GLIE policy

Definition

A learning Policy is called GLIE (Greedy in Limit with Infinite Exploration) if it satisfies:

• All state-action pairs are explored infinitely many times $\forall s\in \mathcal{S},a\in \mathcal{A}(S),{\lim }_{k\to \infty }n(s,a)=\infty$ where $n(s,a)$ is incremental count of a $(s,a)$.
• The learning policy converges to a greedy policy. ${\lim }_{k\to \infty }{\pi }_k(a|s)=1$ where $a=\underset{a^{\prime }}{\mathrm{argmax}}{Q}_k(s,a^{\prime })$