# Tag Info

Accepted

### Why does the state-action value function, defined as an expected value of the reward and state value function, not need to follow a policy?

Let's first write the state-value function as $$q_{\pi}(s,a) = \mathbb{E}_{p, \pi}[R_{t+1} + \gamma G_{t+1} | S_t = s, A_t = a]\;,$$ where $R_{t+1}$ is the random variable that represents the reward ...
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### Why is the state-action value function used more than the state value function?

We are ultimately interested in getting an optimal policy, that is the optimal sequence of actions to reach the final goal. State values on its own don't provide that, they tell you expected return ...
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### What is the difference between expected return and value function?

There is a strong relationship between a value function and a return. Namely that a value function calculates the expected return from being in a certain state, or taking a specific action in a ...
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### In Value Iteration, why can we initialize the value function arbitrarily?

Is this something to do with the Bellman optimality constraint itself? That is part of it, and important for episodic problems without discounting. The Bellman equations link between time steps, ...
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### How does the initialization of the value function and definition of the reward function affect the performance of the RL agent?

There seem to be two different ideas in this question here: What's the impact / importance of our choice for reward values? What's the impact / importance of our choice for initial value estimates (...
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### Apart from the state and state-action value functions, what are other examples of value functions used in RL?

Advantage function: $A(s,a) = Q(s,a) - V(s)$ More interesting is the General Value Function (GVF), the expected sum of the (discounted) future values of some arbitrary signal, not necessarily reward. ...
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### How can I ensure convergence of DDQN, if the true Q-values for different actions in the same state are very close?

Let $Q^*(s, a)$ denote the "true" $Q$-value for a state-action pair $(s, a)$, i.e. the values that we're hoping to learn to approximate using a neural network that outputs $Q(s, a)$ values. The ...
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### Why are the value functions sometimes written with capital letters and other times with lower-case letters?

In the Sutton and Barto book $q(s,a)$ is used to denote the true expected value of taking action $a$ in state $s$, whereas capital $Q(s,a)$ is used to denote an estimate of $q(s,a)$. However, there is ...
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### Why is there an inconsistency between my calculations of Policy Iteration and this Sutton & Barto's diagram?

Your calculations are correct, but you have misinterpreted the equations and the diagram. The index $k$ in $v_k$ for the diagram refers to the policy evaluation update iteration only, and is not ...
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### What is the value of a state when there is a certain probability that agent will die after each step?

The value of a state depends on the policy that you use, so I'll make the assumption here that you're talking about value using the optimal policy. According to the optimal policy, the agent would ...
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### Connection between the Bellman equation for the action value function $q_\pi(s,a)$ and expressing $q_\pi(s,a) = q_\pi(s, a,v_\pi(s'))$

Your understanding of the Bellman equation is not quite right. The state-action value function is defined as the expected (discounted) returns when taking action $a$ in state $s$. Now, in your ...
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### Why isn't it wise for us to completely erase our old Q value and replace it with the calculated Q value?

Removing the learning rate will likely yield poor convergence to the optimal policy and optimal Q-values. Note that the current policy is completely dependent on the Q-values, as we take the action ...
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