Policy Improvement Theorem

Definition

Consider two policies $\pi$ and ${\pi }^{\prime }$. $\forall s\in S,Q^{\pi }(s,{\pi }^{\prime }(s))\ge V^{\pi }(s)(=)⟹\forall s\in S,V^{{\pi }^{\prime }}(s)\ge V^{\pi }(s)$ This implies that ${\pi }^{\prime }$ is a better policy than $\pi$.