Sample Complexity Bounds for Stochastic Shortest Path with a Generative Model
Researchers establish tight sample complexity bounds for learning optimal policies in stochastic shortest path problems, proving that instances with zero minimum cost may be fundamentally unlearnable—a finding that distinguishes SSP from finite-horizon and discounted reinforcement learning settings.
Modelwire context
ExplainerThe practical implication buried in the math is this: zero-cost cycles in a stochastic environment can make it impossible to distinguish an optimal policy from a suboptimal one without infinite data, which is a structural property of the problem, not a fixable engineering limitation. This matters because SSP is the formal model underlying many real navigation and planning tasks.
The day before this paper appeared, Modelwire covered 'Generalization in LLM Problem Solving: The Case of the Shortest Path,' which found that LLMs fail on longer-horizon shortest-path instances due to recursive instability. That paper treated the failure as a model limitation. This new work suggests part of the difficulty may be more fundamental: certain shortest-path problem instances are provably hard to learn from samples regardless of the learner, which reframes the LLM generalization failure as potentially touching a theoretical floor, not just an architectural ceiling. The two papers approach the same problem class from opposite directions, empirical and formal, and together they sketch a more complete picture of why planning at scale resists easy solutions.
Watch whether follow-on work identifies tractable structural conditions (such as bounded cycle costs) that restore learnability, which would let practitioners know when SSP-based planners can be trusted in deployment and when they cannot.
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