The Ultraviolet Luminosity Function (UVLF) is a key observable for understanding galaxy formation from cosmic dawn. There has been considerable debate on whether Schechter-like LFs (characterized by an exponential dropoff at the bright end) that describe the LF in our local universe are also a sufficient description of the LF at high redshifts (z > 6). We model the UVLF over cosmic history with a semi-empirical framework and include a log-normal scatter, Sigma, in galaxy luminosities with a conditional luminosity function approach. We show that stochasticity induces a flattening or a feedback scale in the median galaxy luminosity versus halo mass relation, L-c(M-h), to account for the increase of bright objects placed in lower-mass halos. We observe a natural broadening in the bright-end exponential segment of the UVLF for z > 6 if processes that regulate star formation acts on the same mass scale as at z similar to 5, where the degree of broadening is enhanced for larger Sigma. Alternatively, if the brightend feedback is triggered at a near-constant luminosity threshold, the feedback threshold occurs at progressively lower halo masses with increasing redshift, due to galaxies being more luminous on average at a fixed halo mass from rapid halo assembly. Such feedback results in an LF shape with a bright-end closer to that of a Schechter function. We include predictions for the z > 8 UVLFs from future all-sky surveys such as WFIRST, which has the potential to both quantify the scatter and type of feedback, and provide insight behind the mechanisms that drive star formation in the early universe.