Online Sequential Optimization with Biased Gradients: Theory and Applications to Censored Demand
Bibliographic record
Abstract
In this paper, we study a class of stochastic optimization problems, where although the objective functions may not be convex, they satisfy a generalization of convexity called the sequentially convex property. We focus on a setting where the distribution of the underlying uncertainty is unknown and the manager must make a decision in real time based on historical data. Because sequentially convex functions are not necessarily convex, they pose difficulties in applying standard adaptive methods for convex optimization. We propose a nonparametric algorithm based on a gradient descent method and show that the T-season average expected cost differs from the minimum cost by at most [Formula: see text]. Our analysis is based on a careful quantification of the bias that is inherent in gradient estimation because of the adaptive nature of the problem. We demonstrate the usefulness of the concept of sequential convexity by applying it to three canonical problems in inventory control, capacity allocation, and the lifetime buy decision, under the assumption that the manager does not know the demand distributions and has access only to historical sales (censored demand) data.
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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 | 0.005 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".