Asymptotic Optimality of Finite Approximations to Markov Decision\n Processes with Borel Spaces
Bibliographic record
Abstract
Calculating optimal policies is known to be computationally difficult for\nMarkov decision processes (MDPs) with Borel state and action spaces. This paper\nstudies finite-state approximations of discrete time Markov decision processes\nwith Borel state and action spaces, for both discounted and average costs\ncriteria. The stationary policies thus obtained are shown to approximate the\noptimal stationary policy with arbitrary precision under quite general\nconditions for discounted cost and more restrictive conditions for average\ncost. For compact-state MDPs, we obtain explicit rate of convergence bounds\nquantifying how the approximation improves as the size of the approximating\nfinite state space increases. Using information theoretic arguments, the order\noptimality of the obtained convergence rates is established for a large class\nof problems. We also show that, as a pre-processing step the action space can\nalso be finitely approximated with sufficiently large number points; thereby,\nwell known algorithms, such as value or policy iteration, Q-learning, etc., can\nbe used to calculate near optimal policies.\n
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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 | 0.008 | 0.052 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 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".