# Analysis of numerical methods for optimization problems arising in machine learning

Project: Research

## Research areas and keywords

### UKÄ subject classification

**Computational Mathematics**

### Keywords

- numerical analysis, time integration, optimization, machine learning, functional analysis, partial differential equations

### Description

This project aims to analyse and construct new efficient numerical methods for optimization problems arising in machine learning applications. Machine learning is a rapidly growing field with applications such as image recognition, autonomous driving, search engine optimizations and many others. Improvements to the most basic building blocks of this setting, which are still not well understood, would have wide-ranging effects; allowing for faster solvers, the solution of larger problems and lower energy requirements. The project is part of the Wallenberg AI, Autonomous Systems and Software Program (WASP), a national initiative for research in artificial intelligence and autonomous systems.

The main idea is to reformulate the optimization problem as the task of finding a stationary solution to a differential equation. This is a simple concept, but it has not been utilized much in this setting. However, it both allows us to apply modern time-stepping schemes, and to analyse them using powerful machinery from the theory of ordinary and partial (stochastic) differential equations. In particular, the main focus will be on employing the functional analytic framework of maximal monotone operators to perform rigorous mathematical error analyses. We will also investigate time-step adaptivity, parallelization strategies, and the new concept of randomized splitting schemes.

The main idea is to reformulate the optimization problem as the task of finding a stationary solution to a differential equation. This is a simple concept, but it has not been utilized much in this setting. However, it both allows us to apply modern time-stepping schemes, and to analyse them using powerful machinery from the theory of ordinary and partial (stochastic) differential equations. In particular, the main focus will be on employing the functional analytic framework of maximal monotone operators to perform rigorous mathematical error analyses. We will also investigate time-step adaptivity, parallelization strategies, and the new concept of randomized splitting schemes.

Status | Active |
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Effective start/end date | 2019/09/01 → 2024/08/31 |

Links | https://wasp-sweden.org/ |