Maximum Expected Utility
MEU, i.e. Maximum Expected Utility, is a basic principle in decision theory and artificial intelligence. The MEU directs decision-making by suggesting to choose the option that maximizes the expected utility. The MEU suggests selecting the action that is expected to yield the highest utility value while considering the probabilities of different outcomes.
Assume an action (a), then the formula for the expected utility (EU) for that specific action is:
[Tex]EU(a) = Σ (U(s, a) * P(s | a))[/Tex]
where,
- U(s, a) defines the utility of being in a state (s) after taking an action (a). The obtained value is numerical and it reflects preference for that action.
- P(s | a) represents the probability of ending up in a state (s) given an already occured action (a).
MEU only takes the maximum of the expected utility for all possible actions that was calculated:
[Tex]MEU = max(EU(a_1), EU(a_2), ..., EU(a_n))[/Tex]
here a1, a2, a3, .., an are the available actions.
Steps to Calculate Expected Utility
- Specify Actions and States: Define likely actions and states for the decision network.
- Allocate Utility Values: Assign utility values to each state-action pair.
- Specify Probabilities: Use conditional probability relationships to specify the probability of each state occurring given a specific action.
- Multiply Utility and Probability: Multiply the utility of each action by its corresponding probability.
- Sum Products: Sum the products to find the expected utility of each action.
- Repeat: Repeat for all available actions.
- Select MEU: Choose the action with the highest expected utility..
Decision Networks in AI
Decision networks, also known as influence diagrams, play a crucial role in artificial intelligence by providing a structured framework for making decisions under uncertainty. These graphical representations integrate decision theory and probability, enabling AI systems to systematically evaluate various actions and their potential outcomes. In this article, we will explore the components, structure, and applications of decision networks in AI.
Table of Content
- What is a Decision Network?
- Components of Decision Networks
- Example of a Decision Network
- Structure of Decision Networks
- Representing a Decision Problem with a Decision Network
- How to Structure a Decision Network?
- Example of Representing a Decision Problem
- Maximum Expected Utility
- No-Forgetting Agent and Decision Network
- Evaluating Decision Networks
- Applications of Decision Networks in AI
- Advantages of Decision Networks
- Conclusion
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