lecture02.pdf - Lecture 2 Bandit Problem and MDP Chong Li Columbia University Lecture 2 – Bandit MDP 1 Outline • • • • Bandit problem Markov

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Lecture 2: Bandit Problem and MDP Chong Li Columbia University Lecture 2 – Bandit & MDP 1
Bandit problem Markov Process Markov Reward Process Markov Decision Process Columbia University 2 Outline Lecture 2 – Bandit & MDP *Materials of MDP are modified from David Silver’s RL lecture notes
n-armed bandit problem You need to repeatedly take a choice among n different options/actions You receive a numerical reward chosen from a stationary probability distribution that depends on the action you selected Your objective is to maximize the expected total reward over some time period. Invented in early 1950s by Robbins to model decision making under uncertainty when the environment is unknown Columbia University 3 Lecture 2 – Bandit & MDP
Multiple slot machines Columbia University 4 Each machine has a different distribution for rewards with unknown expectation Assume independence of successive plays and rewards across machines A policy is an algorithm that chooses the next machine to play based on the sequence of the past plays and obtained rewards Lecture 2 – Bandit & MDP
Questions If the expected reward from each machine is known, we are done: just pull the lever with the highest expected reward However, expected reward is unknown What should we do? Basic idea: estimate the expectation from the average of the reward received so far Columbia University 5 Lecture 2 – Bandit & MDP
Action-Value Methods : estimated value of action “ a ” at the “ t -th” play : times that action “ a ” has been chosen : reward received from each play Then, we define the action value as Columbia University 6 Lecture 2 – Bandit & MDP
Policies Greedy policy

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• Fall '17
• Chong Li

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