  We revisit the \emph{leaderboard problem} introduced by Blum and Hardt (2015)
in an effort to reduce overfitting in machine learning benchmarks. We show that
a randomized version of their Ladder algorithm achieves leaderboard error
O(1/n^{0.4}) compared with the previous best rate of O(1/n^{1/3}).
  Short of proving that our algorithm is optimal, we point out a major obstacle
toward further progress. Specifically, any improvement to our upper bound would
lead to asymptotic improvements in the general adaptive estimation setting as
have remained elusive in recent years. This connection also directly leads to
lower bounds for specific classes of algorithms. In particular, we exhibit a
new attack on the leaderboard algorithm that both theoretically and empirically
distinguishes between our algorithm and previous leaderboard algorithms.
