SlowGuess/NeurIPS_2023_OCR huggingface dataset:
$$
\mathbb {E} \Delta_ {t} \left(\boldsymbol {W} ^ {(t, 0)}\right) \leq \frac {R _ {\max }}{1 - \gamma} \cdot (1 + \gamma) \tau^ {\star} \cdot \eta_ {t - \tau^ {\star}}. \tag {170}
$$
Combining (169) and (170), we have
$$
\left| I _ {4} \right| \leq \frac {R _ {\max }}{1 - \gamma} \cdot (1 + \gamma) \tau^ {\star} \cdot \eta_ {\max  \{0, t - \tau^ {*} \}}, \tag {171}
$$
where  $\tau^{\star} = \min \{t\mid \lambda \nu^{t}\leq \eta_{T}\}$