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Stochastic sequential decision making often requires hierarchical structurein the problem where each high-level action should be further planned withprimitive states and actions. In addition, many real-world applications requirea plan that satisfies constraints on the secondary costs such as risk measureor fuel consumption. In this paper, we propose a hierarchical constrainedstochastic shortest path problem (HC-SSP) that meets those two crucialrequirements in a single framework. Although HC-SSP provides a useful frameworkto model such planning requirements in many real-world applications, theresulting problem has high complexity and makes it difficult to find an optimalsolution fast which prevents user from applying it to real-time andrisk-sensitive applications. To address this problem, we present an algorithmthat iteratively allocates cost budget to lower level planning problems basedon branch-and-bound scheme to find a feasible solution fast and incrementallyupdate the incumbent solution. We demonstrate the proposed algorithm in anevacuation scenario and prove the advantage over a state-of-the-artmathematical programming based approach.

Hierarchical Constrained Stochastic Shortest Path Planning via Cost Budget Allocation