Beyond the Bellman Fixed Point: Geometry and Fast Policy Identification in Value Iteration
Q-value iteration (Q-VI) is usually analyzed through the \(γ\)-contraction of the Bellman operator. This argument proves convergence to \(Q^*\), but it gives only a coarse account of when the induced greedy policy becomes optimal. We study discounted Q-VI as a switching system and focus on the practically optimal solution set (POSS), the set of \(Q\)-functions whose tie-broken greedy policies are optimal. The main result shows that Q-VI reaches the optimal action class in finite time by entering
Record details
Published: 19 April 2026
Source: arXiv
Category: Research
Topics: Regulation
Retrieved: 14 July 2026
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ethics.ai (19 April 2026), “Beyond the Bellman Fixed Point: Geometry and Fast Policy Identification in Value Iteration,” evidence record 5660, https://ethics.ai/record/5660 (originally published by arXiv).
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