Raghav Somani

Raghav Somani

Quantitative Analyst at
The D. E. Shaw Group

A very important aspect of Machine Learning is Optimization, therefore to have the best results one requires fast and scalable methods before one can appreciate a learning model. Such algorithms involve minimization of a class of functions \(f(\mathbf{x})\), that usually do not have a closed form solution, or even if they have, computing them is expensive in both memory and computation time. Here is where iterative methods turn up to be easy and handy. Analyzing such algorithms involve mathematical analysis of both the function to optimize and the algorithm. This post contains a summary and survey of the theoretical understandings of Large Scale Optimization by referring some talks, papers, and lectures that I have come across in the recent. I hope that the insights of the working of these optimization algorithms will allow the reader to appreciate the rich literature of large scale optimization methods.

The complete PDF post can be viewed here.

Readers please note that the article is a compilation of popular and interesting results, and is not meant for publication at any case.

Leave a Comment

You May Also Enjoy

Note on the Kadison-Singer Problem and its Solution

Posted on:

The Kadison-Singer problem arose from the work on quantum mechanics done by Paul Dirac in the 1930s. The problem is equivalent to fundamental problems in areas like Operator theory, Hilbert and Banach space theory, Frame theory, Harmonic Analysis, Discrepancy theory, Graph theory, Signal Processing and theoretical Computer Science. The Kadison-Singer problem had been long standing and defied the efforts of most Mathematicians until it was recently solved by Adam Wade Marcus, Daniel Alan Spielman and Nikhil Srivastava in 2013. Read more

A note on Conformal Symplectic and Relativistic Optimization

Posted on:

This note on a spotlight paper at NeurIPS 2020, has been made while I had been reading the literature on the principle connections between continuous and discrete optimization. The motivation is to understand and create accelerated discrete large scale optimization algorithms from first principles via considering the geometry of phase spaces and numerical integration, specifically symplectic integration. Recent works successfully have been able to throw sufficient light on the two and therefore has attracted my attention. Read more

Geometry of Relativistic Spacetime Physics

Posted on:

This article introduces and describes the mathematical structures and frameworks needed to understand the modern fundamental theory of Relativistic Spacetime Physics. The self-referential and self-contained nature of Mathematics provides enough power to prescribe a rigorous language needed to formulate the building components of the standard Einstein’s General Theory of Relativity like Spacetime, Matter, and Gravity, along with their behaviors and interactions. In these notes, we will introduce and understand these abstract components, starting with defining the arena of smooth manifolds and then adding the necessary and suffcient differential geometric structures needed to build the primers to the General Theory of Relativity. Read more

Dual spaces and the Fenchel conjugate

Posted on:

Dual spaces lie at the core of linear algebra and allows us to formally reason about the concept of duality in mathematics. Duality shows up naturally and elegantly in measure theory, functional analysis, and mathematical optimization. In this post, I have tried to learn and explore the nature of duality via Dual spaces, its interpretation in general linear algebra, all of which was motivated by the so called convex conjugate, or the Fenchel conjugate in mathematical optimization. Read more