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Accelerated Stochastic Gradient-free and Projection-free Methods

ICML 2020 · Optimization › Nonconvex and smooth optimization · approach: Stochastic Frank-Wolfe methods · 8 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use Acc-ZO-FW instead of FW-BlackFinite-sum optimization · Finite-sum nonconvex optimizationfunction query complexity: O(dnε^{-4}) -> O(dnε^{-2}); improves the existing result by a factor of O(ε^{-2})Helped
Add SPIDER/SpiderBoost variance reduction and momentum accelerationAcc-SZOFW · Finite-sum nonconvex optimizationfunction query complexity: O(dnε^{-4}) -> O(dn^{\frac{1}{2}}ε^{-2}); improves the existing result by a factor of O(\sqrt{n}ε^{-2})Helped
Add SPIDER/SpiderBoost variance reduction and momentum accelerationAcc-SZOFW · Stochastic nonconvex optimizationfunction query complexity: O(dε^{-4}) -> O(dε^{-3}); improves the existing result by a factor of O(ε^{-1})Helped
Replace large-batch SPIDER-style variance reduction with STORM (ablation)Acc-SZOFW · Stochastic nonconvex optimizationfunction query complexity: O(dε^{-3})No clear effect
Replace CooGE with UniGE (ablation)Acc-SZOFW · Stochastic nonconvex optimizationfunction query complexity: O(dε^{-3})No clear effect
Replace CooGE with UniGE (ablation)Acc-SZOFW* · Stochastic nonconvex optimizationfunction query complexity: O(dε^{-3}) -> O(d^{\frac{3}{2}}ε^{-3})Hurt
Use UniGE rather than CooGE (ablation)Acc-SZOFW variants · Universal adversarial perturbation and robust black-box binary classificationfunction query convergence speedHelped
Use CooGE rather than UniGE (ablation)Acc-SZOFW variants · Universal adversarial perturbationattack loss versus function queriesHurt
Use Acc-SZOFW instead of Acc-SZOFW*Stochastic zeroth-order Frank-Wolfe · Universal adversarial perturbationattack lossHelped
Add the proposed momentum acceleration to the deterministic zeroth-order Frank-Wolfe methodAcc-ZO-FW · Single adversarial perturbation (MNIST, CIFAR10)attack lossHelped
Add variance reduction and momentum accelerationAcc-SZOFW algorithms · Universal adversarial perturbation and robust black-box binary classificationconvergence speed per iterationHelped

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