One popular approach to access the importance/influence of a group of nodes in a network is based on the notion of centrality. For a given group, its group betweenness centrality is computed, first, by evaluating a ratio of shortest paths between each node pair in a network that are “covered” by at least one node … Read more
This paper focuses on complete dictionary learning problem, where the goal is to reparametrize a set of given signals as linear combinations of atoms from a learned dictionary. There are two main challenges faced by theoretical and practical studies of dictionary learning: the lack of theoretical guarantees for practically-used heuristic algorithms, and their poor scalability … Read more
We consider dynamic gas transport optimization problems, which lead to large-scale and nonconvex mixed-integer nonlinear optimization problems (MINLPs) on graphs. Usually, the resulting instances are too challenging to be solved by state-of-the-art MINLP solvers. In this paper, we use graph decompositions to obtain multiple optimization problems on smaller blocks, which can be solved in parallel … Read more
Bilevel optimization recently has received tremendous attention due to its great success in solving important machine learning problems like meta learning, reinforcement learning, and hyperparameter optimization. Extending single-agent training on bilevel problems to the decentralized setting is a natural generalization, and there has been a flurry of work studying decentralized bilevel optimization algorithms. However, it … Read more
Two-stage robust optimization problems constitute one of the hardest optimization problem classes.One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets, and optimizesdecisions corresponding to each of these subsets. In general case, it is solved using the … Read more
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We study network flow interdiction problems with nonlinear and nonconvex flow models. The resulting model is a max-min bilevel optimization problem in which the follower’s problem is nonlinear and nonconvex. In this game, the leader attacks a limited number of arcs with the goal to maximize the load shed and the follower aims at minimizing … Read more
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Wasserstein distributionally robust optimization (DRO) finds robust solutions by hedging against data perturbation specified by distributions in a Wasserstein ball. The robustness is linked to the regularization effect, which has been studied for continuous losses in various settings. However, existing results cannot be simply applied to the 0-1 loss, which is frequently seen in uncertainty … Read more
We consider stochastic optimization with side information where, prior to decision-making, covariate data are available to inform better decisions. To hedge against data uncertainty while capturing the information structure revealed from the conditional distribution of random problem parameters given the covariate values, we propose a distributionally robust formulation based on causal transport distance. We derive … Read more