"Simple and near-optimal algorithms for hidden stratification and multi-group learning" https://arxiv.org/abs/2112.12181

Unfortunately, the proof of the theorem concerning "Algorithm 3" (Consistent majority algorithm) in the group-realizable setting, is flawed, due to a incorrect bound on the number of possible hypotheses that could be output by the algorithm.

Replacing this incorrect bound with the conservative $|\mathcal{H}^{|\mathcal{G}|}$ leads to a substantially worse bound of
$$
  L(f \mid g) \leq O(\log(|\mathcal{H}|^{|\mathcal{G}|}/\delta) / \#_n(g))
$$
for all $g in \mathcal{G}$.

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Update 2024-06-17: The "Consistent majority algorithm" and its analysis were removed in v2 of the arxiv paper. (But you can see it in v1.)