Standard stochastic optimization methods are brittle, sensitive to stepsize
choices and other algorithmic parameters, and they exhibit instability outside
of well-behaved families of objectives. To address these challenges, we
investigate models for stochastic minimization and learning problems that
exhibit better robustness to problem families and algorithmic parameters. With
appropriately accurate models---which we call the aProx family---stochastic
methods can be made stable, provably convergent and asymptotically optimal;
even modeling that the objective is nonnegative is sufficient for this
stability. We extend these results beyond convexity to weakly convex
objectives, which include compositions of convex losses with smooth functions
common in modern machine learning applications. We highlight the importance of
robustness and accurate modeling with a careful experimental evaluation of
convergence time and algorithm sensitivity.

通过研究随机最小化和学习问题的模型，我们提出了一种更具鲁棒性的解决方案。通过适当精确的模型，即所谓的 aProx 系列，随机最优化方法可以稳定，可证明收敛且渐近最优。我们将这些结果扩展到弱凸目标，其中包括凸损失与光滑函数的组合，在现代机器学习应用中很常见。通过对收敛时间和算法灵敏度的仔细实验评估，我们强调了鲁棒性和准确的建模的重要性。