Abstract: Real-world tasks involve nuanced combinations of goal and safety specifications, which often directly compete. In high dimensions, the challenge is exacerbated: formal automata become cumbersome, and the combination of sparse rewards tends to require laborious tuning. In this work, we consider the structure of the Bellman Value as a means to naturally organize the problem for improved automatic performance without introducing additional abstractions. Namely, we prove the Bellman Value for a complex task defined in temporal logic can be decomposed into a graph of Bellman Values, where the graph is connected by a set of well-studied Bellman equations (BEs): the Reach-Avoid BE, the Avoid BE, and a novel type, the Reach-Avoid-Loop BE. From this perspective, we design a specialized PPO variant, Value-Decomposition PPO (VDPPO) that uses a single learned representation by embedding the decomposed Value graph. We conduct a variety of simulated and real multi-objective experiments, including delivery and herding, to test our method on diverse high-dimensional systems involving heterogeneous teams and complex agents. Ultimately, we find this approach greatly improves performance over existing baselines, balancing safety and liveness automatically.