# Questions tagged [value-functions]

For questions related to the concept of value (or performance, or quality, or utility) function (as defined in reinforcement learning and other AI sub-fields). An example of this type of functions is the Q function (used e.g. in the Q-learning algorithm), also known as the state-action value function, given that $Q: S \times A \rightarrow \mathbb{R}$, where $S$ and $A$ are respectively the set of states and actions of the environment.

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### When can we unnest the minimizations/recursions in an value function(bellman optimality equation)?

When reading the following paper(page 4): An Approximate Dynamic Programming Approach for Dual Stochastic Model Predictive Control I could see that they were able to unnest the minimization's in the ...
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### Proof of Difference in Return Between Two Policies

I am attempting to understand why Lemma 6.1 holds in this paper on reinforcement learning. I have two questions. First, when defining the value function V(s), why is there a leading (1-γ) term? In the ...
39 views

### How are Target Values Generated in Alpha Zero Architecture

I am a little confused as to how the target values are generated to train the neural network with the Alpha Zero architecture(in specific to a chess game). I understand how the improved policy is ...
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### How do we get the optimal value-function?

In here it says that: (is it correct?) $$V^\pi = \sum_{a \in A}\pi(a|s)*Q^\pi(s,a)$$ And we have: $$V^*(s) = max_\pi V^\pi(s)$$ Also: $$V^*(s) = max_a Q^*(s, a)$$ Can someone demonstrate to me step ...
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### Will my Q values keep going up forever?

In Q-learning,the q values can be updated by the bellman equation. What happens with my Q values is that they keep going up forever, in accordance with the more I train. After 10,000 training episodes,...
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### Why are policy gradient methods more effective in high-dimensional action spaces?

David Silver argues, in his Reinforcement Learning course, that policy-based reinforcement learning (RL) is more effective than value-based RL in high-dimensional action spaces. He points out that the ...
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### What is the difference between these two versions of the Bellman equation?

The first version is the one I am most familiar with: $$V_\pi(s) = \sum_{a}^{}\pi(a|s) \sum_{s'}^{}T(s, a, s')[R(s, a, s') + \gamma V_\pi(s')]$$ where $T(s, a, s')$ represents the probability of ...
1 vote
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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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### Is my derivation of the Bellman equation for $q_{\pi}$ in terms of $p(s'|s,a)$ and $r(s,a)$ correct?

I have done exercise 3.29 from Sutton and Barto and I'd like to check if it's correct. Here's the exercise: Rewrite the Bellman equation for the function $q_{\pi}$ in terms of the three argument ...
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### Policy and Discount Factor

This question is similar to this question, however it has a different question. I'm learning MDP's and I'd like to know if I'm doing these exercises correctly: Consider the following MDP: Suppose a ...
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### Rewrite the four Bellman equations for the four value functions $(v_{\pi},v_*,q_{\pi},q_*)$ in terms of $p$ (3.4) and $r$ (3.5) [duplicate]

I have done exercise 3.29 from Sutton and Barto and I'd like to check if it's correct. Here's the exercise: Rewrite the four Bellman equations for the four value functions $(v_{\pi},v_*,q_{\pi},q_*)$ ...
1 vote
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### Does maximizing the value function and maximizing the state-action value function generate the same optimal policy?

In reinforcement learning, we define the optimal policy $\pi^*$ as the policy that maximizes the value of the state: $$\pi_v^*=\underset{\pi}{\operatorname{argmax}} {V_{\pi}(s)}$$ In Q-learning, we ...
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### How do we estimate the value of a stochastic policy?

I'm learning about reinforcement learning, particularly policy gradient methods and actor-critic methods. I've noticed that many algortihms use stochastic policies during training (i.e. they select ...
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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 ...
1 vote
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### PPO custom implementation: do metrics like value loss, actor loss and entropy move a certain way?

I'm wondering whether problems with a custom PPO implementation (problem couldn't be made into a gym environment) can be debugged considering how the losses change over time. In my current experiment, ...
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### Can we also estimate $V_{\pi}$ with SARSA?

For SARSA, I know we can estimate the action value $Q(s,a)$, and the relationship between $V(s)$ and $Q(s,a)$ is $V_{\pi}(s) = \sum_{a \in \mathcal{A}} \pi(a|s)Q_{\pi} (s,a)$. So my question is, can ...
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### What are the recurrences used for updating state value function in $TD$ and $TD(\lambda)$ learning?

There are two types of value functions in reinforcement learning: State value function $V^{\pi} (s)$, state-action value function $Q^{\pi}(s, a)$. State value function: This value tells us how good ...
1 vote
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### Is there any difference between an objective function and a value function?

I found the usage of both objective function and value function in the same context. Context #1: In the paper titled Generative Adversarial Nets by Ian J. Goodfellow et al. We simultaneously train G ...
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### How can we find the value function by solving a system of linear equations?

I am following the book "Reinforcement Learning: An Introduction" by Richard Sutton and Andrew Barto, and they give an example of a problem for which the value function can be computed ...
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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### How would I compute the optimal state-action value for a certain state and action?

I am currently trying to learn reinforcement learning and I started with the basic gridworld application. I tried Q-learning with the following parameters: Learning rate = 0.1 Discount factor = 0.95 ... 