Abstract
Distributionally robust optimization (DRO) provides a powerful framework for decision-making under uncertainty by focusing on worst-case scenarios within a prescribed ambiguity set. This makes it well-suited for addressing challenges involving data uncertainty. In this thesis, we apply scenario-wise DRO techniques to different domains: federated learning, transportation network design, and inventory management.The first part introduces a novel Distributionally Robust Federated Learning (DRFL) model. This model applies DRO techniques to overcome the challenges posed by data heterogeneity and distributional ambiguity. We derive a tractable reformulation for DRFL and develop first-order methods to efficiently solve the problem in a federated setting. Our experimental results demonstrate that DRFL outperforms standard FL models under data heterogeneity and ambiguity. We also showcase the scalability of the proposed first-order methods compared to a state-of-the-art commercial solver.
The second part studies the service network design problem, focusing on the ferry service network design (FSND) problem as an illustrative application. The FSND problem involves optimizing passenger flows and ferry schedules under uncertain demand, which is difficult to model, particularly in different scenarios with varying conditions such as weather. To address this, we propose a scenario-based joint chance-constrained model that leverages scenario-wise moment and support set information. We reformulate the uncertainty quantification into a convex problem, which can be solved efficiently. Besides, we introduce the optimistic uncertainty quantification as a new evaluation metric for solutions' performance to the FSND problem, and for given scenario weights, derive its conic reformulation. In numerical experiments, we compare the performance of our proposed method with existing approaches, and analyze the impact of scenario-wise information.
In the third part, we extend the DRO framework to inventory management by considering an ambiguity set of uncertain mean and covariance. In particular, we construct the ambiguity set by using the Wasserstein distance and the Kullback–Leibler divergence to capture distributional uncertainty, and reformulate the problem as a finite-dimensional copositive program. We further improve the model by introducing a weighting mechanism that connects it with classical sample average approximation, particularly effective when dealing with large datasets. Numerical studies on the Newsvendor problem demonstrate that this approach is both computationally efficient and competitive in terms of solution quality and runtime.
In conclusion, this thesis demonstrates the flexibility and strength of scenario-wise DRO in tackling uncertainty across diverse fields. By leveraging scenario-wise information, each model provides robust and efficient solutions to optimization problems, offering significant improvements over existing methods.
| Date of Award | 13 May 2025 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Chin Pang HO (Supervisor) & Zhi Chen (External Co-Supervisor) |