• Corpus ID: 235659009

High-probability Bounds for Non-Convex Stochastic Optimization with Heavy Tails

  title={High-probability Bounds for Non-Convex Stochastic Optimization with Heavy Tails},
  author={Ashok Cutkosky and Harsh Mehta},
We consider non-convex stochastic optimization using first-order algorithms for which the gradient estimates may have heavy tails. We show that a combination of gradient clipping, momentum, and normalized gradient descent yields convergence to critical points in high-probability with best-known rates for smooth losses when the gradients only have bounded p th moments for some p ∈ (1 , 2] . We then consider the case of second-order smooth losses, which to our knowledge have not been studied in… 

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