An adaptive mixed-sample SGD procedure is claimed to converge at 1/sqrt(T) to a solution whose target risk matches the better of source-only and target-only ERM, but the main convergence bound contains a non-vanishing constant term, so the claim is not established.
Stochastic gradient descent with only one projection
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Mixed-Sample SGD: an End-to-end Analysis of Supervised Transfer Learning
An adaptive mixed-sample SGD procedure is claimed to converge at 1/sqrt(T) to a solution whose target risk matches the better of source-only and target-only ERM, but the main convergence bound contains a non-vanishing constant term, so the claim is not established.