Implicit differentiation for fast hyperparameter selection in non-smooth convex learning. (arXiv:2105.01637v3 [stat.ML] UPDATED)

Finding the optimal hyperparameters of a model can be cast as a bilevel
optimization problem, typically solved using zero-order techniques. In this
work we study first-order methods when the inner optimization problem is convex
but non-smooth. We show that the forward-mode differentiation of proximal
gradient descent and proximal coordinate descent yield sequences of Jacobians
converging toward the exact Jacobian. Using implicit differentiation, we show
it is possible to leverage the non-smoothness of the inner problem to speed up
the computation. …

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