Functional penalised basis pursuit on spheres

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Within the context of contemporary machine learning problems, efficiency of optimization process depends on the properties of the model and the nature of the data available, which poses a significant problem as the complexity of either increases ad infinit ...

Non-convex constrained optimization problems have become a powerful framework for modeling a wide range of machine learning problems, with applications in k-means clustering, large- scale semidefinite programs (SDPs), and various other tasks. As the perfor ...

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The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

In this thesis, we reveal that supervised learning and inverse problems share similar mathematical foundations. Consequently, we are able to present a unified variational view of these tasks that we formulate as optimization problems posed over infinite-di ...

Strategic information is valuable either by remaining private (for instance if it is sensitive) or, on the other hand, by being used publicly to increase some utility. These two objectives are antagonistic and leaking this information by taking full advant ...

We address the problem of designing stabilizing control policies for nonlinear systems in discrete-time, while minimizing an arbitrary cost function. When the system is linear and the cost is convex, the System Level Synthesis (SLS) approach offers an effe ...

This work develops new algorithms with rigorous efficiency guarantees for infinite horizon imitation learning (IL) with linear function approximation without restrictive coherence assumptions. We begin with the minimax formulation of the problem and then o ...

The purpose of this article is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution, ...

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

Frequency response and voltage support are vital ancillary services for power grids. In this paper, we design and experimentally validate a real-time control framework for battery energy storage systems (BESSs) to provide ancillary services to power grids. ...

Stochastic gradient descent (SGD) and randomized coordinate descent (RCD) are two of the workhorses for training modern automated decision systems. Intriguingly, convergence properties of these methods are not well-established as we move away from the spec ...

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Inverse reconstruction from images is a central problem in many scientific and engineering disciplines. Recent progress on differentiable rendering has led to methods that can efficiently differentiate the full process of image formation with respect to mi ...

We develop a new Newton Frank-Wolfe algorithm to solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO). Unlike L-smooth convex functions, where the Lipschitz continuity of the objective gradient holds gl ...

In this work we investigate stochastic non-convex optimization problems wherethe objective is an expectation over smooth loss functions, and the goal is to find an approximate stationary point. The most popular approach to handling such problems is varianc ...

We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective functional. We show that an under-damped form of the Langevin algorithm perfor ...

Vocal signalling systems, as used by humans and various non-human animals, exhibit discrete and continuous properties that can naturally be used to express discrete and continuous information, such as distinct words to denote objects in the world and proso ...

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

Inspired by the human ability to localize sounds, even with only one ear, as well as to recognize objects using active echolocation, we investigate the role of sound scattering and prior knowledge in regularizing ill-posed inverse problems in acoustics. In ...

Functional penalised basis pursuit on spheres

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