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Like the discrete-time Markov decision processes, in continuous-time Markov decision processes the agent aims at finding the optimal policy which could maximize the expected cumulated reward. The only difference with the standard case stays in the fact that, due to the continuous nature of the time variable, the sum is replaced by an integral:
A partially observable Markov decision process (POMDP) is a generalization of a Markov decision process (MDP). A POMDP models an agent decision process in which it is assumed that the system dynamics are determined by an MDP, but the agent cannot directly observe the underlying state.
A Markov decision process is a Markov chain in which state transitions depend on the current state and an action vector that is applied to the system. Typically, a Markov decision process is used to compute a policy of actions that will maximize some utility with respect to expected rewards.
Figure 1. Probabilistic parameters of a hidden Markov model (example) X — states y — possible observations a — state transition probabilities b — output probabilities. In its discrete form, a hidden Markov process can be visualized as a generalization of the urn problem with replacement (where each item from the urn is returned to the original urn before the next step). [7]
Q-learning can identify an optimal action-selection policy for any given finite Markov decision process, given infinite exploration time and a partly random policy. [2] "Q" refers to the function that the algorithm computes: the expected reward—that is, the quality—of an action taken in a given state. [3]
In probability theory, a Markov reward model or Markov reward process is a stochastic process which extends either a Markov chain or continuous-time Markov chain by adding a reward rate to each state. An additional variable records the reward accumulated up to the current time. [1]
State–action–reward–state–action (SARSA) is an algorithm for learning a Markov decision process policy, used in the reinforcement learning area of machine learning.It was proposed by Rummery and Niranjan in a technical note [1] with the name "Modified Connectionist Q-Learning" (MCQ-L).
In Markov decision processes, a Bellman equation is a recursion for expected rewards. For example, the expected reward for being in a particular state s and following some fixed policy π {\displaystyle \pi } has the Bellman equation: