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 single input value and output a single evaluation of the input. They may be the simplest type of test function to use when studying function […]

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 a function optimization problem. In this tutorial, you will discover a gentle introduction to function optimization. After completing this tutorial, you will know: The three […]

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 machine learning algorithm defines a parameterized mapping function (e.g. a weighted sum of inputs) and an optimization algorithm is used to fund the values […]

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 networks. This motivates the investigation of learning curves and techniques, such as early stopping. If optimization is a process that generates candidate solutions, then convergence […]

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 separate step size for each input variable but may result in a step size that rapidly decreases to very small values. AdaMax is an […]

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 separate step size for each input variable but may result in a step size that rapidly decreases to very small values. AMSGrad is an […]

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 of curvature in different dimensions, and in turn, may require a different sized step to a new point. Adaptive Gradients, or AdaGrad for short, is […]

This tutorial presents two essential concepts in data science and automated learning. One is the machine learning pipeline, and the second is its optimization. These two principles are the key to implementing any successful intelligent system based on machine learning. A machine learning pipeline can be created by putting together a sequence of steps involved in training a machine learning model. It can be used to automate a machine learning workflow. The pipeline can involve pre-processing, feature selection, classification/regression, and […]

Differential evolution is a heuristic approach for the global optimisation of nonlinear and non- differentiable continuous space functions. The differential evolution algorithm belongs to a broader family of evolutionary computing algorithms. Similar to other popular direct search approaches, such as genetic algorithms and evolution strategies, the differential evolution algorithm starts with an initial population of candidate solutions. These candidate solutions are iteratively improved by introducing mutations into the population, and retaining the fittest candidate solutions that yield a lower objective […]