August 5, 2025Mathematics0 citationsOpen Access

LLM-Guided Ensemble Learning for Contextual Bandits with Copula and Gaussian Process Models

Key Points

Core finding shows LLM-guided policies minimize regret and maximize rewards in complex environments.
Evaluation of four decision policies revealed that Thompson sampling excelled with lower cumulative regret compared to Epsilon-greedy.
Simulation integrates Gaussian Process models, copulas, and GARCH processes to enhance decision-making adaptability.
Results indicate combining probabilistic models with LLM guidance advances performance in skewed and high-variance reward settings.

Abstract

Contextual multi-armed bandits (CMABs) are vital for sequential decision-making in areas such as recommendation systems, clinical trials, and finance. We propose a simulation framework integrating Gaussian Process (GP)-based CMABs with vine copulas to model dependent contexts and GARCH processes to capture reward volatility. Rewards are generated via copula-transformed Beta distributions to reflect complex joint dependencies and skewness. We evaluate four policies—ensemble, Epsilon-greedy, Thompson, and Upper Confidence Bound (UCB)—over 10,000 replications, assessing cumulative regret, observed reward, and cumulative reward. While Thompson sampling and LLM-guided policies consistently minimize regret and maximize rewards under varied reward distributions, Epsilon-greedy shows instability, and UCB exhibits moderate performance. Enhancing the ensemble with copula features, GP models, and dynamic policy selection driven by a large language model (LLM) yields superior adaptability and performance. Our results highlight the effectiveness of combining structured probabilistic models with LLM-based guidance for robust, adaptive decision-making in skewed, high-variance environments.

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