Hi, @Raja_Singh. It’s a difficult problem. Unless your cost surface is known to have a unique global minimum (e.g. simple regression with a cost function built on mean-square-error loss), there are no guarantees unless…wait for it…you have an infinite amount of time and maybe a quantum computer.
You will gain more insight into this in Course 2, in particular, with “stochastic gradient descent.” Deep Learning had many engineering aspects to it, where the quality of the solution is gauged by various performance metrics and not whether you have attained a global optimum–which is typically unknowable.
I came from a discipline where uniqueness proofs were once critical. So I too, had a natural discomfort with this idea. Let’s see what you think after the second course of the specialization.