Quantitative T1ρ imaging using biexponential models usually requires multiple spin-lock times, which makes the acquisition time demanding. Recently, Compressed Sensing (CS) has demonstrated significant reduction in data acquisition time in MRI applications in general, and T1ρ relaxation mapping of knee cartilage in particular. However, biexponential T1ρ mapping error using CS is much higher than that of monoexponential T1ρ mapping error for the same acceleration factor. One possible approach to reduce artifacts, improving image and mapping quality, is to learn a Variational Network (VN) for image reconstruction. Here, we compare a VN, trained with real knee cartilage images, against the best CS approaches known for biexponential T1ρ mapping. Our results show that the VN produced biexponential maps superior to CS, with lower T1ρ mapping error.