Introduction
Machine learning is the process of employing an algorithm to learn from past data and generalize it to make predictions about future data.
An approximate function that converts input examples into output examples can be used to describe this issue. By redefining the issue as function optimization, the problem of function approximation can be resolved. Here, an optimization technique is used to generate parameter values (such as model coefficients) that minimize the function's error when used to map the inputs to outputs. A machine learning algorithm produces a parameterized mapping function (for example, a weighted sum of inputs).
Every time we deploy a machine learning algorithm on a training dataset, we solve an optimization problem.
In this blog, we will discover the central role of optimization in machine learning.
Machine Learning and Optimization
Finding a set of inputs to an objective goal function that results in the function's minimum or maximum is known as "function optimization."
This can be a difficult task because the structure of the function is unknown, frequently non-differentiable, and noisy, and it may contain tens, hundreds, thousands, or even millions of inputs.
- Function Optimization: Finding the collection of inputs that results in the minimum or maximum of the objective function is known as function optimization.
Function approximation is a good way to describe machine learning. This means approximating an unknown basis function that maps examples of inputs to outputs to predict new data.
This can be challenging because there are often a limited number of examples from which we can approximate a function. The structure of the function being approximated is often non-linear, noisy, and may even contain contradictions.
- Approximation of Functions: Generalizing from specific examples to a reusable mapping function for making predictions on new examples.
Optimizing functions is often easier than approximating functions. Importantly, in machine learning, we often solve the function approximation problem using function optimization. At the core of almost all Machine Learning Algorithms is an optimization algorithm. In addition, the process of working on a predictive modeling problem involves optimization in
Several Steps in addition to learning the model, including:-
- Selection of model hyperparameters.
- Selection of transformations to apply to data before modeling
- Selecting a modeling pipeline to use as the final model.
Our Learners Also Read: How to crack interviews of IT MNC companies
Model Parameters and Hyperparameters
Before moving on, it's important to comprehend the distinction between a model's parameters and hyperparameters. Although it's simple to mix up these two terms, we shouldn't.
Before you start training the model, you need to set the hyperparameters. They include several clusters, learning rates, etc. Hyperparameters describe the structure of the model.
On the other hand, model parameters are obtained during training. They cannot be obtained beforehand. Weights and biases for neural networks are two examples. The model's internal data is dynamic and depends on inputs.
To tune the model, we need to optimize the hyperparameters. We can reduce the error and create the most accurate model by finding the optimal combination of their values.
How Hyperparameter Tuning Works
As we said, hyperparameters are set before training. But you cannot, for example, know in advance which learning speed (high or low) is best in this or that case. Therefore, it is necessary to optimize the hyperparameters to improve the model's performance.
You evaluate the accuracy, compare the output to the anticipated outcomes, and, if necessary, alter the hyperparameters after each iteration. This procedure is iterative. If you're working with a lot of data, you can utilize one of the various optimization approaches, or you can do it yourself.
Cutting-Edge Optimization Techniques in Machine Learning
Now let's talk about techniques you can use to optimize your model's hyperparameters.
Gradient Descent
The most common technique for optimization is gradient descent. This technique involves updating the variables iteratively in the direction (opposite of) the gradients of the objective function. This approach helps the model locate the target at each update and gradually approaches the objective function's ideal value.
Stochastic Gradient Descent
To solve the computational difficulty inherent in each iteration for large-scale data, stochastic gradient descent (SGD) was developed.
Backpropagation is called taking values and iteratively adjusting them based on various parameters to reduce the loss function.
Instead of determining the gradient's precise value directly, this method updates the gradient (theta) using one sample chosen at random for each cycle. An unbiased estimation of the true gradient is provided by the stochastic gradient. This optimization technique eliminates some computational duplication while reducing the update time for working with several samples.
Optimization without Derivatives
Because the objective function's derivative may not exist or be difficult to determine, some optimization issues can always be handled using a gradient method. Derivative-free optimization comes into play here. Instead of systematically determining answers, it uses a heuristic algorithm to choose approaches that have previously been successful. Particle swarm optimization, genetic algorithms, and traditional simulated annealing math are a few examples.
Zero-Order Optimization
Zero-order optimization was recently introduced to address the shortcomings of derivative-free optimization. Derivative-free optimization methods are challenging to scale to significant problems and suffer from a lack of convergence rate analysis.
Advantages of zero order include:
- Simple to employ, requiring only small alterations to widely used gradient-based methods
- computation-effective derivative approximations when computing them are challenging
- similar rates of convergence to first-order algorithms.
A momentum-Based Optimizer
It is an adaptive optimization algorithm that exponentially uses weighted average gradients over previous iterations to stabilize convergence, resulting in faster optimization. This is done by adding a fraction (gamma) to the values of the previous iteration. Essentially, the momentum term increases when the gradient points are in the same direction and decreases when the gradients fluctuate. As a result, the value of the loss function converges faster than expected.
Adaptive Learning Rate Method
The learning rate is one of the key hyperparameters that undergo optimization. The learning rate determines whether the model skips certain parts of the data. A high learning rate could cause the model to overlook more subtle parts of the data. If it's low, real-world applications will find it useful. SGD is significantly impacted by the learning rate. It can be difficult to determine the right learning rate value. For this tweaking, adaptive approaches were automatically suggested.
DNN has employed adaptive SGD variations frequently. Exponential averaging is used by techniques like AdaDelta, RMSProp, and Adam to deliver effective updates and streamline the computation.
- Adagrad: The learning rate will be lower for weights with a high gradient and vice versa.
- RMSprop: modifies the Adagrad method by reducing its monotonically decreasing learning rate.
What Else to Read About ML Optimization
It is difficult and almost morally wrong to give general advice on optimizing every ML model. Therefore, it is better to learn by example:
- If you are interested in optimizing neural networks and comparing the efficiency of different optimizers, try Sanket Doshi's post.
- You can also study how to optimize models using reinforcement learning with Berkey AI research.
Conclusion
In this blog, we have discussed optimization algorithms like Gradient Descent and Stochastic Gradient Descent. SGD is the most critical optimization algorithm in Machine Learning. Primarily used in logistic regression and linear regression.
