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Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
This paper provides a systematic overview of machine learning methods applied to solve NP-hard Vehicle Routing Problems (VRPs). Recently, there has been a great interest from both machine learning and operations research communities to…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…
Environment perception is a crucial ability for robot's interaction into an environment. One of the first steps in this direction is the combined problem of simultaneous localization and mapping (SLAM). A new method, called G-SLAM, is…
Network traffic data is huge, varying and imbalanced because various classes are not equally distributed. Machine learning (ML) algorithms for traffic analysis uses the samples from this data to recommend the actions to be taken by the…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
Machine learning has increasingly been employed to solve NP-hard combinatorial optimization problems, resulting in the emergence of neural solvers that demonstrate remarkable performance, even with minimal domain-specific knowledge. 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…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
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…
Sampling-based methods are widely adopted solutions for robot motion planning. The methods are straightforward to implement, effective in practice for many robotic systems. It is often possible to prove that they have desirable properties,…
The number of multi-robot systems deployed in field applications has increased dramatically over the years. Despite the recent advancement of navigation algorithms, autonomous robots often encounter challenging situations where the control…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
The Vehicle Routing Problem is about optimizing the routes of vehicles to meet the needs of customers at specific locations. The route graph consists of depots on several levels and customer positions. Several optimization methods have been…
Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the…
Despite the success of deep learning-based algorithms, it is widely known that neural networks may fail to be robust. A popular paradigm to enforce robustness is adversarial training (AT), however, this introduces many computational and…
The significance of transportation efficiency, safety, and related services is increasing in urban vehicular networks. Within such networks, roadside units (RSUs) serve as intermediates in facilitating communication. Therefore, the…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
This paper uses the smoothing and mapping framework to solve the SLAM problem in indoor environments; focusing on how some key issues such as feature extraction and data association can be handled by applying probabilistic techniques. For…