It would, but it would be super inefficient and slow. For smooth functions, gradient information gives more information about the search terrain. The more exac

It would, but it would be super inefficient and slow. For smooth functions, gradient information gives more information about the search terrain. The more exact your gradient information, the higher quality your iterations become. On the other gradients aren't defined everywhere (e.g. non-smooth functions like abs(x), max(0,x), or discontinuous/discrete integer variables like x=1,2,3,4...), and gradient based methods can land on saddle points. This is where derivative free optimization (DFO) can help. The downside is they converge far, far, far slower than gradient based methods. It's unlike DFO would scale to what is needed to solve even basic DL models.