A Nonparametric Learning Algorithm for a Stochastic Multi-echelon Inventory Problem
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Bibliographic record
Abstract
We consider a periodic-review single-product multi-echelon inventory problem with instantaneous replenishment. In each period, the decision-maker makes ordering decisions for all echelons. Any unsatisfied demand is back-ordered, and any excess inventory is carried to the next period. In contrast to the classic inventory literature, we assume that the information of the demand distribution is not known a priori, and the decision-maker observes demand realizations over the planning horizon. We propose a nonparametric algorithm that generates a sequence of adaptive ordering decisions based on the stochastic gradient descent method. We compare the [Formula: see text]-period cost of our algorithm to the clairvoyant, who knows the underlying demand distribution in advance, and we prove that the expected [Formula: see text]-period regret is at most [Formula: see text], matching a lower bound for this problem.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it