he loss function at time \\(t\\):

$$
L\_t = (r\_t + \gamma \max\_a Q(s\_{t+1}, a) - Q(s\_t, a\_t))^2
$$

Here \\(y = r\_t + \gamma \max\_a Q(s\_{t+1}, a)\\) is thought of as a scalar-valued fixed target, while we backpropagate through the neural network that produced the prediction \\(f\_{\theta} = Q(s\_t,a\_t)\\). Note that the loss has a standard L2 norm regression form, and that we nudge the parameter vector \\(\theta\\) in a way that makes the computed \\(Q(s,a)\\) slightly closer to what it should be 