Season 7 

Counterfactual analysis is a powerful tool in explainable machine learning. Given a prediction model and an input record, one seeks a minimal perturbation (with respect to a prescribed metric) of the record such that the prediction for the perturbed instance attains a specified threshold value. This can be formulated as a mathematical optimization problem, whose structural properties depend on the prediction model and the feature space. It is typically assumed that the feature values are unaffected by measurement or aggregation errors, that the counterfactual intervention can be implemented exactly, and that the prediction coincides with the ground-truth value of the response variable. When these assumptions fail, robustness considerations become essential to ensure that the resulting counterfactual explanation is reliable. In this talk, I will review recent research on this topic developed jointly with Renato de Leone (University of Camerino), Marica Magagnini (University of Camerino), and Antonio Navas-Orozco (University of Seville). The focus will be on the corresponding optimization problems and on the approaches proposed to (heuristically) solve them.

Emilio is Full Professor of Statistics and Operations Research at the University of Seville. His research focuses on Mathematical Optimization, Operations Research, and Data Science, with applications in industrial and applied mathematics. He is President of math-in, the Spanish Network for Industrial Mathematics, and has previously served as Director of IMUS, the Institute of Mathematics of the University of Seville, and President of SEIO, the Spanish Society of Statistics, Operations Research and Data Science. He also served as Editor-in-Chief of TOP, the Society’s journal in Operations Research. He is the author of more than 150 publications, including articles in leading journals such as Operations Research, Mathematical Programming, Management Science, and Mathematics of Operations Research. He is actively engaged in knowledge transfer and industrial collaborations across the energy, health, logistics, and technology sectors.

In this talk, we present new perspectives on distributionally robust optimization (DRO) by considering multimodal ambiguity sets and decision-dependent uncertainties with models, solution algorithms, and applications. We first provide a two-stage DRO model with multimodal uncertainty, where both the mode probabilities and uncertainty distributions could be affected by the first-stage decisions. To address this setting, we propose a generic framework by introducing a phi-divergence based ambiguity set to characterize the decision-dependent mode probabilities and consider both moment-based and Wasserstein distance-based ambiguity sets to characterize the uncertainty distribution under each mode. We identify two special phi-divergence examples (variation distance and χ2-distance) and provide specific forms of decision dependence relationships under which we can derive tractable reformulations. Furthermore, we investigate the benefits of considering multimodality in a DRO model compared to a single-modal counterpart through an analytical analysis. Additionally, we develop a separation-based decomposition algorithm to solve the resulting DRO models with finite convergence and optimality guarantee under certain settings. We provide a detailed computational study over two example problem settings, facility location problem and shipment planning problem with pricing, to illustrate our results, which demonstrate that omission of multimodality or decision-dependent uncertainties within DRO frameworks result in inadequately performing solutions with worse in-sample and out-of-sample performances under various settings. We further demonstrate the speed-ups obtained by the solution algorithm against the off-the-shelf solver over various instances. Additionally, we present another application of DRO under decision-dependent uncertainty through a capacity expansion planning problem considering the chicken-and-egg dilemma under uncertain market conditions. We derive tractable reformulations of this problem under certain settings and develop a tailored algorithm based on the column-and-constraint generation approach providing computationally efficient solution approaches. 

Beste Basciftci is an Assistant Professor at the Department of Business Analytics at the Tippie College of Business at the University of Iowa. She is broadly interested in data-driven decision-making problems under uncertainty by developing mixed-integer/discrete optimization, stochastic programming, and distributionally robust optimization approaches to address methodological and computational challenges arising in operations research and management related problems. Main application areas of her research include energy systems and sustainability, supply chains and facility location problems, and emerging transportation and sharing systems. She obtained her PhD in operations research from the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology and obtained bachelor's degrees in industrial engineering and computer engineering (double major) from Bogazici University with High Honors. She has received various recognitions for her research including INFORMS ENRE (Energy, Natural Resources and the Environment Section) Early Career Best Paper Award Runner-up, IISE Transactions Best Paper Award in Focus Issue of Operations Engineering & Analytics, Tippie College of Business Social Impact Research Award, University of Iowa Early Career Scholar Award, and Georgia Tech ISyE Alice and John Jarvis Research Award. Her research is supported by the National Science Foundation and is honored to be elected to the Board of the INFORMS Computing Society and to the Committee on Stochastic Programming of the Mathematical Optimization Society.

We consider a fundamental generalization of the classical newsvendor problem where the seller needs to decide on the inventory of a product jointly for multiple locations on a metric as well as a fulfillment policy to satisfy the uncertain demand that arises sequentially over time after the inventory decisions have been made. To address the distributional-ambiguity, we consider a distributionally robust setting where the decision-maker only knows the mean and variance of the demand, and the goal is to make inventory and fulfillment decisions to minimize the worst-case expected inventory and fulfillment cost (where the expectation is taken over the worst case choice of distribution with given mean and variance).  

We present a significant generalization of the classical result of Scarf (1958) and give a policy with strong theoretical guarantees as well as good practical performance while maintaining the simplicity and interpretability of the solution in Scarf (1958). In particular, our policy first identifies a hierarchical clustering of the locations, and assigns a "virtual-underage cost" for each cluster. Our inventory solution ensures that for each cluster, the total inventory in the cluster is at least as large as the inventory level suggested by Scarf's solution for the virtual-underage cost if the cluster was a single point. We present a worst-case performance guarantee for our policy and also demonstrate that the policy performs well in practice. To the best of our knowledge, this is the first algorithm with provable performance guarantees.  

(This is joint work with Ayoub Foussoul)

Vineet Goyal is Professor in the Industrial Engineering and Operations Research Department at Columbia University where he joined in 2010 after his PhD in Algorithms, Combinatorics, and Optimization (ACO) from Carnegie Mellon University in 2008 and Postdoc at the Operations Research Center at MIT. He is interested in the design of efficient and robust data-driven algorithms for large scale dynamic optimization problems with applications in revenue management, health care and resource allocation problems. His research has been continually supported by grants from NSF, DARPA and industry including NSF CAREER Award in 2014 and faculty research awards from Google, IBM, Adobe, and Amazon.