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This expression: $|\mathcal{A}(s)|$ means $|\quad|$ the size of $\mathcal{A}(s)$ the set of actions in state $s$ or more simply the number of actions allowed in the state. This makes sense in the given formula because $\frac{\epsilon}{|\mathcal{A}(s)|}$ is then the probability of taking each exploratory action in an $\epsilon$-greedy policy. The overall ...

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I'm using OpenAI's cartpole environment. First of all, is this environment not Markov? The OpenAI Gym CartPole environment is Markov. Whether or not you know the transition probabilities does not affect whether the state has the Markov property. All that matters is that knowing the current state is enough to be determine the next state and reward in ...

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I am wondering how to generate datasets when the environment is not as simple as a tic-tac-toe or a maze problem There is no difference in concept, which is why tic-tac-toe and maze problems are used to teach. As you have noted, the main difference between reinforcement learning (RL) and supervised learning is that RL does not use labeled datasets. If you ...

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This post contains many answers that describe the difference between on-policy vs. off-policy. Your book may be referring to how the current (DQN-based) state-of-the-art (SOTA) algorithms, such as Ape-X, R2D2, Agent57 are technically "off-policy", since they use a (very large!) replay buffer, often filled in a distributed manner. This has a number ...

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DDPG is an off-policy algorithm simply because of the objective taking expectation with respect to some other distribution that we are not learning about, i.e. the deterministic policy gradient can be expressed as \nabla _{\theta^\mu} J \approx \mathbb{E}_{s_t \sim \rho^\beta} \left[ \nabla _{\theta^\mu} Q(s,a|\theta^Q) | s=s_t, a=\mu(s_t ; \theta ^\mu) \...

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First, some preliminary questions: in this case, what is the optimal policy? It is the policy that maximises return from any given time step $G_t$. You need to be careful with your definition of return with continuing environments. The simple expected sum of future rewards is likely to be positive or negative infinity. There are three basic approaches: ...

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In the DRL nanodegree in Udacity, the instructor says it is possible to combine on- and off-policy learning and suggests the following paper where this has been done: Q-Prop: Sample-Efficient Policy Gradient with An Off-Policy Critic (ICLR 2017). Citing the paper: The core idea is to use the first-order Taylor expansion of the critic as a control ...

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