Gradient free methods work on any optimization problem, including deep networks, because gradient free methods do not require a smooth parametrization of the se

Gradient free methods work on any optimization problem, including deep networks, because gradient free methods do not require a smooth parametrization of the search space. For deep networks the parameters are on a smooth manifold and that's why gradient based optimizers are used to find near optimal solutions/parameters, i.e. the search space has the structure of a smooth manifold so the parameters can be updated with gradient descent.