Perovskites are promising materials candidates for optoelectronics, but their commercialization is hindered by toxicity and materials instability. While compositional engineering can mitigate these problems by tuning perovskite properties, the enormous complexity of the perovskite materials space aggravates the search for an optimal optoelectronic material. We conducted compositional space exploration through Monte Carlo (MC) convex hull sampling, which we made tractable with machine learning (ML). The ML model learns from density functional theory calculations of perovskite atomic structures, and can be used for quick predictions of energies, atomic forces, and stresses. We employed it in structural relaxations combined with MC sampling to gain access to low-energy structures and compute the convex hull for CsPb(Br1−xClx)3. The trained ML model achieves an energy prediction accuracy of 0.1 meV per atom. The resulting convex hull exhibits two stable mixing concentrations at 1/6 and 1/3 Cl contents. Our data-driven approach offers a pathway towards studies of more complex perovskites and other alloy materials with quantum mechanical accuracy.