Uncertainty-Aware Test-Time Search for Optimization Problem Solving
Linlin Yu Augusta University, Xujiang Zhao NEC Labs America, Dong Li, Yanchi Liu NEC-Labs, Wei Cheng NEC-Labs, Zhengzhang Chen NEC Labs America, Chen Zhao Baylor University, Feng Chen University of Texas, Dallas 等 9 位作者
Automatically solving optimization problems from natural language descriptions with both efficiency and reliability is highly desirable but remains challenging. Language model hallucinations and the limited availability of labeled datasets often result in misaligned formulations, code errors, and feasibility failures We propose UMCTS, an Uncertainty-aware Monte Carlo Tree Search framework that combines the language understanding capability of large language models with the reliability of well-established solvers. UMCTS structures the solution process into four stages: global instruction, assumptions, mathematical formulation, and solver code generation. It employs Monte Carlo Tree Search with semantic-equivalence pruning, prior-guided exploration, and solver-based feasibility checks. An LLM judge provides numerical reward signals, qualitative error information, and uncertainty estimates. These signals are backpropagated to guide the search and flag unreliable outputs. Across six public benchmarks, UMCTS achieves state-of-the-art solution accuracy, improves efficiency by reducing token usage.
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Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表