  We study a problem of best-effort adaptation motivated by several
applications and considerations, which consists of determining an accurate
predictor for a target domain, for which a moderate amount of labeled samples
are available, while leveraging information from another domain for which
substantially more labeled samples are at one's disposal. We present a new and
general discrepancy-based theoretical analysis of sample reweighting methods,
including bounds holding uniformly over the weights. We show how these bounds
can guide the design of learning algorithms that we discuss in detail. We
further show that our learning guarantees and algorithms provide improved
solutions for standard domain adaptation problems, for which few labeled data
or none are available from the target domain. We finally report the results of
a series of experiments demonstrating the effectiveness of our best-effort
adaptation and domain adaptation algorithms, as well as comparisons with
several baselines. We also discuss how our analysis can benefit the design of
principled solutions for fine-tuning.
