Multi-distribution learning is a natural generalization of PAC learning to
settings with multiple data distributions. There remains a significant gap
between the known upper and lower bounds for PAC-learnable classes. In
particular, though we understand the sample complexity of learning a VC
dimension d class on k distributions to be O(ϵ−2ln(k)(d+k)+min{ϵ−1dk,ϵ−4ln(k)d}), the best lower bound is
Ω(ϵ−2(d+kln(k))). We discuss recent progress on this
problem and some hurdles that are fundamental to the use of game dynamics in
statistical learning.Comment: 11 pages. Authors are ordered alphabetically. Open problem presented
at the 36th Annual Conference on Learning Theor