International Workshop on Stochastic Optimization
Summary Report
The International Workshop on Stochastic Optimization was successfully held from July 6 to July 12, 2025, at the Tianyuan Mathematical International Exchange Center in Kunming, Yunnan. The event was attended by 28 scholars and experts from institutions including: Georgia Institute of Technology (USA), The University of Hong Kong, The Chinese University of Hong Kong, Hong Kong Polytechnic University, Shanghai Jiao Tong University, Tongji University, Shanghai University of Finance and Economics, Xi’an Jiaotong University, Nanjing University, Nanjing Normal University, Nanjing University of Posts and Telecommunications, Dalian University of Technology, Sun Yat-sen University, Chongqing University, Chongqing Normal University, Chongqing Jiaotong University, Inner Mongolia University, Xiangtan University, Hunan First Normal University.
The workshop featured in-depth discussions and knowledge exchange on cutting-edge developments in stochastic optimization, promoting international collaboration in this rapidly evolving field.
The workshop included nine one-hour keynote presentations, six one-hour thematic discussions, and two half-day free discussion sessions.
In the keynote presentations:
Professor Guanghui Lan from Georgia Institute of Technology presented his latest research findings titled "Algorithmic Foundations of Risk-Averse Optimization for Trustworthy AI".
Professor Huifu Xu from The Chinese University of Hong Kong delivered a presentation on "Statistical Robustness in Machine Learning and Matrix Optimization".
Professor Enlu Zhou from Georgia Institute of Technology presented "Bayesian Approaches to Stochastic Optimal Control under Distributional Uncertainty".
Professor Yunhe Hou from The University of Hong Kong presented "Navigating Uncertainty in the New Energy Paradigm: From Classical Models to Endogenous and Contextual Decision-Making Methods".
Professor Zhiping Chen from Xi'an Jiaotong University presented "A Bayesian Composite Risk Approach for Stochastic Optimal Control and Markov Decision Processes".
Professor Caihua Chen from Nanjing University on "Robust Solutions to Two Stage Stochastic Programming"
Professor Jia Liu from Xi'an Jiaotong University on "Stochastic Dominance Constrained MDPs: Tractable Sample Approximations and Convergence Guarantees"
Professor Xiao Wang from Sun Yat-sen University on "Stochastic augmented Lagrangian methods for nonconvex constrained optimization"
Associate Professor Jiani Wang from Beijing University of Posts and Telecommunications on "Stochastic Gradient Methods for Solving a Class of Composite Stochastic Minimax Problems"
Through the keynote presentations and focused discussions, participating experts conducted extensive and in-depth exchanges on cutting-edge research directions in stochastic optimization models, algorithmic theories and their applications in artificial intelligence. Additionally, lively discussions were held on how to promote interdisciplinary research in stochastic optimization, machine learning, artificial intelligence, power systems and other related fields.
During the thematic discussion session, Professors Huifu Xu, Guanghui Lan, Enlu Zhou, Yunhe Hou, Zhiping Chen, and Xiaojiao Tong carefully listened to the research introductions and discussion topics presented by young scholars, and provided guidance for their research work. The participating experts and young scholars also conducted in-depth discussions on:
1. The role of stochastic optimization models and algorithmic theories in promoting interdisciplinary development
2. Applications of stochastic optimization theories in power systems, machine learning, and artificial intelligence
3. The opportunities and challenges for the development of stochastic optimization models and algorithms in the AI era
The experts particularly emphasized their hope that more mathematicians would engage in interdisciplinary research on theories and algorithms combining artificial intelligence and stochastic optimization, and further promote applied research of stochastic optimization in fields such as power, transportation, and economic management.
The main research directions reported and discussed during the workshop included:
1. Risk-averse stochastic optimization theory and algorithms for trustworthy AI
In machine learning and AI, most existing models still prioritize minimizing expected loss, making AI-driven decisions prone to costly or catastrophic failures and raising concerns about algorithm reliability in high-risk applications. Experts focused on: Foundations of risk-averse optimization algorithms and risk-aware decision theories, such as stochastic optimization problems based on L_p risk and spectral risk measures; Improving model solvability, developing stochastic approximation algorithms with provable convergence guarantees and establishing fundamental complexity bounds.
2. Statistical robustness in machine learning and stochastic optimization
In data-driven practical problems, observed sample data is often contaminated due to measurement errors, recording mistakes, or unexpected events. This raises a key question: whether statistical estimators based on observed data possess statistical robustness - can their empirical distributions remain stable against data perturbations? During the discussions, experts examined statistical robustness of kernel learning estimators when training data may be perturbed or corrupted, for example: Qualitative statistical robustness of estimators for broad convex cost functions when all training data may be perturbed under certain topological structures; Quantitative statistical robustness of estimators when cost functions are twice continuously differentiable and convex; Statistical robustness of sample covariance matrices; Sparse estimation of precision matrices (inverse covariance matrices) and their applications in financial engineering.
3. Bayesian Approaches to Stochastic Optimal Control and Markov Decision Processes: Theory and Applications
The participating experts examined Bayesian methods for solving stochastic optimal control (SOC) problems where the underlying distributions are unknown but can be estimated via streaming data. To address computational challenges, a phased solution approach was proposed: periodically updating posterior distributions while solving Bayesian counterpart problems under fixed posteriors within each cycle. Discussions also covered integrated SOC-Markov decision process (MDP) models that employ Bayesian composite risk (BCR) measures to assess risks arising from both epistemic and aleatory uncertainties. The experts explored the integration of various existing SOC/MDP frameworks and introduced novel models with corresponding solution algorithms and theoretical guarantees.
4. Modeling and Computational Methods for Stochastic Optimization in Modern Power Systems
Against the backdrop of power systems with high renewable energy penetration, the experts discussed optimization modeling and computational methodologies addressing dual uncertainties in generation-load balance and carbon emission constraints, with particular focus on: Renewable energy planning, Operational dispatch strategies, System resilience enhancement.
Two emerging paradigms were analyzed:
(1) Decision-dependent uncertainty (DDU): Particularly critical for long-term strategic decisions like renewable capacity expansion—where investment choices alter future power flow patterns and market prices—or proactive maintenance scheduling—where maintenance actions directly influence component failure probabilities.
(2) Context-aware stochastic optimization: This approach customizes predictive models for specific decision tasks by leveraging contextual features to generate system-optimized decisions that maintain efficiency even under high-dimensional and heterogeneous uncertainties.
The participating experts unanimously agreed that the new developments in stochastic optimization models and algorithms have enhanced the role of mathematical optimization in the fields of artificial intelligence and power systems. This workshop highlighted the critical role of stochastic optimization as a fundamental tool in AI and energy transition. Moreover, case studies of collaboration between academia and industry demonstrated that theoretical innovations need to be closely integrated with real-world system requirements, and that interdisciplinary teams are the core driving force behind successful technology implementation. It was recommended that future efforts should further strengthen cooperation among experts from different disciplines.
The Tianyuan Mathematics International Exchange Center provided an excellent environment and superior facilities for the workshop. The thoughtful services and professional support from the center's staff ensured the successful organization of this event. The organizing committee would like to express our sincere gratitude to all the staff members!