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Mix and Match: An Optimistic Tree-Search Approach for Learning Models from Mixture Distributions
Matthew Faw · Rajat Sen · Karthikeyan Shanmugam · Constantine Caramanis · Sanjay Shakkottai

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #1002

We consider a covariate shift problem where one has access to several different training datasets for the same learning problem and a small validation set which possibly differs from all the individual training distributions. The distribution shift is due, in part, to \emph{unobserved} features in the datasets. The objective, then, is to find the best mixture distribution over the training datasets (with only observed features) such that training a learning algorithm using this mixture has the best validation performance. Our proposed algorithm, \textsf{Mix\&Match}, combines stochastic gradient descent (SGD) with optimistic tree search and model re-use (evolving partially trained models with samples from different mixture distributions) over the space of mixtures, for this task. We prove a novel high probability bound on the final SGD iterate without relying on a global gradient norm bound, and use it to show the advantages of model re-use. Additionally, we provide simple regret guarantees for our algorithm with respect to recovering the optimal mixture, given a total budget of SGD evaluations. Finally, we validate our algorithm on two real-world datasets.

Author Information

Matthew Faw (University of Texas at Austin)
Rajat Sen (Google)
Karthikeyan Shanmugam (IBM Research, NY)
Constantine Caramanis (UT Austin)
Sanjay Shakkottai (University of Texas at Austin)

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