A conditional universal approximation theorem shows that residual operator-block DQNs with depth aligned to Bellman iterations can approximate the optimal Q-function, assuming a neural operator class with controlled Lipschitz outputs exists.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
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Universal Approximation Theorem for Deep Q-Learning via FBSDE System
A conditional universal approximation theorem shows that residual operator-block DQNs with depth aligned to Bellman iterations can approximate the optimal Q-function, assuming a neural operator class with controlled Lipschitz outputs exists.