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cs229-notes12 - CS229 Lecture notes Andrew Ng Part XIII...

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CS229 Lecture notes Andrew Ng Part XIII Reinforcement Learning and Control We now begin our study of reinforcement learning and adaptive control. In supervised learning, we saw algorithms that tried to make their outputs mimic the labels y given in the training set. In that setting, the labels gave an unambiguous “right answer” for each of the inputs x . In contrast, for many sequential decision making and control problems, it is very difficult to provide this type of explicit supervision to a learning algorithm. For example, if we have just built a four-legged robot and are trying to program it to walk, then initially we have no idea what the “correct” actions to take are to make it walk, and so do not know how to provide explicit supervision for a learning algorithm to try to mimic. In the reinforcement learning framework, we will instead provide our al- gorithms only a reward function, which indicates to the learning agent when it is doing well, and when it is doing poorly. In the four-legged walking ex- ample, the reward function might give the robot positive rewards for moving forwards, and negative rewards for either moving backwards or falling over. It will then be the learning algorithm’s job to figure out how to choose actions over time so as to obtain large rewards. Reinforcement learning has been successful in applications as diverse as autonomous helicopter flight, robot legged locomotion, cell-phone network routing, marketing strategy selection, factory control, and efficient web-page indexing. Our study of reinforcement learning will begin with a definition of the Markov decision processes (MDP) , which provides the formalism in which RL problems are usually posed. 1
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2 1 Markov decision processes A Markov decision process is a tuple ( S, A, { P sa } , γ, R ), where: S is a set of states . (For example, in autonomous helicopter flight, S might be the set of all possible positions and orientations of the heli- copter.) A is a set of actions . (For example, the set of all possible directions in which you can push the helicopter’s control sticks.) P sa are the state transition probabilities. For each state s S and action a A , P sa is a distribution over the state space. We’ll say more about this later, but briefly, P sa gives the distribution over what states we will transition to if we take action a in state s . γ [0 , 1) is called the discount factor . R : S × A 7→ R is the reward function . (Rewards are sometimes also written as a function of a state S only, in which case we would have R : S 7→ R ). The dynamics of an MDP proceeds as follows: We start in some state s 0 , and get to choose some action a 0 A to take in the MDP. As a result of our choice, the state of the MDP randomly transitions to some successor state s 1 , drawn according to s 1 P s 0 a 0 . Then, we get to pick another action a 1 .
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