SOLID: a Framework of Synergizing Optimization and LLMs for Intelligent Decision-Making

2025-11-19

AI Summary

This paper addresses two critical challenges in intelligent decision-making: the disconnection between semantic understanding and numerical optimization, and the difficulty of ensuring data privacy. To this end, we propose a modular framework that synergistically integrates mathematical optimization with large language models (LLMs). Methodologically, we introduce a dual-price mechanism and a deviation penalty term to enable multi-round iterative interaction between the optimizer and the LLM: the optimizer generates dual variables as structured prompts for the LLM, which then outputs semantic constraints or policy suggestions grounded in contextual understanding; these are fed back to the optimization layer. Crucially, raw data never crosses module boundaries, preserving privacy. Theoretically, the framework retains convergence guarantees and informs the design of interpretable prompts. Empirical evaluation on stock investment demonstrates that our approach significantly improves annualized return over pure optimization baselines while maintaining stable convergence across diverse scenarios.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Privacy
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

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.

Problem

• Synergizing optimization and LLMs for intelligent decision-making
• Improving decision quality while maintaining modularity and privacy
• Enhancing automated decision-making with theoretical convergence guarantees

Innovation

• Integrating mathematical optimization with large language models
• Iterative collaboration via dual prices and deviation penalties
• Maintaining modularity and data privacy while improving decisions