Optimal scenario set partitioning for multistage stochastic programming with the progressive hedging algorithm
Bibliographic record
Abstract
In this paper, we propose a new approach to reduce the total running time (RT) of the progressive hedging algorithm (PHA) for solving multistage stochastic programs (MSPs) defined on a scenario tree. Instead of using the conventional scenario decomposition scheme, we apply a multi-scenario decomposition scheme and partition the scenario set in order to minimize the number of non-anticipativity constraints (NACs) on which an augmented Lagrangian relaxation (ALR) must be applied. Our partitioning method is a heuristic algorithm that takes into account the complex branching structure of general multistage scenario trees. Minimizing the number of relaxed NACs (RNACs) enhances the PHA’s convergence rate by decreasing the variability of subproblems solutions at duplicated tree nodes. This is due to the fact that minimizing the RNACs reduces the anticipativity level of subproblems by increasing the branching level of subtrees. This makes RNACs easier to satisfy. Our partitioning method also reduces the total RT per iteration in two different ways. Firstly, it decreases the number of linear and quadratic penalty terms that need to be included in subproblems objective function.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".