Implicit Bias of Mirror Flow on Separable Data

arXiv:2406.12763v1 Announce Type: cross
Abstract: We examine the 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. For exponential tailed losses and under mild assumptions on the potential, we show that the iterates converge in direction towards a $\phi_\infty$-maximum margin classifier. The function $\phi_\infty$ is the $\textit{horizon function}$ of …

abstract algorithm arxiv bias classification continuous cs.lg data flow losses math.oc potential solution solutions stat.ml study the algorithm type