We study synchronization transitions in a population of globally coupled nonidentical pendulum oscillators with inertia, stochastic noise, and adaptive higher-order interactions. Higher-order couplings evolve according to a Hebbian-like learning rule, leading to effective adaptive 2-simplex interactions in the stationary limit. Using a continuum description and the associated Fokker–Planck equation, we perform a linear stability analysis of the incoherent state and derive an analytical expression for the critical coupling strength of the forward synchronization transition. The theoretical prediction is found to be in good agreement with numerical simulations. Although the forward transition remains continuous over the parameter regimes considered, the backward desynchronization transition exhibits a rich behavior. Increasing the higher-order coupling strength or the learning rate induces an explosive desynchronization transition, whereas increasing the noise intensity suppresses the abrupt transition and promotes a continuous loss of synchronization. Our results highlight the competing roles of adaptation and noise in higher-order dynamical systems.