ABSTRACT
If we are given a Banach space F(X , ‖·‖w) on which a policy operator Tφπ or DPO T¯π is contractive then aVIA is simply the sequence of iterationsVk+1 =TφπVk orVk+1 = T¯πVk for any suitable starting point V0 ∈F(X , ‖·‖w). The sequence Vk converges uniformly to V¯π, but since a VIA is exact only in the limit, the remaining component is a stopping rule N which permits the claim
∥∥VN − V¯π∥∥w ≤ for some fixed tolerance >0. The stopping rules discussed in Section 6.2.1 apply to any contractive operator on a metric space (includingmultistage or pseudocontractive), andwill be used to develop stopping rules for VIAs.
