    \begin{algorithmic}[1]
        \State \textbf{Input}: iteration index $t$, $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{t}$, $N_{init}$, $N_{vs}$, set of important variables chosen at iteration $t-N_{vs}$, denote as $\hat{\mathbf{x}}_{ipt}$
        \State \textbf{Output}: Set of important variables chosen at iteration $t$, denote as $\mathbf{x}_{ipt}$
	    \If{$t=N_{init}+N_{vs}$ or $\hat{\mathbf{x}}_{ipt}=\mathbf{x}$} \Comment{First time to do variable selection or $\hat{\mathbf{x}}_{ipt}$ contains all variables}
	        \State \Return Algorithm~\ref{alg:VS_detail}
	   \ElsIf{$\max_{k\in \{t-N_{vs}+1, t-N_{vs}+2, \dots, t\}}y^{k}\leq\max_{k\in \{1,\dots, t-N_{vs}\}}y^{k}$}  \Comment{Inaccurate case}
	        \State \Return Algorithm~\ref{alg:momentum_inacc}
	   \Else \Comment{Accurate case}
	        \State \Return Algorithm~\ref{alg:momentum_acc}
	    \EndIf
    \end{algorithmic} 

\begin{algorithmic}
[1]
\State \textbf{Input}: iteration index $t$, $\mathcal{D}=\{(\mathbf{x}^{i},y^{i})\}_{i=1}^{t}$, $N_{init}$, $N_{vs}$, set of important variables chosen at iteration $t-N_{vs}$, denote as $\hat{\mathbf{x}}_{ipt}$
\State \textbf{Output}: Set of important variables chosen at iteration $t$, denote as $\mathbf{x}_{ipt}$
\If{$t=N_{init}+N_{vs}$ or $\hat{\mathbf{x}}_{ipt}=\mathbf{x}$} \Comment{First time to do variable selection or $\hat{\mathbf{x}}_{ipt}$ contains all variables}
\State \Return Algorithm~\ref{alg:VS_detail}
\ElsIf{$\max_{k\in \{t-N_{vs}+1, t-N_{vs}+2, \dots, t\}}y^{k}\leq\max_{k\in \{1,\dots, t-N_{vs}\}}y^{k}$} \Comment{Inaccurate case}
\State \Return Algorithm~\ref{alg:momentum_inacc}
\Else \Comment{Accurate case}
\State \Return Algorithm~\ref{alg:momentum_acc}
\EndIf
\end{algorithmic}
{
    "title": "computationally efficient high-dimensional bayesian optimization via   variable selection",
    "id": "2109.09264",
    "abstract": "bayesian optimization (bo) is a method for globally optimizing black-box functions. while bo has been successfully applied to many scenarios, developing effective bo algorithms that scale to functions with high-dimensional domains is still a challenge. optimizing such functions by vanilla bo is extremely time-consuming. alternative strategies for high-dimensional bo that are based on the idea of embedding the high-dimensional space to the one with low dimension are sensitive to the choice of the embedding dimension, which needs to be pre-specified. we develop a new computationally efficient high-dimensional bo method that exploits variable selection. our method is able to automatically learn axis-aligned sub-spaces, i.e. spaces containing selected variables, without the demand of any pre-specified hyperparameters. we theoretically analyze the computational complexity of our algorithm and derive the regret bound. we empirically show the efficacy of our method on several synthetic and real problems.",
    "categories": "cs.lg stat.ml",
    "doi": "",
    "created": "2021-09-19",
    "updated": "2024-02-12",
    "authors": [
        "yihang shen",
        "carl kingsford"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2109.09264"
}
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