Reinforcement learning can provide effective reasoning for sequential decision-making problems with variable dynamics. Such reasoning in practical implementation, however, poses a persistent challenge in interpreting the reward function and the corresponding optimal policy. Consequently, representing sequential decision-making problems as probabilistic inference can have considerable value, as, in principle, the inference offers diverse and powerful mathematical tools to infer the stochastic dynamics whilst suggesting a probabilistic interpretation of policy optimization. In this study, we propose a novel Adaptive Wasserstein Variational Optimization, namely AWaVO, to tackle these interpretability challenges. Our approach uses formal methods to achieve the interpretability for convergence guarantee, training transparency, and intrinsic decision-interpretation. To demonstrate its practicality, we showcase guaranteed interpretability with an optimal global convergence rate in simulation and in practical quadrotor tasks. In comparison with state-of-the-art benchmarks including TRPO-IPO, PCPO and CRPO, we empirically verify that AWaVO offers a reasonable trade-off between high performance and sufficient interpretability.