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Is there any known error bounds for the TD(0) algorithm for the value function after a finite number of iterations?

$$ \Delta_t=\max_{s \in \mathcal{S}}|v_t(s)-v_\pi(s)|$$ $$v_{t+1}(s_t)=v_t(s_t)+\alpha(r+v_t(s_{t+1})-v_t(s_t))$$

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The paper "Bias-Variance" Error Bounds for Temporal Difference Updates (2000) by M. Kearns and S. Singh provides error bounds for temporal-difference algorithms, i.e. TD($k$) and TD($\lambda$) (see theorem 1 and theorem 2, respectively). Note that both TD($k$) and TD($\lambda$) include TD($0$) as a special case.

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  • $\begingroup$ I'm confused, is this for situations where the environment states can be enumerated or does it apply in general? I didn't see a parametrization. $\endgroup$ Sep 14 '20 at 7:50
  • $\begingroup$ @FourierFlux Do you mean if they assume that the state space is discrete? I need to read this paper again. It was a long time ago that I skimmed through it. $\endgroup$
    – nbro
    Sep 14 '20 at 20:54

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