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Using the sum-to-product formulae for trigonometric functions you have the exact equation: \begin{align} \cos (t+m) &= \cos ((t+\tfrac{m}{2})+\tfrac{m}{2}) \\[6pt] &= \cos((t+\tfrac{m}{2})-\tfrac{m}{2}) - 2 \sin(\tfrac{m}{2}) \sin(t+\tfrac{m}{2}) \\[6pt] &= \cos(t) - 2 \sin(\tfrac{m}{2}) \sin(t+\tfrac{m}{2}). \\[6pt] \end{align} Now, if $m$ ...

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I think the phenomenon you're observing is just a consequence of the optimization procedure terminating prematurely. The softmax network is not obtaining a parameter configuration that is equivalent to the sigmoid loss. The sigmoid network has a lower loss, so we know the softmax network isn’t done training. We can prove that mathematically there must be ...

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The policy network can output a constant length vector the same size as the action space. Then you can simply mask out the invalid actions so that they aren't chosen.

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Yes, your idea is right. When unrolled in time, the RNN looks like this I am going out . ↓ ↓ ↓ ↓ ↓ █ → █ → █ → █ → █ → □ where █ is the recurrently applied function and □ is the classifier. The so-called back-propagation in time is nothing but pretending that the RNN is a very deep feed-forward network with the same layer ...

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