Hyperband bracket generation is inconsistent with the original Hyperband paper

[nabenabe0928]

The DEHB paper says that each SH bracket samples $n = \lceil \frac{s{\max} + 1}{s + 1} \eta^s \rceil$ configurations; however, this line samples $n = \lfloor\lfloor \frac{s{\max} + 1}{s + 1} \rfloor \eta^s\rfloor$ configurations. In reality, this line should be:

n0 = int(np.ceil(self.max_SH_iter / (s + 1) * self.eta ** s))

Note that self.max_SH_iter is $s_{\max} + 1$.

[Neeratyoy]

Hi

The implementation details were verified and cross-checked by the then official implementation of HyperBand as seen here. Therefore, in our experiments, the comparison of DEHB with HB and BOHB is much fairer as one can see that during the first HB iteration, all 3 algorithms perform similarly.