Q-value iteration enters an invariant tube around Q* plus the all-ones vector in finite time, with distance decaying at rate given by the joint spectral radius of the transverse projected switching family, which can be strictly faster than the discount factor.
In this case, there exists a constant Dε∗ > 0 such that ∥QKid+ℓ − Q∗ ∥2 ≤ Dε∗ γ ℓ∥QKid − Q∗∥2, ∀ℓ ≥ 0
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Beyond the Bellman Fixed Point: Geometry and Fast Policy Identification in Value Iteration
Q-value iteration enters an invariant tube around Q* plus the all-ones vector in finite time, with distance decaying at rate given by the joint spectral radius of the transverse projected switching family, which can be strictly faster than the discount factor.