Multi-Agent submodular optimization: Variations and generalizations
Bibliographic record
Abstract
Given a finite ground set V and its power set 2 V , submodular optimization is the class of problems where we either minimize or maximize a submodular set function f : 2 V → R over a family F ⊆ 2 V of feasible sets.These problems have been extensively studied for both minimization and maximization under very general types of constraints F. The last ten years, in particular, have seen a great amount of progress on this area.Along with these algorithmic advances, many interesting applications of these problems have been found in areas of computer science such as machine learning, robotics, and algorithmic game theory.This thesis extends the submodular optimization class of problems to frameworks where we have different agents competing for subsets of items.Different variants of these multi-agent frameworks are introduced and studied.Specifically this thesis studies 1) the extent to which the approximability of these more general problems is linked to the submodular optimization (i.e., single-agent) versions; and 2) the extent to which the approximability for the different multi-agent frameworks relate to each other.We believe that the results in this thesis substantially expand the family of tractable models for submodular optimization problems, especially for maximization.and support during these years have been a great source of professional and personal growth.I have learned so much from him.His sense of humor and unending optimism made my PhD journey incredibly pleasant and smooth, even during the tougher times.I am very grateful to him for numerous interesting and inspiring conversations over dinners and lunch.Also, for providing generous financial support that allowed me to do several academic travels during my PhD.My studies were partially financially supported by the Computer Science department at McGill; I am very grateful to them.I would also like to thank the Mathematics and Statistics department's administrative staff for all their help in terms of paperwork, especially Jackie and Raffaella.I am grateful to the examiners of this thesis: Roy Schwartz and Adrian Vetta, for taking the time to read it and providing valuable comments and suggestions
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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 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".