# Decision Networks in Artificial Intelligence: Nodes & Uses

Instructor: Srinivasa krishna Goparaju
In decision making under uncertainty, a graphical model known as a decision network is used to evaluate the feasibility of a decision. In this lesson, you will learn about decision networks, their structure and how an AI agent uses them in decision making.

Have you ever wondered how the Google Maps service in your smart phone is able to direct you to the given destination and reroute itself in case of any unforeseen situations? An AI agent in the device gathers information on traffic, road conditions, etc. and makes a decision on alternative routes to the destination. How did the agent make a decision on a particular route? It evaluated the feasibility of all available routes using a graphical structure called a decision network.

## What Is a Decision Network?

Decision networks are generalized Bayes Belief Networks with chance nodes, decision nodes, and a utility node. These networks are used to make decisions under uncertainty.

A Bayes Belief Network is a graphical model that describes the conditional dependencies between different random variables through a directed acyclic graph (DAG). DAG is a graph that is directed and without cycles connecting the other edges. The nodes in DAG represent the random variables, and edges represent the conditional dependency between the random variables.

For example, a Bayesian network may represent the probabilistic relationships between diseases and symptoms. The network can use known symptoms to compute the probabilities of the presence of various diseases.

In decision networks, utility of a decision, maximum expected utility, value of information and perfect value of information are important computations that affect the decision making process.

• Utility of a decision is a function of random variables of the decision problem.
• Expected utility of each decision is calculated as a sum of probabilities of the decision multiplied by the utility value of that decision.
• Maximum expected utility (MEU) is a decision with high expected utility from the available decisions to take.
• Value of information is the price paid to obtain a piece of information. The information obtained may or may not be useful in arriving at a correct decision.
• Value of perfect information is the price paid to obtain a piece of information that helps in making the right decision.

Both value of information and value of perfect information may be used in a sequential decision problem where a decision impacts subsequent decisions.

## Evaluation of Decision Network by an AI Agent

An AI agent uses decision networks to make decisions under uncertainty by:

• Assigning conditional probabilities to each random variable (chance nodes).
• Assigning utility to a decision.
• Rating the utility of each possible decision.
• Computing expected utility of each possible decision and arriving at a decision with maximum expected utility (MEU).
• Computing value of information and value of perfect information in case of sequential decisions.

## A Real World Example

Let's look at a real world decision problem under uncertainty to understand how an artificial agent evaluates decision networks to arrive at a decision with MEU.

John wants to purchase a flat. He has two options: Flat A or Flat B. He wants to resell the flat in a few years. So, he is interested in how the flat's value may increase. Depending on the place he chooses, there is some probability of increase in the value of the property. John uses a bus to go to work. So, he is also interested in the distance from the bus stop to the flat.

In the above problem, there is uncertainty about the increase of the flat's value and about the distance to the bus stop; they both depend on which flat is chosen. A rational decision in the above circumstances would be buying a flat that is nearest to the bus stop and also has maximum value increase amongst the two flats.

Here is a decision network diagram for the given problem:

Conditional probability tables of chance nodes (random variables) are given below:

Flat P(BS)
A 0.5
B 0.5

#### Flat Value (FV):

Flat P(FV)
A 0.6
B 0.4

The utility table for each possible outcome/decision in the above problem is given below:

Flat BS FV Utility(U)
A T T 0.8
A T F 0.4
A F T 0.6
A F F 0.1
B T T 0.8
B T F 0.3
B F T 0.5
B F F 0.05

The following table gives expected utility computations of the above decision problem:

Decision P(BS) P(FV) U Expected Utility(EU)=P(BS)*U+P(FV)*U
EU(A|BS=T,FV=T) 0.5 0.6 0.8 0.88
EU(A|BS=T,FV=F) 0.5 0.6 0.4 0.44
EU(A|BS=F,FV=T) 0.5 0.6 0.6 0.66
EU(A|BS=F,FV=F) 0.5 0.6 0.1 0.11
EU(B|BS=T,FV=T) 0.5 0.4 0.8 0.72
EU(B|BS=T,FV=F) 0.5 0.4 0.3 0.27
EU(B|BS=F,FV=T) 0.5 0.4 0.5 0.45
EU(B|BS=T,FV=T) 0.5 0.4 0.05 0.045

In the above table:

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