LLM Agents for Combinatorial Efficient Frontiers: Investment Portfolio Optimization

2026-01-02

arXiv.org

AI Summary

This work addresses cardinality-constrained mean-variance portfolio optimization (CCPO), an NP-hard mixed-integer quadratic programming problem traditionally tackled by manually designed heuristics. For the first time, we introduce a large language model (LLM)-driven multi-agent framework to this domain, enabling automated construction of optimization workflows and generation of efficient frontier solutions without human intervention. By integrating domain knowledge from combinatorial optimization and financial engineering, our approach explores diverse agent collaboration mechanisms to autonomously synthesize algorithms and streamline the optimization pipeline. Empirical evaluations on standard benchmarks demonstrate that the proposed method matches the performance of state-of-the-art heuristics while substantially reducing development effort, and maintains acceptable approximation error even in worst-case scenarios.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work
• 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

Abstract

Investment portfolio optimization is a task conducted in all major financial institutions. The Cardinality Constrained Mean-Variance Portfolio Optimization (CCPO) problem formulation is ubiquitous for portfolio optimization. The challenge of this type of portfolio optimization, a mixed-integer quadratic programming (MIQP) problem, arises from the intractability of solutions from exact solvers, where heuristic algorithms are used to find approximate portfolio solutions. CCPO entails many laborious and complex workflows and also requires extensive effort pertaining to heuristic algorithm development, where the combination of pooled heuristic solutions results in improved efficient frontiers. Hence, common approaches are to develop many heuristic algorithms. Agentic frameworks emerge as a promising candidate for many problems within combinatorial optimization, as they have been shown to be equally efficient with regard to automating large workflows and have been shown to be excellent in terms of algorithm development, sometimes surpassing human-level performance. This study implements a novel agentic framework for the CCPO and explores several concrete architectures. In benchmark problems, the implemented agentic framework matches state-of-the-art algorithms. Furthermore, complex workflows and algorithm development efforts are alleviated, while in the worst case, lower but acceptable error is reported.

Problem

• Portfolio Optimization
• Combinatorial Optimization
• Mean-Variance
• Cardinality Constraint
• Heuristic Algorithms

Innovation

• LLM agents
• combinatorial optimization
• portfolio optimization
• heuristic algorithms
• efficient frontiers