Graphical regularized quantile regression with Reinforcement Learning

He Jiang（通讯作者）， Qiang Liu

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 modelingconditional distributions without stringent parametric assumptions. However, traditionalQR approaches often overlook the geometric dependencies and structural relationshipsamong predictors, leading to suboptimal performance in complex forecastingscenarios. To address this gap, this paper proposes a novel framework that integratesgraphical regularization with sparse quantile regression, enhanced by an  greedy reinforcement learning (RL) strategy for efficient parameter tuning. Our model incorporatesa graph Laplacian matrix to preserve spatial structures among predictors while maintainingthe robustness of QR. The resulting optimization problem is solved efficiently usingthe 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 outperformsstate-of-the-art statistical and deep learning models. These improvements arerigorously validated by Diebold-Mariano tests, Giacomini-White tests, and Hansen’sSuperior Predictive Ability test. The framework offers enhanced accuracy and interpretabilityby effectively leveraging predictor structures.