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Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to…
This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…
The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be…
This paper establishes the minimum entropy principle (MEP) for the relativistic Euler equations with a broad class of equations of state (EOSs) and addresses the challenge of preserving the local version of the discovered MEP in high-order…
Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the…
In forecasting multiple time series, accounting for the individual features of each sequence can be challenging. To address this, modern deep learning methods for time series analysis combine a shared (global) model with local layers,…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
For many computational problems involving randomness, intricate geometric features of the solution space have been used to rigorously rule out powerful classes of algorithms. This is often accomplished through the lens of the multi Overlap…
When the predicted sequence length exceeds the length seen during training, the transformer's inference accuracy diminishes. Existing relative position encoding methods, such as those based on the ALiBi technique, address the length…
The performance of many machine learning models depends on their hyper-parameter settings. Bayesian Optimization has become a successful tool for hyper-parameter optimization of machine learning algorithms, which aims to identify optimal…
The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…
Efficient approximation lies at the heart of large-scale machine learning problems. In this paper, we propose a novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally…
We consider a discrete optimization formulation for learning sparse classifiers, where the outcome depends upon a linear combination of a small subset of features. Recent work has shown that mixed integer programming (MIP) can be used to…
We propose two algorithms for the solution of the optimal control of ergodic McKean-Vlasov dynamics. Both algorithms are based on approximations of the theoretical solutions by neural networks, the latter being characterized by their…
Memetic algorithms are popular hybrid search heuristics that integrate local search into the search process of an evolutionary algorithm in order to combine the advantages of rapid exploitation and global optimisation. However, these…
In this paper, we consider convex stochastic optimization problems arising in machine learning applications (e.g., risk minimization) and mathematical statistics (e.g., maximum likelihood estimation). There are two main approaches to solve…
We consider the problem of testing graph cluster structure: given access to a graph $G=(V, E)$, can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph?…
Subspace optimization methods have the attractive property of reducing large-scale optimization problems to a sequence of low-dimensional subspace optimization problems. However, existing subspace optimization frameworks adopt a fixed…