What can we learn from No Free Lunch? a first attempt to characterize the concept of a searchable function
Bibliographic record
Abstract
The No Free Lunch theorem has had considerable impact in the field of optimization research. A terse definition of this theorem is that no algorithm can outperform any other algorithm when performance is amortized over all functions. Once that theorem has been proven, the next logical step is to characterize how effective optimization can be under reasonable restrictions. We operationally define a technique for approaching the question of what makes a function searchable in practice. This technique involves defining a scalar field over the space of all functions that enables one to make decisive claims concerning the performance of an associated algorithm. We then demonstrate the effectiveness of this technique by giving such a field and a corresponding algorithm; the algorithm performs better than random search for small values of this field. We then show that this algorithm will be effective over many, perhaps most functions of interest to optimization researchers. We conclude with a discussion about how such regularities are exploited in many popular optimization algorithms. 1
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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 | 0.007 | 0.042 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.004 | 0.028 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".