Mixed-Sample SGD: an End-to-end Analysis of Supervised Transfer Learning
This addresses efficient optimization for supervised transfer learning, an incremental improvement over prior statistical-focused works.
The paper tackles the problem of designing an SGD procedure for supervised transfer learning that alternates sampling between source and target data without prior knowledge of source quality, showing convergence with a 1/√T rate to a solution adaptive to source informativeness.
Theoretical works on supervised transfer learning (STL) -- where the learner has access to labeled samples from both source and target distributions -- have for the most part focused on statistical aspects of the problem, while efficient optimization has received less attention. We consider the problem of designing an SGD procedure for STL that alternates sampling between source and target data, while maintaining statistical transfer guarantees without prior knowledge of the quality of the source data. A main algorithmic difficulty is in understanding how to design such an adaptive sub-sampling mechanism at each SGD step, to automatically gain from the source when it is informative, or bias towards the target and avoid negative transfer when the source is less informative. We show that, such a mixed-sample SGD procedure is feasible for general prediction tasks with convex losses, rooted in tracking an abstract sequence of constrained convex programs that serve to maintain the desired transfer guarantees. We instantiate these results in the concrete setting of linear regression with square loss, and show that the procedure converges, with $1/\sqrt{T}$ rate, to a solution whose statistical performance on the target is adaptive to the a priori unknown quality of the source. Experiments with synthetic and real datasets support the theory.