Policy-Dependent and Policy-Independent Static Reduction of Stochastic Dynamic Teams and Games and Fragility of Equivalence Properties
Bibliographic record
Abstract
In stochastic control, information structure arguments have been crucial for stochastic analysis. Such an approach is often called static reduction in dynamic team theory (or decentralized stochastic control) and has been an effective method for establishing existence and approximation results for optimal policies. In this paper, we classify such static reductions into three categories: (i) those that are policy-independent (introduced by Witsenhausen in [17]), (ii) those that are policy-dependent (introduced by Ho and Chu [7], [8] for partially nested dynamic teams), and (iii) static measurement with control-sharing reduction (where the measurements become static although control actions are shared according to the partially nested information structure). For these reductions, while there exist bijection relationships between glob-ally optimal solutions of dynamic teams and their reductions, in general there is no bijection for person-by-person optimal policies. We also establish a similar result (but not identical) concerning stationary solutions. We present sufficient conditions under which bijection relationships hold. Under static measurement with control-sharing reduction, connections between optimality concepts can be established under relaxed conditions. An implication is a convexity characterization of dynamic teams under static measurement with control-sharing reduction. Some counterparts for stochastic games are also discussed.
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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 | 0.004 | 0.019 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 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".