  We present photometry and spectroscopy of four hydrogen-poor luminous
supernovae discovered during the two-month science commissioning and early
operations of the Zwicky Transient Facility (ZTF) survey. Three of these
objects, SN2018bym (ZTF18aapgrxo), SN2018avk (ZTF18aaisyyp) and SN2018bgv
(ZTF18aavrmcg) resemble typical SLSN-I spectroscopically, while SN2018don
(ZTF18aajqcue) may be an object similar to SN2007bi experiencing considerable
host galaxy reddening, or an intrinsically long-lived, luminous and red SN Ic.
We analyze the light curves, spectra, and host galaxy properties of these four
objects and put them in context of the population of SLSN-I. SN2018bgv stands
out as the fastest-rising SLSN-I observed to date, with a rest-frame g-band
rise time of just 10 days from explosion to peak -- if it is powered by
magnetar spin-down, the implied ejecta mass is only ~1 M$_{\odot}$. SN2018don
also displays unusual properties -- in addition to its red colors and
comparatively massive host galaxy, the light curve undergoes some of the
strongest light curve undulations post-peak seen in a SLSN-I, which we
speculate may be due to interaction with circumstellar material. We discuss the
promises and challenges of finding SLSNe in large-scale surveys like ZTF given
the observed diversity in the population.
