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What does optimal value mean?
(definition) Definition: The minimum (or maximum) value of the objective function over the feasible region of an optimization problem. See also optimal solution.
What is optimal solution and optimal value?
An optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value – for example, the most profit or the least cost. A globally optimal solution is one where there are no other feasible solutions with better objective function values.
What is optimal parabola value?
The optimal value is the highest or the lowest point on the parabola. The optimal value, also known as the vertex of the parabola would be maximum if only the parabola opens down words. One opening upwards has a minimum value.
How is the Bellman optimality equation solved in DP?
At the core of all these successful projects lies — The Bellman optimality equation for Markov decision processes (MDPs). The Bellman optimality equation is a recursive equation that can be solved using dynamic programming (DP) algorithms to find the optimal value function and the optimal policy.
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 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).
How are Bellman equations derived from argmax?
Finally with Bellman Expectation Equations derived from Bellman Equations, we can derive the equations for the argmax of our value functions However, typically we don’t know the environment entirely then there is not closed form solution in getting optimal action-value and state-value functions.