Generalization Bounds for Data-Driven Numerical Linear Algebra. (arXiv:2206.07886v1 [cs.LG])

Data-driven algorithms can adapt their internal structure or parameters to
inputs from unknown application-specific distributions, by learning from a
training sample of inputs. Several recent works have applied this approach to
problems in numerical linear algebra, obtaining significant empirical gains in
performance. However, no theoretical explanation for their success was known.

In this work we prove generalization bounds for those algorithms, within the
PAC-learning framework for data-driven algorithm selection proposed by Gupta
and Roughgarden (SICOMP 2017). Our main results are …

arxiv data data-driven lg linear linear algebra numerical