EUROPT 2024
Abstract Submission

49. Implicit Regularisation of Mirror Flow on Separable Classification Problems

Invited abstract in session FD-2: Deterministic and stochastic optimization beyond Euclidean geometry, stream Advances in first-order optimization.

Friday, 14:10 - 15:50
Room: M:O

Authors (first author is the speaker)

1. Radu-Alexandru Dragomir
Telecom Paris

Abstract

We study continuous-time counterpart of mirror descent, namely mirror flow, on classification problems which are linearly separable. Such problems are minimised `at infinity' and have many possible solutions; we study which solution is preferred by the algorithm depending on the mirror potential.
We show that the iterates converge in direction towards the solution of a certain max-margin problem. This problem is determined by the horizon function of the potential, which can be seen as the norm induced by its shape `at infinity'. When the potential is separable, a simple formula allows to compute this function. We also prove the general existence of the horizon shape for subanalytic potentials.

Joint work with Scott Pesme and Nicolas Flammarion.

Keywords

Status: accepted


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