Truncated Back-propagation for Bilevel Optimization
release_wwjtv6kdqffcbed27exojrlvva
by
Amirreza Shaban, Ching-An Cheng, Nathan Hatch, Byron Boots
2018
Abstract
Bilevel optimization has been recently revisited for designing and analyzing
algorithms in hyperparameter tuning and meta learning tasks. However, due to
its nested structure, evaluating exact gradients for high-dimensional problems
is computationally challenging. One heuristic to circumvent this difficulty is
to use the approximate gradient given by performing truncated back-propagation
through the iterative optimization procedure that solves the lower-level
problem. Although promising empirical performance has been reported, its
theoretical properties are still unclear. In this paper, we analyze the
properties of this family of approximate gradients and establish sufficient
conditions for convergence. We validate this on several hyperparameter tuning
and meta learning tasks. We find that optimization with the approximate
gradient computed using few-step back-propagation often performs comparably to
optimization with the exact gradient, while requiring far less memory and half
the computation time.
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