Stochastic optimal transport with free end time
Bibliographic record
Abstract
We consider a stochastic transportation problem between two prescribed probability distributions (a source and a target) over processes with general drift dependence and with free end times. First, and in order to establish a dual principle, we associate two equivalent formulations of the primal problem in order to guarantee its convexity and lower semi-continuity with respect to the source and target distributions. We exhibit an equivalent Eulerian formulation, whose dual variational principle is given by Hamilton–Jacobi–Bellman type variational inequalities. In the case where the drift is bounded, regularity results on the minimizers of the Eulerian problem then enable us to prove attainment in the corresponding dual problem. We also address attainment when the drift component of the cost defining Lagrangian L is superlinear L≈|u|p with 1<p<2, in which case the setting is reminiscent of our approach – in a previous work – on deterministic controlled transport problems with free end time. We finally address criteria under which the optimal drift and stopping time are unique, namely strict convexity in the drift component and monotonicity in time of the Lagrangian.
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How this classification was reachedexpand
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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.003 |
| 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; both teacher heads agree on what is shown here.
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".