Hyperparameter Optimisation of Convex Portfolio Trajectories Using Large Language Models

Multi-period portfolio allocation often requires solving complex convex trajectory optimisation problems where hyperparameters dictate the critical trade-offs between expected returns, risk aversion, and temporal reallocation smoothness. Identifying the optimal hyperparameter configuration is challenging due to the computationally expensive evaluation of simulated economic regimes and the non-convex nature of the resulting hyperparameter landscape. In this paper, we introduce a novel Hybrid Search methodology that combines the contextual reasoning capabilities of Large Language Models (LLMs) with the precise local exploitation of quadratic surrogate models. Evaluated across four distinct simulated economic regimes, our approach demonstrates statistically significant improvements in optimisation efficacy and sample efficiency compared to standard grid search, random search, and pure LLM-guided search. Specifically, the LLM proposes candidate hyperparameters based on historical evaluation traces, providing an adaptive search mechanism that complements traditional surrogate modelling. The Hybrid Search achieves the highest mean objective score of 0.022688, requiring only 3.1 evaluations to reach the 95% performance threshold. This work bridges the gap between generative AI and quantitative finance, providing a robust, sample-efficient framework for financial hyperparameter tuning.