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However, limited characterizations have been discussed on the rate (exponent) of this value. In this paper, we characterize the minimax optimal rate as a result of an optimization over all possible parameters. We introduce two rates, $R^{\\mathrm{go}}$ and $R^{\\mathrm{go}}_{\\infty}$, corresponding to lower bounds on the probability of misidentification, each of which is associated with a proposed algorithm. The rate $R^{\\mathrm{go}}$ is associated with $R^{\\mathrm{go}}$-tracking, which can be efficiently implemented by a neural network and is shown to outperform existing algorithms. However, this rate requires a nontrivial condition to be achievable. To address this issue, we introduce the second rate $R^{\\mathrm{go}}_\\infty$. 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