Deep Teams: Decentralized Decision Making With Finite and Infinite Number of Agents
Bibliographic record
Abstract
Inspired by the concepts of deep learning in artificial intelligence and fairness in behavioral economics, we introduce deep teams in this article. In such systems, agents are partitioned into a few subpopulations so that the dynamics and cost of agents in each subpopulation is invariant to the indexing of agents. The goal of agents is to minimize a common cost function in such a manner that the agents in each subpopulation are not discriminated or privileged by the way they are indexed. Two nonclassical information structures are studied. In the first one, each agent observes its local state as well as the empirical distribution of the states of agents in each subpopulation, called deep state, whereas in the second one, the deep states of a subset (possibly all) of subpopulations are not observed. Novel dynamic programs are developed to identify globally optimal and suboptimal solutions for the first and second information structures, respectively. The computational complexity of finding the optimal solution in both space and time is polynomial (rather than exponential) with respect to the number of agents in each subpopulation and is linear (rather than exponential) with respect to the control horizon. This complexity is further reduced in time by introducing a forward equation, which we call deep Chapman-Kolmogorov equation, described by multiple convolutional layers of binomial probability distributions. Two different prices are defined for computation and communication, and it is shown that under mild conditions they converge to zero as the number of quantization levels and the number of agents tend to infinity. In addition, the main results are extended to infinite-horizon discounted models and arbitrarily asymmetric cost functions. Finally, a service management example with 200 users is presented.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".