Augmented Lagrangian Methods for Provable and Scalable Machine Learning

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Balancing economic and environmental goals in industrial applications is critical amid challenges like climate change. Multi-objective optimization (MOO) and multi-criteria decision analysis (MCDA) are key tools for addressing conflicting objectives. MOO g ...

This paper proposes a methodology to optimize the dispatch and reserve between multiple units in a Hydroelectric Power Plant (HPP) that makes use of the Hydraulic Short Circuit (HSC) operating mode. HSC allows for the simultaneous generation and pumping fr ...

This paper offers a new algorithm to efficiently optimize scheduling decisions for dial-a-ride problems (DARPs), including problem variants considering electric and autonomous vehicles (e-ADARPs). The scheduling heuristic, based on linear programming theor ...

Distributed learning is the key for enabling training of modern large-scale machine learning models, through parallelising the learning process. Collaborative learning is essential for learning from privacy-sensitive data that is distributed across various ...

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We form ...

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

Quantum support vector machines employ quantum circuits to define the kernel function. It has been shown that this approach offers a provable exponential speedup compared to any known classical algorithm for certain data sets. The training of such models c ...

We introduce an algorithm to reconstruct a mesh from discrete samples of a shape's Signed Distance Function (SDF). A simple geometric reinterpretation of the SDF lets us formulate the problem through a point cloud, from which a surface can be extracted wit ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

Clustering in education, particularly in large-scale online environments like MOOCs, is essential for understanding and adapting to diverse student needs. However, the effectiveness of clustering depends on its interpretability, which becomes challenging w ...

Driven by the need for more efficient and seamless integration of physical models and data, physics -informed neural networks (PINNs) have seen a surge of interest in recent years. However, ensuring the reliability of their convergence and accuracy remains ...

Sample efficiency is a fundamental challenge in de novo molecular design. Ideally, molecular generative models should learn to satisfy a desired objective under minimal calls to oracles (computational property predictors). This problem becomes more apparen ...

Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous fractional opti ...

In this thesis, we study two closely related directions: robustness and generalization in modern deep learning. Deep learning models based on empirical risk minimization are known to be often non-robust to small, worst-case perturbations known as adversari ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

Augmented Lagrangian Methods for Provable and Scalable Machine Learning

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On the role of artificial intelligence in feature oriented multi-criteria decision analysis

Optimal Short-Term Dispatch of Pumped-Storage Hydropower Plants Including Hydraulic Short Circuit

A ride time-oriented scheduling algorithm for dial-a-ride problems

Optimization Algorithms for Decentralized, Distributed and Collaborative Machine Learning

Scalable constrained optimization

Perturbed Utility Stochastic Traffic Assignment

The effect of smooth parametrizations on nonconvex optimization landscapes

The complexity of quantum support vector machines

Reach For the Arcs: Reconstructing Surfaces from SDFs via Tangent Points

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Interpret3C: Interpretable Student Clustering Through Individualized Feature Selection

Residual-based attention in physics-informed neural networks

Augmented Memory: Sample-Efficient Generative Molecular Design with Reinforcement Learning

Learning to Remove Cuts in Integer Linear Programming

Understanding generalization and robustness in modern deep learning

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

On the Generalization of Stochastic Gradient Descent with Momentum

COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

From low-rank retractions to dynamical low-rank approximation and back

A Combination Technique for Optimal Control Problems Constrained by Random PDEs