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Policies found by Deep Q-Learning, even after convergence, are not guaranteed to be optimal. The reason is that the neural networks that approximate the Q function in DQN inherently come with a statistical error (bias and variance), a pointer can be found here. Furthermore, convergence to the optimal policy for tabular Q-learning is only guaranteed when ...


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Looks 'correct' to me, in the sense that it satisfies the requirements for being an MDP. Whether it models the underlying real-world problem correctly cannot be validated with the information given here.


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In the long-run, tabular Q-learning converges toward the optimal regardless of initialization. However, the speed of convergence may be affected, similarly to an n-armed bandit setting : http://incompleteideas.net/book/first/ebook/node21.html For more on initialization in Q learning, I recommend "Potential-based shaping and Q-value initialization are ...


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