Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions

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 $\mathcal{O}(ε^{-2})$ calls to the stochastic gradient oracle to find an $ε$-optimal solution. Furthermore, by including a gradient sliding step, we show that the number of calls reduces to $\mathcal{O}(ε^{-1.5})$.

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