An $O(\log \log n)$-approximate budget feasible mechanism for subadditive valuations
Bibliographic record
Abstract
In budget-feasible mechanism design, there is a set of items $U$, each owned by a distinct seller. The seller of item $e$ incurs a private cost $\overline{c}_e$ for supplying her item. A buyer wishes to procure a set of items from the sellers of maximum value, where the value of a set $S\subseteq U$ of items is given by a valuation function $v:2^U\to \mathbb{R}_+$. The buyer has a budget of $B \in \mathbb{R}_+$ for the total payments made to the sellers. We wish to design a mechanism that is truthful, that is, sellers are incentivized to report their true costs, budget-feasible, that is, the sum of the payments made to the sellers is at most the budget $B$, and that outputs a set whose value is large compared to $\text{OPT}:=\max\{v(S):\overline{c}(S)\le B,S\subseteq U\}$. Budget-feasible mechanism design has been extensively studied, with the literature focussing on (classes of) subadditive valuation functions, and various polytime, budget-feasible mechanisms, achieving constant-factor approximation, have been devised for the special cases of additive, submodular, and XOS valuations. However, for general subadditive valuations, the best-known approximation factor achievable by a polytime budget-feasible mechanism (given access to demand oracles) was only $O(\log n / \log \log n)$, where $n$ is the number of items. We improve this state-of-the-art significantly by designing a randomized budget-feasible mechanism for subadditive valuations that achieves a substantially-improved approximation factor of $O(\log\log n)$ and runs in polynomial time, given access to demand oracles.
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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 | 0.019 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.004 | 0.003 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.011 |
| Open science | 0.006 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.021 | 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 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".