Gauss meets Canadian traveler: shortest-path problems with correlated natural dynamics
Bibliographic record
Abstract
In a variety of real world problems from robot navigation to logistics, agents face the challenge of path optimization on a graph with unknown edge costs. These settings can be generally formalized as the Canadian Traveler Problems (CTPs) [?]. Although in many applications the edge costs have dependencies resulting from world dynamics, CTPs with such structure have received considerably less attention than those with independent edge costs, largely because the dependence structure is often problem-specific and difficult to state compactly. Yet, in a wide variety of navigation tasks, spatial correlations between edge traversal costs are governed by natural phenomena such as winds, congestion, or ocean currents, which are conveniently described with a well-understood machine learning model — Gaussian Process (GP). In this article, we propose a synthesis of CTPs and GPs, the Gaussian Traveler Problem (GTP). In GTPs, an agent observes the costs of graph edges when traversing them, and uses the observed costs to adjust its belief over other edges via Gaussian Process updates. Examples of GTP instances include aircraft, traffic, and vessel navigation, to name just a few. Computing optimal agent behavior for a GTP turns out to be equivalent to solving a Partially Observable MDP with continuous observation space. We present an approximate algorithm for solving GTPs with efficient machine-learning and decision-making components, whose design is influenced by the challenges of real-world problems. Despite the intractability of computing an optimal policy, our experiments in the aircraft navigation scenario with real wind data demonstrate that our framework can significantly improve upon state-of-the-art techniques for planning airplane routes.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".