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This paper is motivated by structured sparsity for deep neural networktraining. We study a weighted group L0-norm constraint, and present theprojection and normal cone of this set. Using randomized smoothing, we developzeroth and first-order algorithms for minimizing a Lipschitz continuousfunction constrained by any closed set which can be projected onto.Non-asymptotic convergence guarantees are proven in expectation for theproposed algorithms for two related convergence criteria which can beconsidered as approximate stationary points. Two further methods are givenusing the proposed algorithms: one with non-asymptotic convergence guaranteesin high probability, and the other with asymptotic guarantees to a stationarypoint almost surely. We believe in particular that these are the first suchnon-asymptotic convergence results for constrained Lipschitz continuous lossfunctions.

Sparse Training with Lipschitz Continuous Loss Functions and a Weighted Group L0-norm Constraint