Stochastic Physical Search (SPS) refers to the search for an item in a physical environment where the item's price is stochastic, and where the cost to obtain the item includes both travel and purchase costs. This type of problem models task planning scenarios where the cost of completing an objective at a location is drawn from a probability distribution, reflecting the influence of unknown factors. Prior work on this domain has focused on solutions where the expected cost is minimized. Recently, SPS problems with other objectives have been proposed and theoretically analyzed, in particular when either the budget or the desired probability of success is fixed. However, general optimal solvers for these new variants do not yet exist. We present algorithms for optimal solution of these variants on general graphs. We formulate them as mixed integer linear programming problems, and solve them using an off-the-shelf MILP solver. We then develop custom branch and bound algorithms which result in a dramatic reduction in computation speed. Using these algorithms, we generate empirical insights into the hardness landscape of the fixed budget and fixed probability of success SPS variants.

Solving games of imperfect information with linear programming took a significant leap forward when Koller, Megiddo, and Stengel (KMS) proposed an exponentially more compact way to represent two-player games of imperfect information as linear programs. Despite this substantial advancement many recent works on solving these games rely on Counter Factual Regret Minimization (CFR) as opposed to linear programming. One reason CFR became a standard approach is that CFR is easily parallelizable whereas the linear program defined by KMS's technique is difficult to solve in parallel. Convenient parallelism made CFR more amenable to multi-core computing environments and large games. This paper presents a method to parallelize the linear programing techniques of KMS. The proposed iterative method divides a potentially intractable linear program representing a large game of imperfect information into many smaller linear programs. Each of the smaller LPs can be processed independently and in parallel. It is shown that the solutions to the smaller LPs interact together over multiple iterations of this algorithm to produce a strategy pair that converges to the Nash Equilibrium solution to the original undivided problem. This is the first work to propose a Dantzig-Wolfe style decomposition for solving two-player games of imperfect information.

Operating vehicles in adversarial environments between a recurring origin-destination pair requires new planning techniques. Such a technique, presented in this paper, is a game inspired by Ruckle’s original contribution. The goal of the first player is to minimize the expected casualties undergone by a moving agent. The goal of the second player is to maximize this damage. The outcome of the game is obtained via a linear program that solves the corresponding minmax optimization problem over this outcome. The formulation originally proposed by Feron and Joseph is extended to different environment models in order to compute routing strategies over unstructured environments. To compare these methods for increasingly accurate representations of the environment, a grid-based model is chosen to represent the environment and the existence of a sufficient network size is highlighted. A global framework for the generation of realistic routing strategies between any two points is described. Finally the practicality of the proposed framework is illustrated on real world environments.

Energy consumption in commercial and educational buildings is impacted by group activities such as meetings, workshops, classes and exams, and can be reduced by scheduling these activities to take place at times and locations that are favorable from an energy standpoint. This paper improves on the effectiveness of energy-aware room-booking and occupancy scheduling approaches, by allowing the scheduling decisions to rely on an explicit model of the building's occupancy-based HVAC control. The core component of our approach is a mixed-integer linear programming (MILP) model which optimally solves the joint occupancy scheduling and occupancy-based HVAC control problem. To scale up to realistic problem sizes, we embed this MILP model into a large neighbourhood search (LNS). We obtain substantial energy reduction in comparison with occupancy-based HVAC control using arbitrary schedules or using schedules obtained by existing heuristic energy-aware scheduling approaches.

Algorithm portfolios seek to determine an effective set of algorithms that can be used within an algorithm selection framework to solve problems. A limited number of these portfolio studies focus on generating different versions of a target algorithm using different parameter configurations. In this paper, we employ a Design of Experiments (DOE) approach to determine a promising range of values for each parameter of an algorithm. These ranges are further processed to determine a portfolio of parameter configurations, which would be used within two online Algorithm Selection approaches for solving different instances of a given combinatorial optimization problem effectively. We apply our approach on a Simulated Annealing-Tabu Search (SA-TS) hybrid algorithm for solving the Quadratic Assignment Problem (QAP) as well as an Iterated Local Search (ILS) on the Travelling Salesman Problem (TSP). We also generate a portfolio of parameter configurations using best-of-breed parameter tuning approaches directly for the comparison purpose. Experimental results show that our approach lead to improvements over best-of-breed parameter tuning approaches.

