Achieving Target State-Action Frequencies in Multichain Average-Reward Markov Decision Processes
Why this work is in the frame
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Bibliographic record
Abstract
In this paper we address a basic problem that arises naturally in average-reward Markov decision processes with constraints and/or nonstandard payoff criteria: Given a feasible state-action frequency vector (“the target”), construct a policy whose state-action frequencies match those of the target vector. While it is well known that the solution to this problem cannot, in general, be found in the space of stationary randomized policies, we construct a solution that has “ultimately stationary” structure: It consists of two stationary policies where the first one is used initially, and then the switch to the second one is made at a certain random switching time. The computational effort required to construct this solution is minimal. We also show that our problem can always be solved by a stationary policy if the original MDP is “extended” by adding certain states and actions. The solution in the original MDP is obtained by mapping the solution in the extended MDP back to the original process.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it