Articles by category: optimization

Non-convex First Order Methods

20 Jun 2017

Non-convex First Order MethodsThis is a high-level overview of the methods for first order local improvement optimization methods for non-convex, Lipschitz, (sub)differentiable, and regularized functions with efficient derivatives, with a particular focus on neural networks (NNs).$\argmin_\vx f(\vx) = \argmin_\vx \frac{1}{n}\sum_{i=1}^nf_i(\vx)+\Omega(\vx)$Make sure to read the general overview post first. I’d also reiterate as Moritz Hardt has that one should be wary of only looking at con...

Neural Network Optimization Methods

19 Jun 2017

Neural Network Optimization MethodsThe goal of this post and its related sub-posts is to explore at a high level how the theoretical guarantees of the various optimization methods interact with non-convex problems in practice, where we don’t really know Lipschitz constants, the validity of the assumptions that these methods make, or appropriate hyperparameters. Obviously, a detailed treatment would require delving into intricacies of cutting-edge research. That’s not the point of this post, w...