Related papers: Sampling-Based Global Optimal Control and Estimati…
This paper studies an optimization problem on the sum of traces of matrix quadratic forms in $m$ semi-orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the…
Shape constraints such as positive semi-definiteness (PSD) for matrices or convexity for functions play a central role in many applications in machine learning and sciences, including metric learning, optimal transport, and economics. Yet,…
In order to address the imprecision often introduced by widening operators in static analysis, policy iteration based on min-computations amounts to considering the characterization of reachable value set of a program as an iterative…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
This paper studies distributionally robust optimization (DRO) with polynomial robust constraints. We give a Moment-SOS relaxation approach to solve the DRO. This reduces to solving linear conic optimization with semidefinite constraints.…
We study generalization properties of kernel regularized least squares regression based on a partitioning approach. We show that optimal rates of convergence are preserved if the number of local sets grows sufficiently slowly with the…
We develop an approach that benefits from large simulated datasets and takes full advantage of the limited online data that is most relevant. We propose a variant of Bayesian optimization that alternates between using informed and…
Designing optimisation algorithms that perform well in general requires experimentation on a range of diverse problems. Training neural networks is an optimisation task that has gained prominence with the recent successes of deep learning.…
Kulldorff's (1997) seminal paper on spatial scan statistics (SSS) has led to many methods considering different regions of interest, different statistical models, and different approximations while also having numerous applications in…
In this paper we present a theoretical analysis of the deterministic on-line {\em Sum of Squares} algorithm ($SS$) for bin packing introduced and studied experimentally in \cite{CJK99}, along with several new variants. $SS$ is applicable to…
We study optimization algorithms for the finite sum problems frequently arising in machine learning applications. First, we propose novel variants of stochastic gradient descent with a variance reduction property that enables linear…
This paper introduces a novel approach for learning polynomial representations of physical objects. Given a point cloud data set associated with a physical object, we solve a one-class classification problem to bound the data points by a…
Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…
Improvement of statistical learning models in order to increase efficiency in solving classification or regression problems is still a goal pursued by the scientific community. In this way, the support vector machine model is one of the…
Collaborating teams of robots show promise due in their ability to complete missions more efficiently and with improved robustness, attributes that are particularly useful for systems operating in marine environments. A key issue is how to…
A kernelization is an efficient algorithm that given an instance of a parameterized problem returns an equivalent instance of size bounded by some function of the input parameter value. It is quite well understood which problems do or…
This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from…
The problem of classification in machine learning has often been approached in terms of function approximation. In this paper, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields…
Robotic Mobile Fulfillment Systems (RMFS) rely on mobile robots for automated inventory transportation, coordinating order allocation and robot scheduling to enhance warehousing efficiency. However, optimizing RMFS is challenging due to…
Earth imaging satellites are a crucial part of our everyday lives that enable global tracking of industrial activities. Use cases span many applications, from weather forecasting to digital maps, carbon footprint tracking, and vegetation…