Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions. (arXiv:2006.08167v2 [math.OC] UPDATED)

Web: http://arxiv.org/abs/2006.08167

We analyze stochastic conditional gradient methods for constrained
optimization problems arising in over-parametrized machine learning. We show
that one could leverage the interpolation-like conditions satisfied by such
models to obtain improved oracle complexities. Specifically, when the objective
function is convex, we show that the conditional gradient method requires
$\mathcal{O}(\epsilon^{-2})$ calls to the stochastic gradient oracle to find an
$\epsilon$-optimal solution. Furthermore, by including a gradient sliding step,
we show that the number of calls reduces to $\mathcal{O}(\epsilon^{-1.5})$.

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