Sample complexity lower bounds for generic algorithms in contaminated PAC learning

Derive sample complexity lower bounds for generic learning algorithms in the iterative PAC learning model with contamination rate α, quantifying the minimal number of labeled examples (as a function of VC dimension, α, n, and t) required to achieve a target generalization error.

Background

Beyond the specific lower bound showing repeated ERM can stall and the upper bounds for two proposed algorithms, the paper does not provide general lower bounds applicable to arbitrary learning procedures in the contaminated setting.

The authors explicitly identify obtaining sample complexity lower bounds for generic algorithms as an open problem, aiming to understand fundamental limits under recursive synthetic contamination.