We consider multistage robust linear optimization problems with time-varying exogenous ellipsoidal uncertainty sets. We show the problems can be equivalently reformulated into single-level second-order cone optimization problems. We also show a case study on optimal bidding to allocate electricity resources to day-ahead and real-time energy markets.

We consider two-stage robust linear programs with uncertain righthand side.
We develop a General Polyhedral Approximation (GPA), in which the uncertainty set U is substituted by a finite set of polytopes derived from the vertex set of an arbitrary polytope that dominates U.
We analyse and computationally test the performance of GPA for the budgeted uncertainty set U (with m rows).
El Housni et al. showed that for budgeted uncertainty affine policies are best possible approximations.
In practice calculating affine policies typically requires inhibitive running times.
Therefore an approximation of U by a single simplex has been proposed by Ben-Tal et al..
GPA maintains the low practical running times of the simplex based approach while improving the quality of approximation by a constant factor.
The generality of our method allows to use any polytope dominating U (including the simplex).
We provide a family of polytopes that allows for a trade-off between running time and approximation factor.
The previous simplex based approach reaches a threshold at the square root of m after which it is not better than a quasi nominal solution.
Before this threshold, GPA significantly improves the approximation factor.
After the threshold, it is the first fast method to outperform the quasi nominal solution.

We study the problem of modeling purchase of multiple products and utilizing it to display optimized recommendations for online retailers and e-commerce platforms. Rich modeling of users and fast computation of optimal products to display given these models can lead to significantly higher revenues and simultaneously enhance the user experience. We present a parsimonious multi-purchase family of choice models called the BundleMVL-K family, and develop a binary search based iterative strategy that efficiently computes optimized recommendations for this model. We establish the hardness of computing optimal recommendation sets, and derive several structural properties of the optimal solution that aid in speeding up computation. This is one of the first attempts at operationalizing multi-purchase class of choice models. We show one of the first quantitative links between modeling multiple purchase behavior and revenue gains. The efficacy of our modeling and optimization techniques compared to competing solutions is shown using several real world datasets on multiple metrics such as model fitness, expected revenue gains and run-time reductions. For example, the expected revenue benefit of taking multiple purchases into account is observed to be ∼ 5\% in relative terms for the Ta Feng and UCI shopping datasets, when compared to the MNL model for instances with ∼ 1500 products. Additionally, across 6 real world datasets, the test log-likelihood fits of our models are on average 17\% better in relative terms. Our work contributes to the study multi-purchase decisions, analyzing consumer demand and the retailers optimization problem. The simplicity of our models and the iterative nature of our optimization technique allows practitioners meet stringent computational constraints while increasing their revenues in practical recommendation applications at scale, especially in e-commerce platforms and other marketplaces.

The advent of generative AI and foundational models has opened up promising avenues to enhance the efficiency of many service systems. However, their wider application has been stymied by the persistent presence of model errors and inaccuracies. These errors represent an intrinsic characteristic of current AI models, and not just a transient hurdle. In this talk, we present a Robust Optimization based approach that embraces this reality and seeks to optimize performance within this context.
We present a Robust optimization-based algorithmic framework and develop the Fast Algorithm for Classification and Truth-validation (FACT), which aims to address the critical need for rigorous truth-validation in service systems. FACT is designed to leverage the decision-making competencies of both humans and foundational Large Language Models (LLMs) through a dynamic task routing strategy, informed by task complexity, projected cost, and the capacity of the decision-making entity.
We present our results from a pilot implementation at a customer service portal of an online education company, which demonstrates significant efficiency benefits. This approach offers a promising trajectory for future research and practical implementations, especially in the context of systems where AI and human decision-making must be effectively integrated.