Graphical Regularized Quantile Regression With Reinforcement Learning

Abstract

Time series forecasting is a fundamental task in scientific and engineering disciplines. Quantile regression (QR) has gained substantial popularity due to its flexibility in modeling conditional distributions without stringent parametric assumptions. However, traditional QR approaches often overlook the geometric dependencies and structural relationships among predictors, leading to suboptimal performance in complex forecasting scenarios. To address this gap, this paper proposes a novel framework that integrates graphical regularization with sparse quantile regression, enhanced by an $ϵ$-greedy reinforcement learning (RL) strategy for efficient parameter tuning. Our model incorporates a graph Laplacian matrix to preserve spatial structures among predictors while maintaining the robustness of QR. The resulting optimization problem is solved efficiently using the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Empirical studies on real-world electricity market datasets (Belgian and American markets) demonstrate that our approach, designated as RL-RG-SCAD(0.5), significantly outperforms state-of-the-art statistical and deep learning models. These improvements are rigorously validated by Diebold-Mariano tests, Giacomini-White tests, and Hansen's superior predictive ability test. The framework offers enhanced accuracy and interpretability by effectively leveraging predictor structures.