Scenario Tree Design under Wasserstein and Fused GromovWasserstein Distances

Ayşenur Karagöz

A central challenge in multi-stage stochastic programs (MSP) lies in constructing scenario trees that approximate the underlying stochastic process with sufficient accuracy while maintaining computational tractability. In this work, we consider the case where the true stochastic process is discretely distributed, and the topology of the approximating scenario tree is fixed. We propose two novel scenario tree approximation methods grounded in optimal transport theory. The first approach minimizes the stagewise Wasserstein distance between the empirical distributions of the true process, ensuring stage-by-stage closeness. The second approach leverages the Fused Gromov-Wasserstein (FGW) distance, which integrates both the feature-level differences (captured by the Wasserstein distance) and structural discrepancies (captured by the GromovWasserstein distance) between distributions. This is particularly suitable for scenario trees, which are structured objects combining probabilistic and topological information. Both approaches formulate the scenario tree generation as a continuous, nonconvex optimization problem. To solve this, we employ a block coordinate descent method that alternates between optimizing over the discrete distribution assignments and the associated cost structure. This enables efficient computation while preserving fidelity to the underlying stochastic process. Our methods offer a principled way to balance the trade-off between approximation accuracy and computational feasibility.

Short Bio

Ayşenur Karagöz is an Assistant Professor in the Industrial Engineering Department at Bilkent University. She obtained her PhD from the Department of Computational Applied Mathematics and Operations Research at Rice University, with a joint appointment at MD Anderson Cancer Center. Her interdisciplinary research specializes in stochastic optimization methodologies applied to healthcare, particularly in cancer treatment planning. Her expertise includes polyhedral theory for stochastic mixedinteger programs and scenario tree design. She earned her BS and MS from Bilkent University.

Venue

Friday, December 12, 2025, 4.00 pm

IE Building, Halim Doğrusöz Auditorium (IE 03)