Reinforcement Learning or optimal control 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 corresponding optimal policy. Consequently, formalizing the sequential decision-making problems as inference has a considerable value, as probabilistic inference in principle offers diverse and powerful mathematical tools to infer the stochastic dynamics whilst suggesting a probabilistic interpretation of the reward design and policy convergence. In this study, we propose a novel Adaptive Wasserstein Variational Optimization (AWaVO) to tackle these challenges in sequential decision-making. Our approach utilizes formal methods to provide interpretations of reward design, transparency of training convergence, and probabilistic interpretation of sequential decisions. To demonstrate practicality, we show convergent training with guaranteed global convergence rates not only in simulation but also in real robot tasks, and empirically verify a reasonable tradeoff between high performance and conservative interpretability.

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