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Questions tagged [optimal-policy]

For questions related to the concept of "optimal policy" in reinforcement learning.

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How is policy iteration capable of improving on a deterministic policy?

Given a policy $\pi$ and the improved version upon it using policy iteration $\pi'$ we have, for $\forall s \in S$, $v_{\pi'}(s)\geq v_{\pi}(s)$. I think the way we choose $\pi'$ makes it ...
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How do you determine the optimal policy?

I am following some Grid world examples to understand reinforcement learning. I have a deterministic grid (part of which I have reconstructed below). I am trying to understand how the optimal policy ...
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Determine Gridworld values

I am learning Reinforcement learning for games following Gridworld examples. Apologies in advance if this is a basic question, very new to reinforcement learning. I am slightly confused in scenarios ...
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What is the difference between a greedy policy and an optimal policy?

I am struggling to understand what is the difference between an optimal policy and a greedy policy. Let $F(r_{t+1},s_{t+1}| s_t,a_t)$ be the probability distribution accorting to which, given action $...
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Can an optimal policy have a value function that has a smaller value for a state than a non-optimal policy?

I'm starting to learn about the Bellman Equation and a question came to my mind. A policy $\pi$ is optimal if the value $v_\pi(s)$ is greater or equal than the value $v_{\pi'}(s)$ for all states $s \...
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Doubt in calculating the optimal costs and value after n steps of a MDP problem

MDP problem - A server requires information from a sensor. The server would like the information to be fresh. However, there is a cost to querying information from the sensor. Specifically, the state ...
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What does $v(S_{t+1})$ mean in the optimal state-action value function?

In Sutton & Barto's Reinforcement Learning: An Introduction page 63 the authors introduce the optimal state value function in the expression of the optimal action-value function as follows: $q_{*}(...
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How is $v_*(s) = \max_{\pi} v_\pi(s)$ also applicable in the case of stochastic policies?

I am reading Sutton & Bartos's Book "Introduction to reinforcement learning". In this book, the defined the optimal value function as: $$v_*(s) = \max_{\pi} v_\pi(s),$$ for all $s \in \...
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Equivalence of the $Q(s,a)$ and $V(s)$ under optimality conditions?

Are the state-action values and the state value function equivalent for a given policy? I would assume so as the value function is defined as $V(s)=\sum_a \pi(a|s)Q_{\pi}(s,a)$. If we are operating a ...
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5 votes
2 answers
398 views

Given two optimal policies, is an affine combination of them also optimal?

If there are two different optimal policies $\pi_1, \pi_2$ in a reinforcement learning task, will the linear combination (or affine combination) of the two policies $\alpha \pi_1 + \beta \pi_2, \alpha ...
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What's the optimal policy in the rock-paper-scissors game?

A deterministic policy in the rock-paper-scissors game can be easily exploited by the opponent - by doing just the right sequence of moves to defeat the agent. More often than not, I've heard that a ...
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Why is the optimal policy for an infinite horizon MDP deterministic?

Could someone please help me gain some intuition as to why the optimal policy for a Markov Decision Process in the infinite horizon case (agent acts forever) is deterministic?
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An example of a unique value function which is associated with multiple optimal policies

In the 4th paragraph of http://www.incompleteideas.net/book/ebook/node37.html it is mentioned: Whereas the optimal value functions for states and state-action pairs are unique for a given MDP, ...
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