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SP10 cs188 lecture 8 -- utilities (2PP)

# SP10 cs188 lecture 8 -- utilities (2PP) - CS 188 Artificial...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 8: MEU / Utilities 2/11/2010 Pieter Abbeel – UC Berkeley Many slides over the course adapted from Dan Klein 1 Announcements square4 W2 is due today (lecture or drop box) square4 P2 is out and due on 2/18 2

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2 Expectimax Search Trees square4 What if we don’t know what the result of an action will be? E.g., square4 In solitaire, next card is unknown square4 In minesweeper, mine locations square4 In pacman, the ghosts act randomly square4 Can do expectimax search square4 Chance nodes, like min nodes, except the outcome is uncertain square4 Calculate expected utilities square4 Max nodes as in minimax search square4 Chance nodes take average (expectation) of value of children square4 Later, we’ll learn how to formalize the underlying problem as a Markov Decision Process 10 4 5 7 max chance 4 Maximum Expected Utility square4 Why should we average utilities? Why not minimax? square4 Principle of maximum expected utility: an agent should choose the action which maximizes its expected utility, given its knowledge square4 General principle for decision making square4 Often taken as the definition of rationality square4 We’ll see this idea over and over in this course! square4 Let’s decompress this definition… square4 Probability --- Expectation --- Utility 5
3 Reminder: Probabilities square4 A random variable represents an event whose outcome is unknown square4 A probability distribution is an assignment of weights to outcomes square4 Example: traffic on freeway? square4 Random variable: T = amount of traffic square4 Outcomes: T in {none, light, heavy} square4 Distribution: P(T=none) = 0.25, P(T=light) = 0.55, P(T=heavy) = 0.20 square4 Some laws of probability (more later): square4 Probabilities are always non-negative square4 Probabilities over all possible outcomes sum to one square4 As we get more evidence, probabilities may change: square4 P(T=heavy) = 0.20, P(T=heavy | Hour=8am) = 0.60 square4 We’ll talk about methods for reasoning and updating probabilities later 6 What are Probabilities? square4 Objectivist / frequentist answer: square4 Averages over repeated experiments square4 E.g. empirically estimating P(rain) from historical observation square4 Assertion about how future experiments will go (in the limit) square4 New evidence changes the reference class square4 Makes one think of inherently random events, like rolling dice square4 Subjectivist / Bayesian answer: square4 Degrees of belief about unobserved variables square4 E.g. an agent’s belief that it’s raining, given the temperature square4 E.g. pacman’s belief that the ghost will turn left, given the state square4 Often learn probabilities from past experiences (more later) square4 New evidence updates beliefs (more later) 7

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4 Uncertainty Everywhere square4 Not just for games of chance!
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SP10 cs188 lecture 8 -- utilities (2PP) - CS 188 Artificial...

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