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Table of contents
1.
Introduction
2.
What is Utility Theory in Artificial Intelligence?
3.
What is Utility Function?
4.
Representation of Utility Function
4.1.
Utility Functions as Functions
4.2.
Numerical Representation of Utility Function
4.3.
Representations Based on Machine Learning
5.
Notation of Utility Theory in Artificial Intelligence
6.
Frequently Asked Questions
6.1.
How does AI apply utility theory?
6.2.
Why is utility theory necessary for AI uncertainty?
6.3.
What are the drawbacks of utility theory in artificial intelligence?
6.4.
How do you calculate the expected utility?
7.
Conclusion
Last Updated: Mar 27, 2024
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Utility Theory In Artificial Intelligence

Author Nidhi Kumari
1 upvote

Introduction

Artificial intelligence significantly affects our daily lives, from intelligent search engines to innovative home technologies. AI is widespread in different areas and brings about necessary changes in the real world. This article aims to explain one of the fundamental concepts of artificial intelligence, i.e., Utility theory. It offers a mathematical framework for making decisions in a situation of ambiguity. So, let’s start discussing Utility Theory in Artificial Intelligence without further ado.

Utility Theory In Artificial Intelligence

What is Utility Theory in Artificial Intelligence?

Utility theory offers a framework for making decisions in situations of ambiguity by putting utilities(values) on several possible results. It is very useful in optimising and modelling decision-making processes by considering uncertain and probabilistic outcomes in different situations.

In artificial intelligence(AI), utility theory aims to represent and measure the choices and ideas of an intelligent entity(agent). It offers a framework for making decisions in situations of ambiguity by putting utilities(values) on several possible results.

It can be used in various artificial intelligence areas, such as game theory, reinforcement learning, decision making etc. It is very useful in optimising and modelling decision-making processes by considering uncertain and probabilistic outcomes in different situations.

A utility function is used in utility theory to represent an agent's preferences. It maps potential outcomes or states to fundamental values expressing the agent's desirability. Let’s discuss the utility function in detail.

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What is Utility Function?

Utility function is an intelligent entity's(agent) preferences over various possible outcomes. Based on how desirable or satisfied an agent is with a result, it gives each outcome or condition a numerical value, known as utility.

To learn more about agents in AI, you can visit Agents in artificial intelligence.

For example, consider a simple decision-making process with two outcomes. Utility function may provide a higher value to a desired outcome and a lower value to an undesirable one. More precisely, suppose the outcome is 0 and 1. The utility function will assign 1 to the favourable outcome and 0 to the undesirable one.

So, simply we can say that the utility function is a mapping from a range of potential outcomes to actual numbers. The specific situation, the agent's preferences, and goals determine the utility function's precise structure and features. Also, different conditions, values, and ideas can alter the utility function’s structure and features. Accurate utility value estimation or determination can be difficult, particularly in complicated or ambiguous situations.

Note: It's crucial to remember that utility functions are subjective and differ among agents.

Utility Function Graph

Representation of Utility Function

A utility function in artificial intelligence is a mathematical representation which evaluates the desired outcome of various events or states. The utility function is represented by U. Depending on the particular problem, utility functions in AI can be represented in various ways.

The issue domain, the data that is accessible, and the particular needs of the AI system all influence the utility function representation that is used.

Here is a few examples of the utility function’s representation:

Utility Functions as Functions

Utility functions are mathematical functions that input particular variables or parameters and give an output utility value.
For example, utility functions are frequently modelled as functions of money, expenditure, or other relevant factors in financial decision-making.

Numerical Representation of Utility Function

Utility functions can be used for numerical representation. The utility function gives each result or state a numerical value in this representation.

For example, a utility function may place a larger value on preferable results and a lower value on undesirable ones.

Representations Based on Machine Learning

Utility functions can be trained in some AI applications using machine learning techniques. This representation method is helpful when the utility function is complicated or challenging to define manually.

Notation of Utility Theory in Artificial Intelligence

Utility functions and their attributes are represented using a variety of notations in utility theory. Some typical notations are as follows:

  • U(x): This represents the utility function, where 'x' typically denotes a result or a state. U(x) gives each outcome a numerical value, reflecting its utility.
     
  • V(x): The utility function is sometimes denoted by the notation V(x) rather than U(x).
     
  • u(x): When discussing individual preferences(utilities) instead of aggregate utilities, lowercase 'u' is sometimes utilised to represent utility functions.
     
  • U(x, y): It represents the situation when utility functions accept multiple input variables. Here x and y variables represent the properties and qualities of an outcome. U(x, y) represents the utility related to that set of variables.

 

Now, let’s understand the formula for utility theory in artificial intelligence. 

Let x stand for a possible result or option, and the utility function  U(x) represents the function that converts x into its utility value. 

Let [ E[U(x)] stand for the expected utility of outcome x, which is the total of the utility values of every possible outcome weighted by the probability associated with each one.

Applying the following formula, the [E[U(x)] is calculated:

[E[U(x)] = Σi P(xi).U(xi)

Frequently Asked Questions

How does AI apply utility theory?

According to utility theory, specific outcomes and activities are given numerical values, also called utility or preference values. These numbers show the agent's preferences or the desirability of each result.

Why is utility theory necessary for AI uncertainty?

Utility theory aims to represent and measure the choices and ideas of an intelligent entity(agent). It offers a framework for making decisions in situations of ambiguity by putting utilities(values) on several possible results.

What are the drawbacks of utility theory in artificial intelligence?

People might not always behave in a way that maximises their expected benefit. In such situations where the presumptions of rationality, completeness, and transitivity may not hold true, expected utility theory can be unrealistic or impractical.

How do you calculate the expected utility?

The probability is multiplied by the utility of each possible result, and the sum of all the results is used to compute the expected utility. In mathematical terms, [E[U(x)] = Σi P(xi).U(xi) is the formula for expected utility.

Conclusion

In this article, we extensively discussed the utility theory in artificial intelligence. It offers a framework for making decisions in situations of ambiguity by putting utilities(values) on several possible results.

We hope this article helps you. To read more about AI, you can visit more articles.

 

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