Related papers: Optimization via Information Geometry
The main theme of this thesis is the development of computational methods for classes of infinite-dimensional optimization problems arising in optimal control and information theory. The first part of the thesis is concerned with the…
A physical field has an infinite number of degrees of freedom since it has a field value at each location of a continuous space. Therefore, it is impossible to know a field from finite measurements alone and prior information on the field…
One of the most common problem-solving heuristics is by analogy. For a given problem, a solver can be viewed as a strategic walk on its fitness landscape. Thus if a solver works for one problem instance, we expect it will also be effective…
We identify fundamental issues with discretization when estimating information-theoretic quantities in the analysis of data. These difficulties are theoretical in nature and arise with discrete datasets carrying significant implications for…
We develop an integrated framework for information design and mechanism design in screening environments with quasilinear utility. Using the tools of majorization theory and quantile functions, we show that both information design and…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of…
Network structure optimization is a fundamental task in complex network analysis. However, almost all the research on Bayesian optimization is aimed at optimizing the objective functions with vectorial inputs. In this work, we first present…
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum…
Data driven algorithm design is an important aspect of modern data science and algorithm design. Rather than using off the shelf algorithms that only have worst case performance guarantees, practitioners often optimize over large families…
We solve the Matrix Completion (MC) problem based on manifold optimization by incorporating the side information under which the columns of the intended matrix are drawn from a union of low dimensional subspaces. It is proved that this side…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
This introductory text arises from a lecture given in G\"oteborg, Sweden, given by the first author and is intended for undergraduate students, as well as for any mathematically inclined reader wishing to explore a synthesis of ideas…
As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…
In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
This essay provides a comprehensive analysis of the optimization and performance evaluation of various routing algorithms within the context of computer networks. Routing algorithms are critical for determining the most efficient path for…
The article discusses the concept of hyperparametric optimization of recommendation algorithms using an integral assessment that combines various performance indicators into a single consolidated criterion. This approach is opposed to…
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…