Compositional search within multinary perovskites employing brute force synthesis are prohibitively expensive in large chemical spaces. To identify the most stable multi-cation lead iodide perovskites containing Cs, formamidinium (FA) and methylammonium (MA), we fuse results from density functional theory (DFT) calculations and in situ thin-film degradation test within an end-to-end machine learning (ML) algorithm to inform the compositional optimization of CsxMAyFA1-x-yPbI3. We integrate phase thermodynamics modelling as a probabilistic constraint in a Bayesian optimization (BO) loop, which effectively guides the experimental search while considering both structural and environmental stability. After three optimization rounds and only sampling 1.8% of the compositional space, we identify thin-film compositions centred at Cs0.17MA0.03FA0.80PbI3 that achieve a 3x delay in macroscopic degradation onset under elevated temperature, humidity, and light compared with the more complex state-of-the-art Cs0.05(MA0.17FA0.83)0.95Pb(I0.83Br0.17)3. We find up to 8% of MA can be incorporated into the perovskite structure before stability is significantly compromised. Cs is beneficial at low concentrations, however, beyond 17% is found to contribute to reduced stability. Synchrotron-based grazing-incidence wide-angle X-ray scattering (GIWAXS) further validates that the interplay of chemical decomposition and phase separation governs the non-linear instability landscape of this compositional space. We reveal the detrimental role of the ẟ-CsPbI3 minority phase in accelerating degradation and it can be kinetically suppressed by co-optimising Cs and MA content, providing insights into simplifying perovskite compositions for further environmental stability enhancement. Our approach realizes the effectiveness of ML-enabled data fusion in achieving a holistic, efficient, and physics-informed experimentation for multinary systems, potentially generalisable to materials search in the vast structural and alloyed spaces beyond halide perovskites.