In the last 20 years, the study of compact interacting binaries has led to two major breakthroughs in astrophysics: the discovery of dark energy and the first detection of gravitational waves. Although binaries are critically important to probe the properties of the Universe and to test fundamental physical theories, our understanding of their evolution and final fate is still far from being complete. Accreting white dwarfs are ideal laboratories in which to test the models of compact binary evolution. We here propose a COS Treasury program specifically designed to explore those regions of the parameter space that have been previously poorly studied and where major discrepancies between the theory and observations are found. Combining the high-quality ultraviolet data with the parallaxes from Gaia, we will accurately measure effective temperatures, masses and accretion rates for 43 accreting white dwarfs (the minimum number required to homogeneously sample the entire physical parameter space spanned by this diverse population) thereby testing the mechanisms of angular momentum loss which drive the evolution of all kinds of binaries. The white dwarf masses are a key ingredient in the pathway toward Supernova Type Ia explosions and by obtaining their accurate values, we will constrain both the single and the double-detonation scenarios. Finally, only the ultraviolet allows the detection of the nitrogen and carbon resonance lines. From their abundances, we will establish the formation channel for the most compact systems, which will later be used to verify the performance of the space-mission LISA and calibrate the detector for future gravitational wave source discoveries.