths are much longer than those of NL4OPT and MAMO. Through extensive experiments, we demonstrate that models of various sizes (0.5B–32B parameters) trained on OptMATH achieve superior results on multiple modeling benchmarks, thereby validating the effectiveness and scalability of our approach.
Talk 2: LMask: Learn to Solve Constrained Routing Problems with Lazy Masking
Speaker: Tianyou Li
Abstract: Routing problems are canonical combinatorial optimization tasks with wide-ranging applications in logistics, transportation, and supply chain management. However, efficiently generating high-quality feasible solutions for routing problems with complex constraints remains a challenging goal in practice. In this talk, we introduce LMask, a novel unsupervised learning framework that utilizes a dynamic masking mechanism to solve constrained routing problems effectively. The decoding method of LMask lazily refines feasibility masks to guide the auto-regressive neural network decoder with backtracking. By incorporating mask embedding into the transformer-based model architecture, LMask enhances constraint awareness and generalization across routing problems. To reduce computational costs during training, we limit the number of backtracking steps while the constraints are satisfied as much as possible, and penalize the violations in the loss function. We provide theoretical guarantees for the validity and probabilistic optimality of our approach. Extensive experiments show that LMask achieves state-of-the-art feasibility rates and solution quality compared to existing neural methods.
Talk 3: Learning to Optimize in a Changing World
Speaker: Ming Jin
Abstract: This talk introduces a unified framework for adaptive optimization in nonstationary environments, where objectives, constraints, and formulations evolve over time. We begin by detailing a meta-learning approach to safe reinforcement learning that employs a two-timescale structure for rapid policy adaptation with formal safety guarantees. Applications in critical load restoration and cybersecurity penetration testing demonstrate its effectiveness in sequential constrained decision-making. We then extend these principles to classical optimization, introducing methods for dynamically adapting objectives, solution spaces, and penalty terms based on prior problem instances. Finally, we explore how large language models can be integrated to autoformalize high-level problem specifications and manage ambiguity via uncertainty-aware planning. These capabilities broaden access to optimization tools and introduce new modes of interaction with dynamic, human-centric systems.
