Efficient Constraint Generation for Stochastic Shortest Path Problems

2026-04-02

AI Summary

This work addresses the computational inefficiency of traditional stochastic shortest path (SSP) solvers, which exhaustively evaluate all actions during Bellman backups—even those deemed suboptimal by heuristics—leading to significant wasted computation. To overcome this limitation, the paper introduces CG-iLAO*, a novel algorithm that integrates heuristic information directly into the constraint generation process, reformulating heuristic search as a linear programming problem. By selectively retaining only promising actions for backup, CG-iLAO* drastically reduces unnecessary evaluations. Empirical results demonstrate that CG-iLAO* considers on average only 40% of the actions evaluated by iLAO* (as low as 1% in some cases), yielding a 3.5-fold reduction in action cost computations and achieving speedups of 2.8× over iLAO* and 3.7× over LRTDP, thereby substantially enhancing SSP solving efficiency.

Abstract

Stochastic Shortest Path problems (SSPs) are traditionally solved by computing each state's cost-to-go by applying Bellman backups. A Bellman backup updates a state's cost-to-go by iterating through every applicable action, computing the cost-to-go after applying each one, and selecting a minimal action's cost-to-go. State-of-the-art algorithms use heuristic functions; these give an initial estimate of costs-to-go, and lets the algorithm apply Bellman backups only to promising states, determined by low estimated costs-to-go. However, each Bellman backup still considers all applicable actions, even if the heuristic tells us that some of these actions are too expensive, with the effect that such algorithms waste time on unhelpful actions. To address this gap we present a technique that uses the heuristic to avoid expensive actions, by reframing heuristic search in terms of linear programming and introducing an efficient implementation of constraint generation for SSPs. We present CG-iLAO*, a new algorithm that adapts iLAO* with our novel technique, and considers only 40% of iLAO*'s actions on many problems, and as few as 1% on some. Consequently, CG-iLAO* computes on average 3.5x fewer costs-to-go for actions than the state-of-the-art iLAO* and LRTDP, enabling it to solve problems faster an average of 2.8x and 3.7x faster, respectively.

Problem

• Stochastic Shortest Path
• Bellman backup
• heuristic search
• constraint generation
• action pruning

Innovation

• constraint generation
• stochastic shortest path
• heuristic search
• Bellman backup
• linear programming