Solution methods for a class of finite-horizon vector-valued Markov decision processes
Why this work is in the frame
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Bibliographic record
Abstract
This paper investigates and develops solution methods for a class of finite-horizon Markov decision processes characterized by additive or multiplicative vector rewards. Two concepts of optimality are treated: (1) optimality in the space of return vectors, whereby a policy is optimal if it delivers a maximal total reward from any initial state; and (2) optimality in the space of return functions, whereby a policy is optimal if its total reward function is maximal among all total reward functions. The paper elucidates the relation between the two concepts, proposes a procedure for utilizing this relation to determine the set of optimal policies under concept (1), and formulates a dynamic programming approach to calculating optimal policies under concept (2). The paper demonstrates that dynamic programming yields all optimal policies under concept (2). The paper’s results are illustrated with numerical experiments and a multi-objective stochastic inventory control problem.
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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 | 0.005 | 0.009 |
| 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 | 0.000 | 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