Session: Distributional Shift and Systemic Risk
Chair: Lai Tian
Cluster: nan
Talk 1: Sample-average approximations for systemic risk measures
Speaker: Çağın Ararat
Abstract: We investigate the convergence properties of sample-average approximations (SAA) for set-valued systemic risk measures. We assume that the systemic risk measure is defined using a general aggregation function with some continuity properties and value-at-risk applied as a monetary risk measure. Our focus is on the theoretical convergence of its SAA under Wijsman and Hausdorff topologies for closed sets. After building the general theory, we provide an in-depth study of an important special case where the aggregation function is defined based on the Eisenberg-Noe network model. In this case, we provide mixed-integer programming formulations for calculating the SAA sets via their weighted-sum and norm-minimizing scalarizations. When value-at-risk is replaced with expectation, we also provide lower bounds on the required sample size for a sufficiently close SAA with high probability. Based on joint works with Wissam AlAli and Nurtai Meimanjan.
Talk 2: Mixed-feature Logistic Regression Robust to Distribution Shifts
Speaker: Qingshi Sun
Abstract: Logistic regression models are widely used in the social and behavioral sciences and in high-stakes domains, due to their simplicity and interpretability properties. At the same time, such domains are permeated by distribution shifts, where the distribution generating the data changes between training and deployment. In this paper, we study a distributionally robust logistic regression problem that seeks the model that will perform best against adversarial realizations of the data distribution drawn from a suitably constructed Wasserstein ambiguity set. Our model and solution approach differ from prior work in that we can capture settings where the likelihood of distribution shifts can vary across features, significantly broadening the applicability of our model relative to the state-of-the-art. We propose a graph-based solution approach that can be integrated into off-the-shelf optimization solvers. We evaluate the performance of our model and algorithms on numerous publicly available datasets. Our solution achieves a 408x speed-up relative to the state-of-the-art. Additionally, compared to the state-of-the-art, our model reduces average calibration error by up to 36.19% and worst-case calibration error by up to 41.70%, while increasing the average area under the ROC curve (AUC) by up to 18.02% and worst-case AUC by up to 48.37%.
Talk 3: Stabilizing Stochastic Programs with Rockafellian Relaxation: Theoretical Results and Chance-Constrained Applications
Speaker: Lai Tian
Abstract: Solutions of a stochastic optimization problem tend to change disproportionally under small changes to its probability distribution. This sensitivity is particularly concerning, as it is virtually impossible to identify the “correct” distribution in real-world applications. In this talk, we demonstrate how Rockafellian relaxations provide a principled and effective approach to improving the stability of solutions under distributional changes. Unlike previous efforts that primarily focus on finite or discrete distributions, our framework accommodates general Borel probability measures and handles discontinuous integrands, such as those arising in chance-constrained formulations. These advances broaden the scope of robust solution techniques in modern stochastic optimization.
