Mixing incompatible polymers in water to form homogeneous hydrogels possessing both hydrophilic and lipophilic components is challenging due to high enthalpic penalty and negligible entropic gain in total Gibbs free energy. Here we performed dissipative particle dynamics simulations and machine learning to uncover the influence of Janus nanoparticles on immiscible polymer mixtures with high water content and to predict the phase behavior of bicomponent hydrogels. An intriguing transition from kinetically arrested demixing to spontaneous mixing was observed with increasing particle concentration and decreasing particle size. The analysis reveals that the mixing is driven by a significant entropic gain of small nanoparticles being well dispersed in aqueous solvent of high-volume fraction. This finding highlights an entropy-driven mixing mechanism for nanocomposite bicomponent hydrogels. Supervised machine learning algorithms were used to establish a microstructure phase diagram with respect to particle concentration and radius, in which homogeneous, percolated, clustered, and separated phases, as well as corresponding phase boundaries, were clearly identified.