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The answer to your first question is because the line 'update the critic by minimising the loss $L = \frac{1}{N} \sum_i \left( y_i - Q(s_i, a_i |\theta^Q)\right)^2$ is implying that you will do this by using a gradient, i.e. you calculate the gradient of the loss wrt the parameters and perform a gradient descent step. For the second question, I am not 100% ...


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