Efficient Strategy Synthesis for MDPs with Resource Constraints

TL;DR

This paper introduces polynomial-time algorithms for strategy synthesis in consumption Markov decision processes, enabling resource-aware planning with resource replenishment and heuristics to optimize mission completion time.

Contribution

It presents novel polynomial-time algorithms for resource-constrained strategy synthesis in consumption MDPs, including heuristics to improve practical planning efficiency.

Findings

Algorithms are effective in polynomial time.

Heuristics reduce expected mission completion time.

Numerical examples demonstrate practical applicability.

Abstract

We consider qualitative strategy synthesis for the formalism called consumption Markov decision processes. This formalism can model dynamics of an agents that operates under resource constraints in a stochastic environment. The presented algorithms work in time polynomial with respect to the representation of the model and they synthesize strategies ensuring that a given set of goal states will be reached (once or infinitely many times) with probability 1 without resource exhaustion. In particular, when the amount of resource becomes too low to safely continue in the mission, the strategy changes course of the agent towards one of a designated set of reload states where the agent replenishes the resource to full capacity; with sufficient amount of resource, the agent attempts to fulfill the mission again. We also present two heuristics that attempt to reduce expected time that the agent needs to fulfill the given mission, a parameter important in practical planning. The presented algorithms were implemented and numerical examples demonstrate (i) the effectiveness (in terms of computation time) of the planning approach based on consumption Markov decision processes and (ii) the positive impact of the two heuristics on planning in a realistic example.