Computational learning theory (CoLT) refers to applying formal mathematical methods to learning systems using theoretical computer science tools to quantify learning problems. This task includes discerning how hard it is for an artificial intelligence (AI) system to learn specific tasks.

Simply put, CoLT is an AI subfield devoted to studying the design and analysis of machine learning (ML) algorithms. It analyzes how difficult it will be for an AI system to learn a task.

Other interesting terms…

CoLT is typically applied to supervised learning, an ML technique requiring a human to train a machine by giving it data specifically meant to help the computer achieve the desired results. Apart from determining the level of difficulty of performing a task, CoLT also gauges how much time it will take a machine to achieve the desired outcome and even if it’s feasible to begin with.

### What Does Computational Learning Theory Determine?

CoLT formalizes three key aspects, namely:

• The way the learner interacts with its environment
• The definition of success in terms of completing the learning task
• A formal definition of efficiency of both data usage (sample complexity) and processing time (time complexity)

CoLT considers a computation feasible if it can be performed in polynomial time. That means the number of steps required to complete the algorithm for a given input is not infinite. CoLT produces two kinds of results for this—positive (the machine can learn the task in polynomial time) and negative (the device can’t learn the task in polynomial time).

### Why Is Computational Learning Theory Important?

You should remember that the theoretical learning models AI systems analyze represent real-life problems abstractly. As such, ML experts have to validate or change the abstractions to ensure that the computers will produce theoretical results that represent real-life solutions.

CoLT is thus critical to ML research. Besides the predictive capability CoLT offers, it also addresses other vital factors, including simplicity, robustness to variations in the learning scenario, and the ability to create insights into empirically observed phenomena. In other words, CoLT simplifies the data the AI system has to process. Finally, it helps users ensure the computer can adapt to changes in its environment even while learning a task. And it lets users understand and apply the results to real-life situations.

### What Fields Employ Computational Learning Theory?

CoLT is usually applied to statistics, calculus, geometry, information theory, probability theory, and programming optimization.

### What Questions Can Computational Learning Theory Answer?

CoLT can respond to questions, such as:

• How can you tell if a model decently approximates the goal function? (How can you tell if an ML algorithm accurately represents your objective?)
• How can you determine if you have a good answer at the local or global level? (How can you tell if the ML model successfully provided you with the correct results for a specific or general task?)
• What type of hypothesis space should be employed? (How many hypotheses should the machine come up with?)
• What can you do to avoid overfitting? (What can you do to prevent the results from becoming only applicable to the data studied?)
• How many examples of data are required?

### What Are the Practical Applications of Computational Learning Theory?

CoLT has several uses, including:

• It can help programmers predict how well their algorithms will do in processing and analyzing specific volumes of data. Will they work as well on 5 million data points as they did on 1 million data points? Were the results just as accurate?
• It simplifies the process of modifying algorithms by limiting the possible parameters, making software development and upgrading faster. Here, unsupervised learning plays a huge part, specifically in labeling data and choosing data points that are likely to produce the best results.

As this post showed, CoLT studies the design and analysis of ML algorithms to determine how hard it will be and how long it will take for an AI system to learn a task.