Markov Decision Process

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Markov Decision Process

Markov decision process (MDP) is a discrete time stochastic control process. It provides a mathematical framework for modeling decision making in situations where outcomes are partly random and partly under the control of a decision maker. MDPs are useful for studying optimization problems solved via dynamic programming and reinforcement learning. MDPs were known at least as early as the 1950s;[1] a core body of research on Markov decision processes resulted from Howard‘s 1960 book, Dynamic Programming and Markov Processes.[2] They are used in many disciplines, including roboticsautomatic controleconomics and manufacturing. The name of MDPs comes from the Russian mathematician Andrey Markov.

• Components:
– States  s, beginning with initial state s0

– Actions

• Each state s has actions A(s) available from it

– Transition model P(s’ | s, a)

• Markov assumption: the probability of going to s’ from s depends only on depends only on
s and not on any of the previous and not on any of the previous states

– Reward function R (s)

• Policy

π(s): the action that an agent takes in any given state

– The “solution” to an MDP

 

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