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Taking total expectation and setting ak :=E[V ∞ ε (ek)] gives the scalar recursion ak+1 ≤β 2 ε ak +α 2C2 ε Wmax + (4(1 +γ)B Q)2

Hence, it follows from Equation (56) that E[V ∞ ε (ek+1)| F M k ]≤β 2 ε V ∞ ε (ek) +α 2Cε(Cε −1) Wmax + (4(1 +γ)B Q)2 +α 2Cε Wmax + (4(1 +γ)B Q)2 =β 2 ε V ∞ ε (ek) +α 2C2 ε Wmax +

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Lyapunov-Certified Direct Switching Theory for Q-Learning

cs.LG · 2026-04-21 · unverdicted · novelty 7.0

Q-learning error is recast as a switched linear recursion whose exponential rate is exactly the joint spectral radius of a direct switching family, yielding finite-time bounds via a product-defined Lyapunov function.

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  • Lyapunov-Certified Direct Switching Theory for Q-Learning cs.LG · 2026-04-21 · unverdicted · none · ref 40

    Q-learning error is recast as a switched linear recursion whose exponential rate is exactly the joint spectral radius of a direct switching family, yielding finite-time bounds via a product-defined Lyapunov function.