Optimization for Supervised Machine Learning: Randomized Algorithms for Data and Parameters

TL;DR

This paper develops randomized optimization algorithms for supervised machine learning that efficiently handle large data, complex models, and ill-conditioned problems by using stochastic updates and higher-order information.

Contribution

It introduces new randomized algorithms for data and parameter updates, improving efficiency and scalability in training supervised models under challenging conditions.

Findings

Algorithms outperform traditional methods in large-scale settings

Randomized updates reduce computational cost per iteration

Methods effectively handle ill-conditioned problems

Abstract

Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used to formulate these often ill-conditioned optimization tasks, there is a need for new efficient algorithms able to cope with these challenges. In this thesis, we deal with each of these sources of difficulty in a different way. To efficiently address the big data issue, we develop new methods which in each iteration examine a small random subset of the training data only. To handle the big model issue, we develop methods which in each iteration update a random subset of the model parameters only. Finally, to deal with ill-conditioned problems, we devise methods that incorporate either higher-order information or Nesterov's acceleration/momentum. In all cases, randomness is viewed as a powerful algorithmic tool that we tune, both in theory and in experiments, to achieve the best results. Our algorithms have their primary application in training supervised machine learning models via regularized empirical risk minimization, which is the dominant paradigm for training such models. However, due to their generality, our methods can be applied in many other fields, including but not limited to data science, engineering, scientific computing, and statistics.