I try to get Roman numbering but couldn't find how to change it in the package documentation. After some research, I figured out how to do it using the algorithm2e package. (Use algonl as optional command and then \renewcommand{\theAlgoLine}{\Roman{AlgoLine}}).
If I know the counter name for the algorithmicx package I could add the \renewcommand{thecountername}{\Roman{countername}} command.
I already wrote 8 algorithmns so if possible I would like to avoid rewriting them using the algorithm2e package.
My Example:
\usepackage[section]{algorithm}
\usepackage{algpseudocode}
\begin{document}
\begin{algorithm}
\caption{Algo-name}
\label{arnoldi}
\begin{algorithmic}[1]
\State algo
\end{algorithmic}
\end{algorithm}
\end{document}