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What is a one armed bandit
An illustration of how a Bernoulli multi-armed seneca allegany casino hours bandit works.
One-armed bandit - a slot machine that is used for gambling; "they spend hours and hours just playing the slots" slot fruit machine - a coin-operated gambling machine that produces random combinations of symbols (usually pictures of different fruits) on rotating dials; certain combinations win.The result of a small experiment on solving a Bernoulli bandit with K 10 slot machines with reward probabilities,.0,.1,.2,.9.This tutorial presents a comprehensive review; military books emmett ra thompson jr strongly recommend it if you want to learn more about Thompson sampling.Check my toy implementation here.A Bernoulli multi-armed bandit can be described as a tuple of, where: We have machines with reward probabilities.See you in the next post 1 CS229 Supplemental Lecture notes: Hoeffdings inequality.For example, if we expect the mean reward of every slot machine to be Gaussian as in Fig 2, we can set the upper bound as 95 confidence interval by setting to be twice the standard deviation.With exploration, we take some risk to collect information about unknown options.(Credit goes to Ben Taborsky ; he has a full theorem of how Thompson invented while pondering over who to pass the ball.Imagine you are in a casino facing multiple slot machines and each is configured with an unknown probability of how likely you can get a reward at one play.Then for u 0, we have: Given one target action a, let us consider: as the random variables, as the true mean, as the sample mean, And as the upper confidence bound, Then we have, We want to pick a bound so that with high.The multi-armed bandit problem is a classic problem that well demonstrates the exploration vs exploitation dilemma.Upper Confidence Bounds Random exploration gives us an opportunity to try out options that we have not known much about.Thus should be a small probability.
To avoid such inefficient exploration, one approach is to decrease the parameter in time and the other is to be optimistic about options with high uncertainty and thus to prefer actions for which we havent had a confident value estimation yet.
It is a simplified version.
The action value is estimated according to the past experience by averaging the rewards associated with the target action a that we have observed so far (up to the current time step t where is a binary indicator function and is how many times the.