Non-convex optimization for machine learning

What makes non-convex optimization hard? Such optimization problems may have multiple feasible and very flat regions, a widely varying curvature, several saddle points, and multiple local minima within each region._{Jul 27, 2020}

Many modern learning problems boil down to a nonconvex optimization problem, where the objective function is the average or the expectation of some loss function over a finite or infinite dataset. Solving such nonconvex optimization problems, in general, can be NP-hard.

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