  This paper presents a novel optimization framework to address key challenges
presented by modern machine learning applications: High dimensionality,
distributional uncertainty, and data heterogeneity. Our approach unifies
regularized estimation, distributionally robust optimization (DRO), and
hierarchical Bayesian modeling in a single data-driven criterion. By employing
a hierarchical Dirichlet process (HDP) prior, the method effectively handles
multi-source data, achieving regularization, distributional robustness, and
borrowing strength across diverse yet related data-generating processes. We
demonstrate the method's advantages by establishing theoretical performance
guarantees and tractable Monte Carlo approximations based on Dirichlet process
(DP) theory. Numerical experiments validate the framework's efficacy in
improving and stabilizing both prediction and parameter estimation accuracy,
showcasing its potential for application in complex data environments.
