# An Approach that Combines Mathematical Optimization and Machine Learning

Machine learning (ML) is a type of artificial intelligence (AI) that allows businesses to make sense of large amounts of data and learn something. Through mathematical optimization, it can help to interpret the correctness of data and improve the decision-making basis of machine learning.
Published: Sep 20, 2022

#### Mathematical Optimization and Machine Learning:

Mathematical optimization is a powerful decision-making tool. Mathematical optimization helps to make the best decision in the current situation by formulating the objective within the objective and specifying constraints and variables. The value of mathematical optimization has been demonstrated in many different industries such as aviation, logistics, power, and finance.

Machine learning is a subfield of artificial intelligence. Computers can recognize patterns in data and learn to predict the future, can generate clusters, detect anomalies, or generate new music or images. The possibilities are endless. Machine learning methods of supervised, unsupervised, and reinforcement learning can all be applied in a variety of industries, such as healthcare and even the arts. Machine learning models are all about probability and predicting the probability of something that will happen.

But be aware that when the data changes too much, the machine learning model becomes useless and the model needs to be retrained or rebuilt from scratch. Mathematical optimization requires clear instructions and a good mathematical description. It cannot handle unstructured data like machine learning. Also, if the problem becomes too large, you may need a commercial solver to solve the problem. Some problems are better suited for machine learning, while in other cases mathematical optimization is better. You should use machine learning when you want to discover patterns in data, find similar data samples, or predict the weather. Mathematical optimization is a better choice if you want to create a schedule, find the best location for a facility, or minimize the cost of a problem.

#### How do you Combine ML and MO?

• Use machine learning predictions as constraints in the optimization model:
This is the most straightforward way to combine ML and MO. Machine learning is first used to make predictions, which are used as input to an optimization problem. You can use the output of a machine learning model to set constraints.
• Use optimization decisions as training features in machine learning models:
The model is first optimized to make decisions, and the decisions are used as features in the machine learning model. In practice, this approach is less common as most decisions (MO) follow prediction (ML). But it is possible and may be useful in specific projects. Mathematical optimization is widely used in logistics. If you use optimization to decide how much supply you need to ship from the production plant to the market, it can save a lot of time, money, and resources.
• Use the machine learning output to determine the scope of the mathematical optimization model:
In addition to using machine learning outputs directly in optimization problems, you can also choose to combine them more separately. You use them in the same project, but not in the same process. You can use machine learning output to make mathematical optimization problems smaller. You can use machine learning to determine the scope of an optimized model that can be solved in less time.
• Using optimization to solve machine learning research problems:
This is an area of research that uses optimization to help solve machine learning challenges. You can use optimization to find an optimal set of parameters for a machine learning problem. ML and MO are tightly integrated here because you use optimization in your ML problem. When building regression models, removing irrelevant features will make the model more interpretable and less prone to overfitting the data. It is difficult to find the optimal subset of features, which is called the optimal subset selection problem. The speed of mixed integer programming has improved significantly over the past few decades, making it useful to test it on existing problems. Tested this issue and it works fine.

#### What is the Improvement of Machine Learning?

Building a machine learning application involves taking a single learner, such as logistic regression, decision tree, support vector machine, or artificial neural network, feeding it data, and using that data to teach it to perform a specific task.

Whereas ensemble methods involve using many learners to improve the performance of any one learner individually. These methods can be described as techniques that use a set of weak learners together to create a more powerful aggregated learner. Usually, ensemble methods are built by grouping variants of a single decision tree.

#### What are the Different Types of Machine Learning Systems?

The amount and type of supervision that a machine learning model requires during training.

• Supervised learning:
Machine learning systems are translated into computer algorithms. All data are labeled, telling the machine the corresponding value to provide the machine learning to use when judging the error in the output. This method is manual classification, such as telling the machine the standard answer, and the machine will answer according to the standard answer, and the correctness will be higher. If the data you use to feed the algorithm includes the desired solution, you are in front of a supervised learning system.
• Unsupervised learning:
This type of system is provided without the required solution (without the label). All data are not marked, and the machine classifies them by looking for the characteristics of the data. such as anomaly detection. This algorithm is useful for situations such as detecting product defects or product label records.
• Semi-supervised learning:
In this case, you have both labeled and unlabeled data. A small part of the data is marked, and the computer only needs to find the features through the marked data and classify the other data. So, a semi-supervised learning algorithm is a combination of an unsupervised algorithm and a supervised algorithm.
• Batch learning:
The system cannot do incremental learning, it must be trained using all available data. Since this is an expensive and time-consuming process, it is usually done offline. Once the system is in production, it will only apply what it has learned before, and not learn anymore.
• e-learning:
In online learning, the system is incrementally trained by providing data instances sequentially using mini-batches of data. Each learning step is fast and cheap, so the system can learn about new data instantly as it arrives. These algorithms are useful when your data changes rapidly or when computing resources are limited.
• Example-based learning:
In instance-based learning, the system learns from examples and then generalizes to new cases by comparing them to the learned examples using a similarity measure.
• Model-based learning:
Another way to generalize from a set of examples is to build a model of those examples and then use that model to make predictions.

2022-09-20
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