Kavli Affiliate: Ran Wang
| First 5 Authors: Raman Goyal, Suman Chakravorty, Ran Wang, Mohamed Naveed Gul Mohamed,
We consider the problem of Reinforcement Learning for nonlinear stochastic
dynamical systems. We show that in the RL setting, there is an inherent “Curse
of Variance" in addition to Bellman’s infamous “Curse of Dimensionality", in
particular, we show that the variance in the solution grows
factorial-exponentially in the order of the approximation. A fundamental
consequence is that this precludes the search for anything other than “local"
feedback solutions in RL, in order to control the explosive variance growth,
and thus, ensure accuracy. We further show that the deterministic optimal
control has a perturbation structure, in that the higher order terms do not
affect the calculation of lower order terms, which can be utilized in RL to get
accurate local solutions.
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