[Abbreviated] We search for scaling relations between the fundamental AGN parameters and rest-frame UV/optical variability properties for a sample of $sim$90 X-ray selected AGNs covering a wide redshift range from the XMM-COSMOS survey, with optical light curves in four bands provided by the Pan-STARRS1 (PS1) Medium Deep Field 04 survey. To estimate the variability amplitude we utilize the normalized excess variance ($sigma_{mathrm{rms}}^{2}$) and probe variability on rest-frame timescales of several months and years by calculating $sigma_{mathrm{rms}}^{2}$ from different parts of our light curves. In addition, we derive the rest-frame optical PSD for our sources using continuous-time autoregressive moving average (CARMA) models. We observe that the excess variance and the PSD amplitude are strongly anti-correlated with wavelength, bolometric luminosity and Eddington ratio. There is no evidence for a dependency of the variability amplitude on black hole mass and redshift. These results suggest that the accretion rate is the fundamental physical quantity determining the rest-frame UV/optical variability amplitude of quasars on timescales of months and years. The optical PSD of all of our sources is consistent with a broken power law showing a characteristic bend at rest-frame timescales ranging between $sim$100 and $sim$300 days. The break timescale exhibits no significant correlation with any of the fundamental AGN parameters. The low frequency slope of the PSD is consistent with a value of $-1$ for most of our objects, whereas the high frequency slope is characterized by a broad distribution of values between $sim-2$ and $sim-4$. These findings unveil significant deviations from the simple damped random walk model, frequently used in previous optical variability studies. We find a weak tendency for AGNs with higher black hole mass having steeper high frequency PSD slopes.
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