홈 › Papers

Gradient Descent Converges Linearly for Logistic Regression on Separable Data

We show that running gradient descent with variable learning rate guarantees loss $f(x) \leq 1.1 \cdot f(x^*) + \epsilon$ for the logistic regression objective, where the error $\epsilon$ decays exponentially with the number of iterations and polynomially with the magnitude of the entries of an arbitrary fixed solution $x^*$. This is in contrast to the common intuition that the absence of strong convexity precludes linear convergence of first-order methods, and highlights the importance of variable learning rates for gradient descent. We also apply our ideas to sparse logistic regression, where they lead to an exponential improvement of the sparsity-error tradeoff.

Code (0)

등록된 구현이 없습니다.

Tasks

Methods 이 논문이 사용한 방법론

Similar Papers 제목 키워드 기반