  Excessive reuse of holdout data can lead to overfitting. However, there is
little concrete evidence of significant overfitting due to holdout reuse in
popular multiclass benchmarks today. Known results show that, in the
worst-case, revealing the accuracy of $k$ adaptively chosen classifiers on a
data set of size $n$ allows to create a classifier with bias of
$\Theta(\sqrt{k/n})$ for any binary prediction problem. We show a new upper
bound of $\tilde O(\max\{\sqrt{k\log(n)/(mn)},k/n\})$ on the worst-case bias
that any attack can achieve in a prediction problem with $m$ classes. Moreover,
we present an efficient attack that achieve a bias of $\Omega(\sqrt{k/(m^2
n)})$ and improves on previous work for the binary setting ($m=2$). We also
present an inefficient attack that achieves a bias of $\tilde\Omega(k/n)$.
Complementing our theoretical work, we give new practical attacks to
stress-test multiclass benchmarks by aiming to create as large a bias as
possible with a given number of queries. Our experiments show that the
additional uncertainty of prediction with a large number of classes indeed
mitigates the effect of our best attacks.
  Our work extends developments in understanding overfitting due to adaptive
data analysis to multiclass prediction problems. It also bears out the
surprising fact that multiclass prediction problems are significantly more
robust to overfitting when reusing a test (or holdout) dataset. This offers an
explanation as to why popular multiclass prediction benchmarks, such as
ImageNet, may enjoy a longer lifespan than what intuition from literature on
binary classification suggests.
