Decentralized Stochastic Control in Borel Spaces: Centralized MDP Reductions, Near Optimality of Finite Window Local Information, and Q-Learning
Bibliographic record
Abstract
Decentralized stochastic control problems are challenging as their decentralized information structure may prevent the applicability of standard tools in stochastic control. In this paper, we study such problems in general Borel spaces and present novel structural, approximation, and learning results. We consider three related information structures, and study them under a unified theme. (i) We first consider the one-step delayed information sharing pattern (OSDISP) and the K-step periodic information sharing pattern (KSPISP), where we show that these can be reduced to a centralized MDP, generalizing prior results which considered finite or linear models. The separated nature of policies under both information structures, even when all spaces are standard Borel, is then established. (ii) We provide sufficient conditions for the transition kernels of the centralized reductions of both problems to be weakly continuous (weak-Feller), which facilitates rigorous approximation and learning theoretic results. (iii) We will then show that for the completely decentralized information structure (CDIS), which consists of problems where agents can only rely on their local information, finite memory policies are asymptotically near optimal as the memory size increases under a joint conditional mixing condition. This will be achieved by providing a performance bound on the use of finite memory policies. This bound can also be used to provide an upper limit on the performance loss that results from a reduction of the action space associated with the centralized reduction of the KSPISP problem. (iv) Additionally, we will prove that sliding finite-window policies are near optimal for the latter under a predictor stability condition. (v) Finally, we establish that for the OSDISP problem and the KSPISP problem a quantized Q-learning algorithm converges asymptotically towards a near optimal solution.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.002 | 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".