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Stay positive! The importance of better models in stochastic optimization

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Stay positive! The importance of better models in stochastic optimization


John Duchi


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.


He is an assistant professor of Statistics and Electrical Engineering at Stanford University. He completed his PhD in computer science at Berkeley in 2014. His research interests are a bit eclectic, and they span computation, statistics, optimization, and machine learning. At Berkeley, He worked in the Statistical Artificial Intelligence Lab (SAIL) under the joint supervision of Michael Jordan and Martin Wainwright.


2019-07-18 at 3:30 pm (subject to variability)