Related papers: Benders, Nested Benders and Stochastic Programming…
Many tasks can be easily solved using machine learning techniques. However, some tasks cannot readily be solved using statistical models, requiring a symbolic approach instead. Program induction is one of the ways that such tasks can be…
A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively splits the set of classes into two subsets, and trains a binary classifier to distinguish…
The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space $\Omega$ by an integral over the unit line $[0,1]$ by employing a push-forward with respect to a suitable transformation.…
Robot-assisted surgery has made great progress with the development of medical imaging and robotics technology. Medical scene understanding can greatly improve surgical performance while the semantic segmentation of the robotic instrument…
We propose a novel approach to solve K-adaptability problems with convex objective and constraints and integer first-stage decisions. A logic-based Benders decomposition is applied to handle the first-stage decisions in a master problem,…
Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…
Real-world decision-making problems often involve decision-dependent uncertainty, where the probability distribution of the random vector depends on the model decisions. Few studies focus on two-stage stochastic programs with this type of…
Several structural learning algorithms for staged tree models, an asymmetric extension of Bayesian networks, have been defined. However, they do not scale efficiently as the number of variables considered increases. Here we introduce the…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Stochastic acceptors or probabilistic automata are stochastic automata without output that can model components in machine learning…
Current bundle adjustment solvers such as the Levenberg-Marquardt (LM) algorithm are limited by the bottleneck in solving the Reduced Camera System (RCS) whose dimension is proportional to the camera number. When the problem is scaled up,…
Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression…
This paper considers optimization problems over networks where agents have individual objectives to meet, or individual parameter vectors to estimate, subject to subspace constraints that require the objectives across the network to lie in…
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…
We study a stochastic and distributed algorithm for nonconvex problems whose objective consists of a sum of $N$ nonconvex $L_i/N$-smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
Supply chain transportation operations often account for a large proportion of product total cost to market. Such operations can be optimized by solving the Logistics Service Network Design Problem (LSNDP), wherein a logistics service…
We study a ranking and selection problem of learning from choice-based feedback with dynamic assortments. In this problem, a company sequentially displays a set of items to a population of customers and collects their choices as feedback.…
This paper proposes a data-driven version of the Benders decomposition algorithm applied to the stochastic unit commitment (SUC) problem. The proposed methodology aims at finding a trade-off between the size of the Benders master problem…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…