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bayesian_optimization.ipynb

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"\\end{cases}\n",
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"where $\\mu(\\mathbf{x})$ and $\\sigma(\\mathbf{x})$ are the mean and the standard deviation of the GP pesterior predictive at $\\mathbf{x}$, respectively. $\\Phi$ and $\\phi$ are the CDF and PDF of the standard normal distribution, respectively. The first summation term in Equation (2) is the exploitation term and second summation term is the exploration term.\n",
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"where $\\mu(\\mathbf{x})$ and $\\sigma(\\mathbf{x})$ are the mean and the standard deviation of the GP posterior predictive at $\\mathbf{x}$, respectively. $\\Phi$ and $\\phi$ are the CDF and PDF of the standard normal distribution, respectively. The first summation term in Equation (2) is the exploitation term and second summation term is the exploration term.\n",
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"\n",
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"Parameter $\\xi$ in Equation (2) determines the amount of exploration during optimization and higher $\\xi$ values lead to more exploration. In other words, with increasing $\\xi$ values, the importance of improvements predicted by the GP posterior mean $\\mu(\\mathbf{x})$ decreases relative to the importance of potential improvements in regions of high prediction uncertainty, represented by large $\\sigma(\\mathbf{x})$ values. A recommended default value for $\\xi$ is $0.01$.\n",
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