Zeroth-order methods achieve mean-square stability when the step size satisfies a condition involving the entire Hessian spectrum, with full-batch ZO optimizers operating at the edge of stability and large steps regularizing the Hessian trace.
Type-ii saddles and probabilistic stability of stochastic gradient descent
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Zeroth-Order Optimization at the Edge of Stability
Zeroth-order methods achieve mean-square stability when the step size satisfies a condition involving the entire Hessian spectrum, with full-batch ZO optimizers operating at the edge of stability and large steps regularizing the Hessian trace.