Stochastic Weakly Convex Optimization Beyond Lipschitz Continuity
This work addresses optimization challenges in machine learning by relaxing standard assumptions, though it appears incremental as it extends existing convergence guarantees to broader conditions.
The paper tackles stochastic weakly convex optimization without requiring Lipschitz continuity, showing that stochastic algorithms like the subgradient method achieve an O(1/√K) convergence rate with constant failure probability under weaker assumptions.
This paper considers stochastic weakly convex optimization without the standard Lipschitz continuity assumption. Based on new adaptive regularization (stepsize) strategies, we show that a wide class of stochastic algorithms, including the stochastic subgradient method, preserve the $\mathcal{O} ( 1 / \sqrt{K})$ convergence rate with constant failure rate. Our analyses rest on rather weak assumptions: the Lipschitz parameter can be either bounded by a general growth function of $\|x\|$ or locally estimated through independent random samples.