Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. A limitation of gradient descent is that it uses the same step size (learning rate) for each input variable. This can be a problem on objective functions that have different amounts […]

# Author Archive | Jason Brownlee

## Gradient Descent Optimization With AMSGrad From Scratch

Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. A limitation of gradient descent is that a single step size (learning rate) is used for all input variables. Extensions to gradient descent like the Adaptive Movement Estimation (Adam) algorithm use […]

## Gradient Descent Optimization With AdaMax From Scratch

Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. A limitation of gradient descent is that a single step size (learning rate) is used for all input variables. Extensions to gradient descent, like the Adaptive Movement Estimation (Adam) algorithm, use […]

## A Gentle Introduction to Premature Convergence

Convergence refers to the limit of a process and can be a useful analytical tool when evaluating the expected performance of an optimization algorithm. It can also be a useful empirical tool when exploring the learning dynamics of an optimization algorithm, and machine learning algorithms trained using an optimization algorithm, such as deep learning neural […]

## Why Optimization Is Important in Machine Learning

Machine learning involves using an algorithm to learn and generalize from historical data in order to make predictions on new data. This problem can be described as approximating a function that maps examples of inputs to examples of outputs. Approximating a function can be solved by framing the problem as function optimization. This is where […]

## A Gentle Introduction to Function Optimization

Function optimization is a foundational area of study and the techniques are used in almost every quantitative field. Importantly, function optimization is central to almost all machine learning algorithms, and predictive modeling projects. As such, it is critical to understand what function optimization is, the terminology used in the field, and the elements that constitute […]

## One-Dimensional (1D) Test Functions for Function Optimization

Function optimization is a field of study that seeks an input to a function that results in the maximum or minimum output of the function. There are a large number of optimization algorithms and it is important to study and develop intuitions for optimization algorithms on simple and easy-to-visualize test functions. One-dimensional functions take a […]

## Line Search Optimization With Python

The line search is an optimization algorithm that can be used for objective functions with one or more variables. It provides a way to use a univariate optimization algorithm, like a bisection search on a multivariate objective function, by using the search to locate the optimal step size in each dimension from a known point […]

## Gradient Descent With RMSProp from Scratch

Gradient descent is an optimization algorithm that follows the negative gradient of an objective function in order to locate the minimum of the function. A limitation of gradient descent is that it uses the same step size (learning rate) for each input variable. AdaGrad, for short, is an extension of the gradient descent optimization algorithm […]

## Dual Annealing Optimization With Python

Dual Annealing is a stochastic global optimization algorithm. It is an implementation of the generalized simulated annealing algorithm, an extension of simulated annealing. In addition, it is paired with a local search algorithm that is automatically performed at the end of the simulated annealing procedure. This combination of effective global and local search procedures provides […]