# A Cost-based Optimizer for Gradient Descent Optimization

## TL;DR

This paper introduces a cost-based optimizer for gradient descent algorithms that selects the most efficient plan for machine learning tasks expressed as optimization problems, significantly improving performance.

## Contribution

It presents a novel cost-based GD optimizer with abstract operators and a new method for estimating convergence iterations, enabling better plan selection.

## Key findings

- Optimizer achieves orders of magnitude speed-up
- Effectively selects optimal GD plans for various tasks
- Demonstrates significant performance improvements on real and synthetic data

## Abstract

As the use of machine learning (ML) permeates into diverse application domains, there is an urgent need to support a declarative framework for ML. Ideally, a user will specify an ML task in a high-level and easy-to-use language and the framework will invoke the appropriate algorithms and system configurations to execute it. An important observation towards designing such a framework is that many ML tasks can be expressed as mathematical optimization problems, which take a specific form. Furthermore, these optimization problems can be efficiently solved using variations of the gradient descent (GD) algorithm. Thus, to decouple a user specification of an ML task from its execution, a key component is a GD optimizer. We propose a cost-based GD optimizer that selects the best GD plan for a given ML task. To build our optimizer, we introduce a set of abstract operators for expressing GD algorithms and propose a novel approach to estimate the number of iterations a GD algorithm requires to converge. Extensive experiments on real and synthetic datasets show that our optimizer not only chooses the best GD plan but also allows for optimizations that achieve orders of magnitude performance speed-up.