BOE optimal policy

Optimal policy

The state value could be used to evaluate if a policy is good or not: if

$$v_{{\pi }_1}(s)\ge v_{{\pi }_2}(s)\forall s\in \mathcal{S}$$

then ${\pi }_1$ is better than ${\pi }_2$

Definition

$\text{Optimal policy}$: A policy ${\pi }^{\ast }$ is optimal if $v_{{\pi }^{\ast }}(s)\ge v_{\pi }(s)$ for all $s$ and for any other policy $\pi$

questions:

• optimal policy exists?
• optimal policy unique?
• policy stochastic or deterministic?
• how to obtain optimal policy? to solve this, see next⇒BOE Bellman Optimality Equation