Training models that perform well under distribution shifts is a central challenge in machine learning. In this paper, we introduce a modeling framework where, in addition to training data, we have partial structural knowledge of the shifted test distribution. We employ the principle of minimum discriminating information to embed the available prior knowledge, and use … Read more
We consider the stochastic dual dynamic programming (SDDP) algorithm, which is a widely employed algorithm applied to multistage stochastic programming, and propose a variant using batch learning, a technique used with success in the reinforcement learning framework. We cast SDDP as a type of Q-learning algorithm and describe its application in both risk neutral and … Read more
We consider the influence maximization problem (IMP) which asks for identifying a limited number of key individuals to spread influence in a social network such that the expected number of influenced individuals is maximized. The stochastic maximal covering location problem (SMCLP) formulation is a mixed integer programming formulation that effectively approximates the IMP by the … Read more
We propose a new solution method for two-stage mixed-integer recourse models. In contrast to existing approaches, we can handle general mixed-integer variables in both stages, and thus, e.g., do not require that the first-stage variables are binary. Our solution method is a Benders’ decomposition, in which we iteratively construct tighter approximations of the expected second-stage … Read more
In this paper, we investigate the Moreau envelope of the supremum of a family of convex, proper, and lower semicontinuous functions. Under mild assumptions, we prove that the Moreau envelope of a supremum is the supremum of Moreau envelopes, which allows us to approximate possibly nonsmooth supremum functions by smooth functions that are also the … Read more
We present JuDGE.jl, an open-source Julia package for solving multistage stochastic capacity expansion problems using Dantzig-Wolfe decomposition. Models for JuDGE.jl are built using JuMP, the algebraic modelling language in Julia, and solved by repeatedly applying mixed-integer programming. We illustrate JuDGE.jl by formulating and solving a toy knapsack problem, and demonstrate the performance of JuDGE.jl on … Read more
Efficient solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We describe the overall architecture and provide computational examples and results showing scalability to the largest instances that we know of for the … Read more
We propose a new universal framework for multi-stage decision making under limited information availability. It is developed as part of a larger research project which aims at providing analytical methods to compare and evaluate different models and algorithms for multi-stage decision making. In our setting, we have an open time horizon and limited information about … Read more
We consider a two player zero-sum game with stochastic linear constraints. The probability distributions of the vectors associated with the constraints are partially known. The available information with respect to the distribution is based mainly on the two first moments. In this vein, we formulate the stochastic linear constraints as distributionally robust chance constraints. We … Read more
Hurricanes can cause severe property damage and casualties in coastal regions. Diesel fuel plays a crucial role in hurricane disaster relief. It is important to optimize fuel supply chain operations so that emergency demand for diesel can be mitigated in a timely manner. However, it can be challenging to estimate demand for fuel and make … Read more