We study a typical optimization model where the optimization variable is composed of multiple probability distributions. Though the model appears frequently in practice, such as for policy problems, it lacks specific analysis in the general setting. For this optimization problem, we propose a new structural condition/landscape description named generalized quasar-convexity (GQC) beyond the realms of convexity. In contrast to original quasar-convexity \citep{hinder2020near}, GQC allows an individual quasar-convex parameter \gamma_i for each variable block i and the smaller of \gamma_i implies less block-convexity. To minimize the objective function, we consider a generalized oracle termed as the internal function that includes the standard gradient oracle as a special case.