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math.OC2021
Stochastic Subgradient Descent on a Generic Definable Function Converges to a Minimizer
Sholom Schechtman
It was previously shown by Davis and Drusvyatskiy that every Clarke critical point of a generic, semialgebraic (and more generally definable in an o-minimal structure), weakly conv…
math.OC2021
Stochastic Subgradient Descent Escapes Active Strict Saddles on Weakly Convex Functions
Pascal Bianchi, Walid Hachem, Sholom Schechtman
In non-smooth stochastic optimization, we establish the non-convergence of the stochastic subgradient descent (SGD) to the critical points recently called active strict saddles by…
math.OC2021★ 6 cited
Stochastic proximal subgradient descent oscillates in the vicinity of its accumulation set
Sholom Schechtman
We analyze the stochastic proximal subgradient descent in the case where the objective functions are path differentiable and verify a Sard-type condition. While the accumulation se…