HpBandSter Number of sampled configurations

Hello, I just tried out your nice package for hyperparameter optimization and it works well. I want to understand how many configs are sampled and with which budget they are executed so I looked into the paper and the source code. I recognized some differences between the paper and the implementation which in the end lead to different number of sampled configs. For instance the number of successive halving runs is self.max_SH_iter = -int(np.log(min_budget/max_budget)/np.log(eta)) + 1 in the code but in the paper :
$s_ {max} = \lfloor log_{\eta} \frac{b_{max}}{b_{min}} \rfloor$ (without the +1) This influences the number of sampled configs: n0 = int(np.floor((self.max_SH_iter)/(s+1)) * self.eta**s) Is there a reason for this difference?

Thanks for any help in advance!

Nov 26 '19 14:11 HannahElisa

I thing here self.max_SH_iter represents the calculation of $\frac{B}{R}$

More precisely, if we look at the original paper, we see that

$B = (s_{max} + 1)R \Rightarrow \frac{B}{R} = (s_{max} + 1)$

And here, self.max_SH_iter = -int(np.log(min_budget/max_budget)/np.log(eta)) + 1

$\begin{align*} &= -1 * \frac{\log{(\frac{b_{min}}{b_{max}})}}{\log{\eta}} + 1 \\ &= -1 * \log_\eta{(\frac{b_{min}}{b_{max}})} + 1 \\ &= \log_\eta{(\frac{b_{min}}{b_{max}})}^{-1} + 1 \\ &= \log_\eta{(\frac{b_{max}}{b_{min}})} + 1 \\ &= s_{max} + 1 \end{align*}$

Dec 08 '19 22:12 Rayn2402

Thanks for your answer. Could you please specify where exactly you found the equation for $\frac{B}{R}$ in the original paper? I searched for it also in the supplementary material but cannot find it there.

Dec 09 '19 12:12 HannahElisa

If you're looking at Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization

It's in the initialization line of Algorithm 1 at page 8.

Dec 09 '19 14:12 Rayn2402

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Number of sampled configurations

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