Reduce vertical spacing itemize and multicols

Question

I have added code to reduce the spacing before itemize. However, when I use multicols still a lot of extra vertical white space is added (see the space before the subitems).

Does anyone know how to remove this?

\documentclass{article}
\usepackage{multicol}
%reduce spacing in itemize, enumerate and titles
\usepackage{enumitem}
\setenumerate{nolistsep}
\setitemize{nolistsep}
\usepackage[compact]{titlesec}

\begin{document}
Some text
\begin{itemize}
  \item item 1
  \begin{multicols}{2}\begin{itemize}
    \item item 1a
    \item item 1b
    \item item 1c
    \item item 1d
  \end{itemize}\end{multicols}
  \item rest of items
\end{itemize}
Rest of the document
\end{document}

Answer 1

You can locally set \multicolsep to 0pt (or another desired value; the default value for \multicolsep is 12pt plus 4pt minus 3pt):

\documentclass{article}
   \usepackage{multicol}
   \usepackage{enumitem}
   \setenumerate{nolistsep}
   \setitemize{nolistsep}
   \usepackage[compact]{titlesec}

   \begin{document}
   Some text
   \begin{itemize}
   \setlength\multicolsep{0pt}
    \item item 1
     \begin{multicols}{2}\begin{itemize}[nolistsep]
       \item item 1a
       \item item 1b
       \item item 1c
       \item item 1d
     \end{itemize}\end{multicols}
   \item rest of items
   \end{itemize}
   Rest of the document
   \end{document}