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I've a Reinforcement Learning problem where I want to learn the Q function. For action space of size in the order of 100s is Q learning a good option? Will it converge?

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Yes, Q learning will work, but the problem is the size of the state-action space. Tabulating the Q function for each state-action pair is infeasible, so you'd need to use function approximation methods. Check out Lecture 6 of David Silver's course notes for details: http://www0.cs.ucl.ac.uk/staff/d.silver/web/Teaching.html

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Are all actions feasible at each step? If there is some feedback that allows you to determine quickly that an action is suboptimal, you can learn to eliminate it - https://openreview.net/forum?id=HyejB4J2xX Maybe there is an updated version on arXiv

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