Neural network terminology "minimize" In the TensorFlow documentation, it appears that the optimizer method "minimize" just takes a single step in the direction of the gradient (rather than doing this repeatedly until a local minimum is found).  Is that terminology standard in machine learning?  For example, the DDPG algorithm given in this paper contains the phrase "Update critic by minimizing the loss...".  Does this actually mean "Take a single step in the direction of the negative loss gradient..."?
 A: The two are different because one is a software method and the other a mathematical concept. The TensorFlow optimizers have methods called minimize which does exactly what you say: takes a single step in the the direction of steepest descent. But minimize is just meant to be evocative -- the goal of taking a step in the steepest descent direction is to minimize the function (perhaps after several iterations), but as we all know there are all sorts of caveats about minimization using steepest descent-type methods. Of course the method name is completely arbitrary: it could, at the cost of having a confusing name, be called foo (or anything else) and the software would work exactly the same, and carry out the exact same computational procedures.
When people are describing algorithms and statistical procedures in contexts like academic articles and textbooks, "minimize" means "find a (possibly global) minimum." When we solve an OLS problem, we minimize the squared error loss by solving for the point where the gradient is zero (assuming the specific problem is strictly convex; otherwise the OLS solution is not uniquely defined).
