Distributed Optimization Under Uncertainty: A Cross-Paradigm Review and Future Directions

Due to its significant importance in many disciplines, distributed optimization under uncertainty has become an active research field over the past decade. This paper presents a cross-paradigm review of this development. We organize the literature around three approaches ordered by how much is known about the uncertainty: robust optimization, which uses set or support information; distributionally robust optimization, which uses partial distributional knowledge; and stochastic programming, which uses an estimated or specified distribution. These are regions of a spectrum rather than disjoint classes, and formulations that combine them are noted where they arise. For each approach, we examine modeling frameworks and distributed algorithmic adaptations, together with representative applications across different domains. We synthesize methodological trends, compare algorithmic properties, and identify open challenges for scalable distributed algorithms under uncertainty. Key findings include the widespread adaptation of classical algorithms, particularly the alternating direction method of multipliers (ADMM), across all uncertainty paradigms, alongside an evolution toward data-driven and adaptive methods for real-time uncertainty handling. We also highlight that many advanced centralized techniques for optimization under uncertainty remain only partially adapted to distributed settings, representing a significant research opportunity. Of the 112 reviewed studies falling within the 2015–2025 eligibility window, 59.8% address power and energy systems, 12.5% federated and distributed learning, and 5.4% robotics and autonomous systems, while other application domains contribute only isolated studies. The paper concludes with critical gaps and future directions spanning distributed reformulations, machine learning integration, multi-stage optimization, privacy-preserving computation, and cross-domain methodological unification.