# Are there known error bounds for TD(0) with a constant learning rate?

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

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

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.