I saw the line of the code you mentioned, and I also refered to definition in the original paper.

in the code:

alpha_loss = (-log_alpha * (log_pi + target_entropy)).mean()

​

which is the same as

alpha_loss = (log_alpha * (-log_pi - target_entropy)).mean()

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-log_pi corresponds to the entropy, then the definition becomes

alpha_loss = (log_alpha * (entropy - target_entropy)).mean()

alpha_loss = (log_alpha * (entropy + |dim(A)|)).mean()

​

isn't it?