A regularization interpretation of the proximal point method for weakly convex functions
By Tim Hoheisel, Maxime Laborde, Adam M. Oberman. 2020
31 citations recorded by the source corpus.
Empirical evidence and theoretical results suggest that the proximal point method can be computed approximately and still converge faster than the corresponding gradient descent method, in both the stochastic and exact gradient case. In this article we provide a perspective on this result by interpreting the method as gradient descent on a regularized function. This perspective applies in the case of weakly convex functions where proofs of the faster rates are not available. Using this analysis we find the optimal value of the regularization parameter in terms of the weak convexity.
Subfields: Artificial Intelligence, Computational Mechanics, Numerical Analysis
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Citations in the corpus
- Personalized Federated Learning with Moreau Envelopes (2020, methodology): “Finally, we review several useful properties of the Moreau envelope such as smoothing and preserving convexity as follows (see the review and proof for the convex case in [40, 46, 47] and for nonconvex smooth case in [48], respectively): Proposition 1.”