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I've been looking at neural networks for control applications. Let's say I used an RL algorithm to train a controller for the cart pole balancing problem.

Assuming the neural network is simple and very small, I can pretty much deduce what exactly the network is doing. For instance, if the network takes inputs for pole angle and cart position and outputs a motor force, the neural network is approximating a function that will move the cart left if the pole is falling left etc. and I can forward propagate through the network manually, again assuming that it is simple. In this case however, I could say that the neural network isn't truly learning a behavior, and instead is just mapping the problem space.

However, what if I trained another, larger network for a similar problem, where there are environmental uncertainties that randomly occur (ie. oil patch on the ground so the cart dynamics change, or the ground is made of ice, or there are stochastic disturbances that simulate someone bumping the cart). If the training is successful, the resulting neural network would be learning the behaviour of balancing the cart for a variety of situations (robustness), instead of just pushing it left or right depending on the pole angle.

The cart pole problem may not be the best example for this since it's a relatively simple control problem, but for more complex behaviors (ie. autonomous driving), where does this inflection point between learning and mapping exist?

Is this even a valid question, or am I just completely mistaken and everything is technically just a function approximation and there is never any "true" robust learning happening?

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