\(\) Motivated by recent progress on online linear programming (OLP), we study the online decision making problem (ODMP) as a natural generalization of OLP. In ODMP, there exists a single decision maker who makes a series of decisions spread out over a total of \(T\) time stages. At each time stage, the decision maker makes … Read more
Adjustable Robust Optimization (ARO) is a paradigm for facing uncertainty in a decision problem, in case some recourse actions are allowed after the actual value of all input parameters is revealed. While several approaches have been introduced for the linear case, little is known regarding exact methods for the convex case. In this work, we … Read more
Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (Math. Program., 2018) to solve a special class of two-stage stochastic programs with binary recourse. In this setting, the … Read more
In a real Hilbert space V, the conic hull of G is the set cone(G) consisting of all nonnegative linear combinations of elements of G. Many optimization problems are sensitive to the changes in cone(G) that result from changes in G itself. Motivated by one such problem, we derive necessary and sufficient conditions for the … 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
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. In particular, we propose to consider a distributionally robust formulation based on causal transport distance. Compared with divergence and Wasserstein metric, the causal transport distance is better at capturing the information structure revealed from the conditional distribution … Read more
We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to solve due to its inherent non-convexity. In this paper, we demonstrate that, under mild conditions, the robust risk evaluation of … Read more
We consider a generalization of two-stage decision problems in which the second-stage decision may be a function of a predictive signal but cannot adapt fully to the realized uncertainty. We will show how such problems can be learned from sample data by considering a family of regularized sample average formulations. Furthermore, our regularized data-driven formulations … Read more
Uncertainty in classical stochastic programming models is often described solely by independent random parameters, ignoring their dependence on multidimensional features. We describe a novel contextual chance-constrained programming formulation that incorporates features, and argue that solutions that do not take them into account may not be implementable. Our formulation cannot be solved exactly in most cases, … Read more