Does an optimal policy always exist for an MDP?

Does an optimal policy always exist for an MDP?

There is always at least one policy that is better than or equal to all other policies. This is an optimal policy.

What does mDP mean?

mDP

Is optimal policy deterministic?

4 Answers. If there is an optimal policy, there is a deterministic optimal policy.

Can there be more than one optimal value function for an MDP?

There can be more than one optimal policy. T(s, a, s )V ∗(s )) . It is well known that there exists an optimal value function (Bellman, 1957). We provide a proof in the Appendix.

What is the full form of MDP in management?

Management Development Programmes (MDP) Office.

How to find optimal policy in a MDP?

Now, let’s define Optimal Policy : Optimal Policy is one which results in optimal value function. Note that, there can be more than one optimal policy in a MDP. But, all optimal policy achieve the same optimal value function and optimal state-action Value Function (Q-function). Now, the question arises how we find Optimal Policy.

How to formulate Bellman equation for a given MDP?

So, this is how we can formulate Bellman Expectation Equation for a given MDP to find it’s State-Value Function and State-Action Value Function. But, it does not tell us the best way to behave in an MDP. For that let’s talk about what is meant by Optimal Value and Optimal Policy Function.

How to solve MDPs using Markov decision process?

Solving MDPs   In an MDP, we want an optimal policy π*: S x 0:H → A   A policy π gives an action for each state for each time   An optimal policy maximizes expected sum of rewards   Contrast: In deterministic, want an optimal plan, or sequence of actions, from start to a goal

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 .