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Monte-Carlo Methods in AI: Overview

Monte-Carlo Methods in AI: Overview. Prasad Tadepalli. What is a Monte-Carlo Method?. Any method that relies on repeated random simulations to estimate something Simplest case: Polling – who wins the election? True probability of a person voting for Obama is

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Monte-Carlo Methods in AI: Overview

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  1. Monte-Carlo Methods in AI: Overview Prasad Tadepalli

  2. What is a Monte-Carlo Method? • Any method that relies on repeated random simulations to estimate something • Simplest case: Polling – who wins the election? • True probability of a person voting for Obama is • Ask N = 1000 random registered voters how they vote. • Calculate = #(Obama voters)/1000 • Apply Chernoff’s bound • Key idea: Although people are complex and varied, they can be treated as independent samples of an identical distribution for estimation

  3. Applications • First modern use in simulating nuclear reactions in 1940’s by Stanislaw Ulam • Predicting the behavior of complex systems – weather, finance, fluid dynamics, markets, … • Planning and optimization - • Computer games: Bridge, Go, Solitaire, StarCraft • Optimal path planning in time-sensitive networks • True model either does not exist or is too complicated to reason about

  4. Two Fundamental Problems • Prediction/Inference Problem • Given a probabilistic model of how the world operates (a “Bayesian Network”) and some observed evidence, what can we infer about a particular query variable? • Draw samples of the model where the observed evidence is true • Estimate the number of times the query variable is true • Planning/Optimization Problem • Given a faithful simulator of an environment, how can we use it to choose an optimal action? • Run lots and lots of trials • Combine the evidence in a “smart” way • Output the action that yields best results

  5. Organization • Monday, Tuesday, Wednesday are divided into 2 parts • Mornings • Inference/Prediction Problem (Experiments with Genie) • Application Talk • Afternoons • Planning/Optimization Problem (Experiments with MCP) • Project/Lab (Galcon) • Wednesday evening dinner @5:30, McMenamins, Monroe • Thursday 2 talks plus tournament project work • Tournament code is due: Friday 9 AM. • Friday – Advanced topics, tournaments, student presentations

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