A SMOOTHING PENALIZED SAMPLE AVERAGE APPROXIMATION METHOD FOR STOCHASTIC PROGRAMS WITH SECOND-ORDER STOCHASTIC DOMINANCE CONSTRAINTS
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Bibliographic record
Abstract
In this paper, we propose a smoothing penalized sample average approximation (SAA) method for solving a stochastic minimization problem with second-order dominance constraints. The basic idea is to use sample average to approximate the expected values of the underlying random functions and then reformulate the discretized problem as an ordinary nonlinear programming problem with finite number of constraints. An exact penalty function method is proposed to deal with the latter and an elementary smoothing technique is used to tackle the nonsmoothness of the plus function and the exact penalty function. We investigate the convergence of the optimal value obtained from solving the smoothed penalized sample average approximation problem as sample size increases and show that with probability approaching to one at exponential rate with the increase of sample size the optimal value converges to its true counterpart. Some preliminary numerical results are reported.
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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 | 0.012 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it