Technical Note—Trading Off Quick versus Slow Actions in Optimal Search
Bibliographic record
Abstract
We consider the search for a target whose precise location is uncertain. The search region is divided into grid cells, and the searcher decides which cell to visit next and whether to search it quickly or slowly. A quick search of a cell containing the target may damage it, resulting in a failed search, or it may locate the target safely. If the target is not in the cell, the search continues over the remaining cells. If a slow search is performed on a cell, then the search ends in failure with a fixed probability regardless of whether or not the target is in that cell (e.g., because of enemy fire while performing the slow search). If the slow search survives this failure possibility, then the search ends in success if the target is in that cell; otherwise, the search continues over the remaining cells. We seek to minimize the probability of the search ending in failure and consider two types of rules for visiting cells: the unconstrained search, in which the searcher may visit cells in any order, and the constrained search, in which the searcher may only visit adjacent cells (e.g., up, down, left, or right of cells already visited). We prove that the optimal policy for the unconstrained search is to search quickly some initial set of cells with the lowest probabilities of containing the target before slowly searching the remaining cells in decreasing order of probabilities. For the special case in which a quick search on a cell containing the target damages it with certainty, the optimal policy is to search all cells slowly, in decreasing order of probabilities. We use the optimal solution of the unconstrained search in a branch-and-bound optimal solution algorithm for the constrained search. For larger instances, we evaluate heuristics and approximate dynamic programming approaches for finding good solutions.
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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 | 0.004 | 0.022 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".