AdaGrad converges at a rate depending on the unknown tail index p for 4/3 < p ≤ 2 in non-convex optimization, with an algorithm-dependent lower bound and an improved rate for AdaGrad-Norm under a mild extra assumption for 1 < p ≤ 2.
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Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? A Case Study of AdaGrad
AdaGrad converges at a rate depending on the unknown tail index p for 4/3 < p ≤ 2 in non-convex optimization, with an algorithm-dependent lower bound and an improved rate for AdaGrad-Norm under a mild extra assumption for 1 < p ≤ 2.