Input Signal Shape Optimization

I have a system, described by a black-box (a fully connected neural network), that takes as input a signal in time (let's say something similar to a sine wave) and returns a single scalar as output.

My goal is to find the optimum signal that maximizes/minimizes the output. As constraints, the time average of the signal must be kept constant and the minimum and maximum value of the signal must be within a specific range.

I wonder what kind of optimization algorithm is more suitable for this kind of problem.

I was thinking of applying reinforcement learning to change the shape of the signal. The idea is to let the agent to modify the value of the signal at a given instant, and then reconstruct the signal to avoid discontinuities or big jumps from one instant to the other.

However, I am not sure this is the best approach for such an application.