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

• URL: http://arxiv.org/abs/2006.08167v2
• Date: Wed, 26 Jan 2022 19:49:59 GMT
• Title: Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions
• Authors: Tesi Xiao, Krishnakumar Balasubramanian, Saeed Ghadimi
• Abstract summary: We show that the conditional gradient method requires $mathcalO(epsilon-1.5)$ calls to the gradient oracle to find an $epsilon$-optimal solution. By including a gradient sliding step, we show that the number of calls reduces to $mathcalO(epsilon-1.5)$.
• Score: 12.096252285460814
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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