Session: Contextual Stochastic Optimization under Streaming Data and Decision Dependency
Chair: Guzin Bayraksan
Cluster: Optimization Under Uncertainty and Data-driven Optimization
Talk 1: Residuals-Based Contextual Distributionally Robust Optimization with Decision-Dependent Uncertainty
Speaker: Xian Yu
Abstract: We consider a residuals-based distributionally robust optimization model, where the underlying uncertainty depends on both covariate information and our decisions. We adopt regression models to learn the latent decision dependency and construct a nominal distribution (thereby ambiguity sets) around the learned model using empirical residuals from the regressions. Ambiguity sets can be formed via the Wasserstein distance, a sample robust approach, or with the same support as the nominal empirical distribution (e.g., phi-divergences), where both the nominal distribution and the radii of the ambiguity sets could be decision- and covariate-dependent. We provide conditions under which desired statistical properties, such as asymptotic optimality, rates of convergence, and finite sample guarantees, are satisfied. Via cross-validation, we devise data-driven approaches to find the best radii for different ambiguity sets, which can be decision-(in)dependent and covariate-(in)dependent. Through numerical experiments, we illustrate the effectiveness of our approach and the benefits of integrating decision dependency into a residuals-based DRO framework.
Talk 2: Distribution-Free Algorithms for Predictive Stochastic Programming in the Presence of Streaming Data
Speaker: Suvrajeet Sen
Abstract: This work studies a fusion of concepts from stochastic programming and nonparametric statistical learning in which data is available in the form of covariates interpreted as predictors and responses. Such models are designed to impart greater agility, allowing decisions under uncertainty to adapt to the knowledge of predictors (leading indicators). This work studies two classes of methods: one of the methods may be classified as a first-order method, whereas the other studies piecewise linear approximations. In addition, our study incorporates several non-parametric estimation schemes, including k nearest neighbors (kNN) and other standard kernel estimators. Our computational results demonstrate that the new algorithms outperform traditional approaches which were not designed for streaming data applications requiring simultaneous estimation and optimization. (This work was performed as part of the first author's doctoral dissertation.)
Talk 3: An Alternating Optimization Method for Contextual Distributionally Robust Optimization under Streaming Data
Speaker: Guzin Bayraksan
Abstract: We consider data-driven decision-making that incorporates a prediction model within the 1-Wasserstein distributionally robust optimization (DRO) given joint observations of uncertain parameters and covariates using regression residuals in a streaming-data setting. In this setting, additional data become available and allow decisions to adapt to the growing knowledge of the underlying uncertainty. The ambiguity set shrinks as more data is observed. We propose an efficient online optimization method for this streaming-data contextual DRO setting, which iteratively alternates between optimizing the decision and determining the worst-case distribution. We analyze the asymptotic convergence properties of this algorithm and establish dynamic regret bounds to certify the performance of online solutions. Through numerical experiments, we validate our theoretical findings and demonstrate that our approach significantly enhances computational efficiency while maintaining high solution quality under streaming data.
