# Questions tagged [value-iteration]

For questions related to the value iteration algorithm, which is a dynamic programming (DP) algorithm used to solve an MDP, that is, it is used to find a policy given the transition and reward functions of the MDP. Value iteration is related to another DP algorithm called policy iteration.

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### Proof that the Policy Iteration Converges?

Let $\mathcal{X}=:\{x_1, x_2, x_3,...,x_n\}$ be the state space. Let $\mathcal{U}:=\{u_1, u_2, u_3,...,u_m\}$ be the set of actions. Let $A^{u_1}, A^{u_2}, A^{u_3},...,A^{u_m}$ be the state transition ...
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### In Value Iteration, why can we initialize the value function arbitrarily?

I have not been able to find a good explanation of this, other than statements that the algorithm is guaranteed to converge with arbitrary choices for initial values in each state. Is this something ...
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1 vote
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### Value iteration algorithm converge to max reward with discount of 1? [duplicate]

I'm running the value iteration algorithm of a gridworld of 4*3, with two terminal nodes with -50 reward and one with +20 reward like so: ...
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### What should the discount factor for the non-slippery version of the FrozenLake environment be?

I was working with FrozenLake 4x4 from open AI gym. In the slippery case, using a discounting factor of 1, my value iteration implementation was giving a success rate of around 75 percent. It was much ...
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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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### How are previous values updated when performing value iteration?

I have been trying to understand how you determine the value for each square in a grid world and I have seen/watched a few different examples to try and apply it to my own grid and I find myself ...
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### Factors that affect the number of iterations of value iteration

I had an assumption that value iteration will take more iterations to converge if the map size increases/environment's complexity increases. I tried to verify this idea by running value iteration on ...
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### calculating the value of a state in an optimal policy analytically and iteratively

I am watching the lecture by Abbeel on MDPs and Reinforcement Learning. The setup of the problem is the classic gridworld with optimal policy (and corresponding values of states) pictured below. The ...
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### Why and how can the policy and value iteration methods converge to the OPTIMAL point?

I am reading Reinforcement Learning: An Introduction by Sutton & Barto. According to this textbook, as far as I understood, the authors claim that the policy and value iteration methods converge ...
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1 vote
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### Can we combine policy evaluation and value iteration steps for solving model-based MDP?

In Sutton & Barto (2nd edition), at the very end on page 83, the following is mentioned: In general, the entire class of truncated policy iteration algorithms can be thought of as sequences of ...
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1 vote
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### In value iteration, what happens if we try to obtain the greedy policy while looping through the states?

I am referring to the Value Iteration (VI) algorithm as mentioned in Sutton's book below. Rather than getting the greedy deterministic policy after VI converges, what happens if we try to obtain the ...
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1 vote
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### Is it possible to have values of the states equal to $0$ at the end of the value iteration?

I am new to Reinforcement Learning and I am trying to self learn it. I have already posted some quesiton here and your answershave been really useful to me, so here I am posting another one. I am ...
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1 vote
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### What is the difference between a reward and a value for a given state?

I am trying to learn reinforcement learning and I am focusing on the value iteration. I am looking at the example of grid world, and I am trying to implement it in python. While doing this, I ...
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### Are policy and value iteration used only in grid world like scenarios?

I am trying to self learn reinforcement learning. At the moment I am focusing on policy and value iteration, and I am finding several problems and doubts. One of the main doubts is given by the fact ...
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### Bellman Expectation Equation leading to results where value iteration would not converge to the optimal policy

When applying the bellman expectation equation: $$v(s)=\mathbb{E}\left[R_{t+1}+\gamma v\left(S_{t+1}\right) \mid S_{t}=s\right]$$ to the MRP below, states further away from the terminal state will ...
1 vote
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### Are the relative magnitudes of the learned and optimal state value function the same?

I have been reading recently about value and policy iteration. I tried to code the algorithms to understand them better and in the process I discovered something and I am not sure why is the case (or ...
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### Why do we need to go back to policy evaluation after policy improvement if the policy is not stable?

Above is the algorithm for Policy Iteration from Sutton's RL book. So, step 2 actually looks like value iteration, and then, at step 3 (policy improvement), if the policy isn't stable it goes back to ...
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1 vote
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### Value Iteration failing to converge to optimal value function in Sutton-Barto's Gambler problem

In Example 4.3:Gambler's Problem of Sutton and Barto's book whose code is given here. In this code the value function array is initialized as np.zeros(states) where ...
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### Why doesn't value iteration use $\pi(a \mid s)$ while policy evaluation does?

I was looking at the Bellman equation, and I noticed a difference between the equations used in policy evaluation and value iteration. In policy evaluation, there was the presence of $\pi(a \mid s)$, ...
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### Is value iteration stopped after one update of each state?

In section 4.4 Value Iteration, the authors write One important special case is when policy evaluation is stopped after just one sweep (one update of each state). This algorithm is called value ...
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### Why are policy iteration and value iteration studied as separate algorithms?

In Sutton and Barto's book about reinforcement learning, policy iteration and value iterations are presented as separate/different algorithms. This is very confusing because policy iteration includes ...
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### What is the value of a state when there is a certain probability that agent will die after each step?

We assume infinite horizon and discount factor $\gamma = 1$. At each step, after the agent takes an action and gets its reward, there is a probability $\alpha = 0.2$, that agent will die. The assumed ...
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### Should the reward or the Q value be clipped for reinforcement learning

When extending reinforcement learning to the continuous states, continuous action case, we must use function approximators (linear or non-linear) to approximate the Q-value. It is well known that non-...
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### How is the fitted Q-iteration algorithm related to $Q^*(s, a)$, and how can we use function approximation with this algorithm?

I hope to get some clarifications on Fitted Q-Iteration (FQI). My Research So Far I've read Sutton's book (specifically, ch 6 to 10), Ernst et al and this paper. I know that $Q^*(s, a)$ expresses the ...
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