Definition

An ε-optimal policy is a Policy whose performance is within $\epsilon$ of the Optimal policy, where $\epsilon \geq 0$  is a small number representing the acceptable margin of sub-optimality. i.e. A policy $\gamma^{*}$ is ε-optimal if, $\forall \gamma$: $$J(\gamma) \geq J(\gamma^{*}) - \epsilon$$