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this factorization one can derive notion of tensor rank, referred to as the tensor tubal rank, which has optimality properties similar to that of matrix rank derived from SVD. As shown in [2] some multidimensional data, such as panning video sequences exhibit low tensor tubal rank and we look at the problem of completing such data under random sampling of the data cube. We show that by solving a convex optimization problem, which minimizes the tensor nuclear norm obtained as the convex relaxation of tensor tubal rank, one can guarantee recovery with overwhelming probability as long as samples in proportion to the degrees of freedom in t-SVD are observed. In this sense our results are order-wise optimal. The conditions under which this result holds are very similar to the incoherency conditions for the matrix completion, albeit we define incoherency under the algebraic set-up of t-SVD. We show the performance of the algorithm on some real data sets and compare it with other existing approaches based on tensor flattening and Tucker decomposition.

Signal, image and data processing for hyperspectral imaging has recently received enormous attention in remote sensing [1, 2], having numerous applications such as environmental monitoring, land mapping and classification, and object detection. Such developments are made possible by exploiting the unique features of hyperspectral images, most notably, their high spectral resolutions. In this scope, blind hyperspectral unmixing (HU) is one of the topics that has aroused much interest not only from remote sensing [3], but also from other communities recently [4-7]. Simply speaking, the problem of blind HU is to solve a problem reminiscent of blind source separation in signal processing, and the desired outcome is to unambiguously separate the endmember spectral signatures and their corresponding abundance maps from the observed hyperspectal scene, with no or little 1 prior information of the mixing system. Being given little information to solve the problem, blind HU is a challenging--but also fundamentally intriguing--problem with many possibilities. Readers are referred to some recent articles for overview of blind HU [3,4], and here we shall not review the numerous possible ways to perform blind HU.

Bayesian optimization is a powerful tool for fine-tuning the hyper-parameters of a wide variety of machine learning models. The success of machine learning has led practitioners in diverse real-world settings to learn classifiers for practical problems. As machine learning becomes commonplace, Bayesian optimization becomes an attractive method for practitioners to automate the process of classifier hyper-parameter tuning. A key observation is that the data used for tuning models in these settings is often sensitive. Certain data such as genetic predisposition, personal email statistics, and car accident history, if not properly private, may be at risk of being inferred from Bayesian optimization outputs. To address this, we introduce methods for releasing the best hyper-parameters and classifier accuracy privately. Leveraging the strong theoretical guarantees of differential privacy and known Bayesian optimization convergence bounds, we prove that under a GP assumption these private quantities are also near-optimal. Finally, even if this assumption is not satisfied, we can use different smoothness guarantees to protect privacy.

In this paper, we focus on developing efficient sensitivity analysis methods for a computationally expensive objective function $f(x)$ in the case that the minimization of it has just been performed. Here "computationally expensive" means that each of its evaluation takes significant amount of time, and therefore our main goal to use a small number of function evaluations of $f(x)$ to further infer the sensitivity information of these different parameters. Correspondingly, we consider the optimization procedure as an adaptive experimental design and re-use its available function evaluations as the initial design points to establish a surrogate model $s(x)$ (or called response surface). The sensitivity analysis is performed on $s(x)$, which is an lieu of $f(x)$. Furthermore, we propose a new local multivariate sensitivity measure, for example, around the optimal solution, for high dimensional problems. Then a corresponding "objective-oriented experimental design" is proposed in order to make the generated surrogate $s(x)$ better suitable for the accurate calculation of the proposed specific local sensitivity quantities. In addition, we demonstrate the better performance of the Gaussian radial basis function interpolator over Kriging in our cases, which are of relatively high dimensionality and few experimental design points. Numerical experiments demonstrate that the optimization procedure and the "objective-oriented experimental design" behavior much better than the classical Latin Hypercube Design. In addition, the performance of Kriging is not as good as Gaussian RBF, especially in the case of high dimensional problems.

In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting from spike and slab prior maximization is known to be a hard non-convex problem, and existing solutions involve simplifying assumptions and/or relaxations. We propose an approach called Iterative Convex Refinement (ICR) that aims to solve the aforementioned optimization problem directly allowing for greater generality in the sparse structure. Essentially, ICR solves a sequence of convex optimization problems such that sequence of solutions converges to a sub-optimal solution of the original hard optimization problem. We propose two versions of our algorithm: a.) an unconstrained version, and b.) with a non-negativity constraint on sparse coefficients, which may be required in some real-world problems. Experimental validation is performed on both synthetic data and for a real-world image recovery problem, which illustrates merits of ICR over state of the art alternatives.