The importance of better models in stochastic optimization
This addresses robustness issues in stochastic optimization for machine learning practitioners, though it appears incremental as it builds on existing modeling approaches.
The paper tackles the brittleness and instability of standard stochastic optimization methods by introducing the aProx family of models, which improve robustness and enable stable, provably convergent, and asymptotically optimal performance, even for weakly convex objectives common in machine learning.
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.