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Which is the optimal state action value function?
Optimal State-Value Function :It is the maximum Value function over all policies. Optimal State-Action Value Function: It is the maximum action-value function over all policies. Now, let’s look at, what is meant by Optimal Policy ?
Is the optimal value function the same for all policies?
They share the same state-value function, called the optimal state-value function, denoted , and defined as for all . Optimal policies also share the same optimal action-value function , denoted , and defined as for all and .
Which is optimal action after one step search?
If you have the optimal value function, , then the actions that appear best after a one-step search will be optimal actions. Another way of saying this is that any policy that is greedy with respect to the optimal evaluation function is an optimal policy.
Which is the optimal value function in MDP?
Defining Optimal State-Value Function In an MDP environment, there are many different value functions according to different policies. The optimal Value function is one which yields maximum value compared to all other value function. When we say we are solving an MDP it actually means we are finding the Optimal Value Function.
What is the relationship between state value and action value?
Here is a more detailed explanation of the relationship between state value and action value in Aaron’s answer. Let’s first take a look at the definitions of value function and action value function under policy π : where G t = ∑ k = 0 ∞ γ k R t + k + 1 is the return at time t. The relationship between these two value functions can be derived as
How is the Bellman equation of optimality calculated?
The Bellman equation of optimality Bellman proved that the optimal state value function in a state s is equal to the action a, which gives us the maximum possible expected immediate reward, plus the discounted long-term reward for the next state s’:
How is the value of a state determined by the Bellman equation?
Mathematically we can define Bellman Expectation Equation as : Let’s call this Equation 1. The above equation tells us that the value of a particular state is determined by the immediate reward plus the value of successor states when we are following a certain policy ( π).
What are the components of a Markov decision process?
Markov decision process is a tuple of 5 components → (S,A,P,R, γ) S → A set of states in the environment A → A finite set of actions an agent can take in the environment P → Transition Probability Matrix (for all states) And it follows the Markov property.
When does a stochastic process have the Markov property?
#Wikipedia → In probability theory and statistics, A stochastic process has the Markov property if the conditional probability distribution of future states of the process depends only upon the present state. Markov decision process is a tuple of 5 components → (S,A,P,R, γ)