A distributed primal-dual hybrid gradient algorithm for fair resource allocation
Bibliographic record
Abstract
Fair resource allocation, which is vital in various fields, including advertising, cloud computing, and loan management, requires a delicate balance between maximizing revenue and ensuring fairness.This problem is commonly defined as constrained and regularized convex programming, where the objective function consists of a linear allocation cost and a nonseparable and nonlinear fairness regularizer.However, solving this problem for large cases, such as those with millions of variables, can be challenging and requires advanced computational methods and expertise.To address this issue, this paper proposes a distributed primal-dual hybrid gradient algorithm by using a tailored Bregman distance to solve a saddle point reformulation of the problem.Our algorithm allows for closed-form solutions to all subproblems and primarily employs matrix-vector multiplications, which can be efficiently executed via distributed parallel computations.Theoretical results demonstrate global iterate convergence and ergodic sublinear convergence rate under a practical stepsize condition.Furthermore, the proposed algorithm is shown to be more efficient and superior to off-the-shelf solvers such as the IPOPT and Gurobi, as evidenced by experimental results on synthetic and real-world industrial datasets.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".