SP10 cs188 lecture 8 -- utilities (2PP)

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

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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 s W2 is due today (lecture or drop box) s P2 is out and due on 2/18 2
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2 Expectimax Search Trees s What if we don’t know what the result of an action will be? E.g., s In solitaire, next card is unknown s In minesweeper, mine locations s In pacman, the ghosts act randomly s Can do expectimax search s Chance nodes, like min nodes, except the outcome is uncertain s Calculate expected utilities s Max nodes as in minimax search s Chance nodes take average (expectation) of value of children s 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 s Why should we average utilities? Why not minimax? s Principle of maximum expected utility: an agent should choose the action which maximizes its expected utility, given its knowledge s General principle for decision making s Often taken as the definition of rationality s We’ll see this idea over and over in this course! s Let’s decompress this definition… s Probability --- Expectation --- Utility 5
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3 Reminder: Probabilities s A random variable represents an event whose outcome is unknown s A probability distribution is an assignment of weights to outcomes s Example: traffic on freeway? s Random variable: T = amount of traffic s Outcomes: T in {none, light, heavy} s Distribution: P(T=none) = 0.25, P(T=light) = 0.55, P(T=heavy) = 0.20 s Some laws of probability (more later): s Probabilities are always non-negative s Probabilities over all possible outcomes sum to one s As we get more evidence, probabilities may change: s P(T=heavy) = 0.20, P(T=heavy | Hour=8am) = 0.60 s We’ll talk about methods for reasoning and updating probabilities later 6 What are Probabilities? s Objectivist / frequentist answer: s Averages over repeated experiments s E.g. empirically estimating P(rain) from historical observation s Assertion about how future experiments will go (in the limit) s New evidence changes the reference class s Makes one think of inherently random events, like rolling dice s Subjectivist / Bayesian answer: s Degrees of belief about unobserved variables s E.g. an agent’s belief that it’s raining, given the temperature s E.g. pacman’s belief that the ghost will turn left, given the state s Often learn probabilities from past experiences (more later) s New evidence updates beliefs (more later) 7
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4 Uncertainty Everywhere s Not just for games of chance! s
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This note was uploaded on 03/01/2010 for the course COMPUTER S 188 taught by Professor Abbel during the Spring '10 term at University of California, Berkeley.

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

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