Questions tagged [markov-decision-process]

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Convergence of policy iteration with discount $\gamma=1$

This question is related to my question (and my comment of RobPratt's answer) at https://math.stackexchange.com/questions/3860303/markov-decision-process-with-target-states-and-shortest-path-as-only-...
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Is a policy $\pi(s)$ on Markov decision process a random variable?

Citing Wikipedia: The goal in a Markov decision process is to find a good "policy" for the decision maker: a function $\pi$ that specifies the action $\pi(s)$ that the decision maker will ...
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How to solve a Markov Decision Problem with State Transition Matrix and Reward Matrix

I'm stuck in solving a simple dynamic probabilistic model. I have Three states {Sunny, Cloudy, Rainy}. I have the ...
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does it make sense to define average reward in finite horizon

I am new to reinforcement learning but there is a situation I am considering using average reward instead of sum reward as objective for a finite horizon application problem. Specifically, there are ...
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Markov Decision Process augmented with latent/hidden variables but does not use a belief state distribution (what do we call this?)

I have a Markov Decision Process where packets arrive to a queue which services them. It has a high cost fast setting and a low cost slow setting. Usually the arrival rates are assumed to follow some ...
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How to calculate the probability Matrix (Alpha) for Regular Markov chains

Pardon me for being a novice here. In the image attached, eq 3.1 represents the transition matrix (it's pretty clear). I am not able to comprehend the eq 3.2, alpha*P = alpha, as well as the further ...
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Bellmans equation and existence of optimal policy for MDPs

I'm trying to understand the proof of existence of an optimal policy from this question Why is there always at least one policy that is better than or equal to all other policies? by Lovelris. - ...
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What is the difference between Reinforcement Learning(RL) and Markov Decision Process(MDP)?

What is the difference between a Reinforcement Learning(RL) and a Markov Decision Process(MDP)? I believed I understood the principles of both, but now when I need to compare the two I feel lost. ...
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States in Bandit Problems

I am wondering if there is an interpretation of the Bandit Problem with more than one states. I know that there are versions which views each slot machine as an independent Markovian machines and as ...
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Subset selection with reinforcement learning

I have a set of $N$ items of which a subset of arbitrary size can be chosen. I want a reinforcement learning (RL) agent to perform the subset selection and am unsure how to best design the action ...
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Calculating Value State matrix for a finite MDP without limit condition

In the book "Reinforcement Learning" From Andrew Sutton and Barto there is an example given for the Bellman equations: Figure 3.2 (left) shows a rectangular gridworld representation of a simple ...
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Markovian Decision Process and inventory problem

I am interested in an inventory problem modelized by an MDP: -my state space is very large (each state is described by a tuple (u_1,u_2,u_3,u_4) where u_1,u_2,u_3,u_4 are integers in the range [0, ...
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Large state space and Markov decision process

I am working on a project where I have an MDP but with a very large state space (each state is described by a tuple (a,b,c,d) where a,b,c,d are integers in the range [0, 1000]). My goal is to compute ...
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Empirical Bernstein Inequalities in Reinforcement Learning

Recently, I have studied the following paper: "Near-optimal Regret Bounds for Optimistic Reinforcement Learning using Empirical Bernstein Inequalities" https://arxiv.org/abs/1905.12425 I was ...
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Does an optimal value function exist for an MDP with continous state and action spaces?

If the state set $\mathcal{S}$ and action set $\mathcal{A}$ of a Markov Decision Process are infinite does an optimal value function $v_\pi(s)$ exist?
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Can someone explain how an action reward function is calculated in markov decision process

In his second lecture on Reinforcement Learning, David Silver, writes the expression for reward function(for MDP) as: Why do we need to calculate the expected value? Because if we are in state s1 and ...
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How to model transition probability if action does not lead to a state change (in MDP)?

An MDP (markov decision process) is defined as a set of states $S$, actions space $A$, Transition Probabilities $T$ and Rewards $R$. An action $a$ in a state $s$ usually result in a change of state ...
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Dyna-Q Algorithm Reinforcement Learning

In step(f) of the Dyna-Q algorithm we plan by taking random samples from the experience/model for some steps. Wouldn't it be more efficient if we construct an MDP from experience by computing the ...
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UCB Exploration in Reinforcement Learning

I have two questions regarding the upper confidence bounds (UCB) exploration in reinforcement learning: UCB exploration is derived from Hoeffding's inequality which assumes that the reward is bounded ...
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Model or State Uncertainty in Queueing Model due to uncertain arrival rate

$\textbf{Introduction}$ I am currently modelling a scenario where two queues need to be served by a single server in a non preemptive discipline. I am quite sorted on generating the optimal policy ...
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What is the point of doing simulation on Markov Chain?

I am studying Markov Chain and I am currently reading about simulation on Markov Chain but I can't see the point of simulation on Markov Chain. What does simulation mean in Markov Chain and what can ...
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How to increase the total number of iterations it takes to converge a MDP?

I was reading about Policy Iteration. What are the factors that influence the total number of iterations the algorithm takes to converge? For a given MDP which converges in 3 iterations, what setting ...
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Uniqueness of the optimal value function for an MDP

Suppose we have a Markov decision process with a finite state set and a finite action set. We calculate the expected reward with a discount of $\gamma \in [0,1]$. In chapter 3.8 of the book "...