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.
By the definition of the JSR, there exists an integer K ≥ 0 such that max ¯σ k∈{ 1,...,M } k ¯Aσ k · · ·¯Aσ 1 1/k 2 ≤ η, ∀k ≥ K
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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.