Solving concisely expressed combinatorial auction problems
Why this work is in the frame
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Bibliographic record
Abstract
Combinatorial auctions provide a valuable mecha-nism for the allocation of goods in settings where buyer valuations exhibit complex structure with re-spect to substitutability and complementarity. Most algorithms are designed to work with explicit “flat” bids for concrete bundles of goods. However, logi-cal bidding languages allow the expression of com-plex utility functions in a natural and concise way, and have recently attracted considerable attention. Despite the power of logical languages, no current winner determination algorithms exploit the spe-cific structure of logically specified bids to solve problems more effectively. In this paper, we de-scribe techniques to do just this. Specifically, we propose a direct integer program (IP) formulation of the winner determination problem for bids in the LGB logical language. This formulation is linear in the size of the problem and can be solved effectively using standard optimization packages. We compare this formulation and its solution time to those of the corresponding set of flat bids, demonstrating the im-mense utility of exploiting the structure of logically expressed bids. We also consider an extension of LGB and show that these can also be solved using linear constraints. 1
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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 | 0.001 | 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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.012 | 0.004 |
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