On Average Reward Policy Evaluation in Infinite-State Partially Observable Systems
Bibliographic record
Abstract
We investigate the problem of estimating the average reward of given decision policies in discrete-time controllable dynamical systems with finite action and observation sets, but possibly infinite state space. Unlike in systems with finite state spaces, in infinite–state systems the expected reward for some policies might not exist, so policy evaluation, which is a key step in optimal control methods, might fail. Our main analysis tool is Ergodic theory, which allows learning potentially useful quantities from the system without building a model. Our main contribution is three-fold. First, we present several dynamical systems that demonstrate the difficulty of learning in the general case, without making additional assumptions. We state the necessary condition that the underlying system must satisfy to be amenable for learning. Second, we discuss the relationship between this condition and state-ofthe-art predictive representations, and we show that there are systems that satisfy the above condition but cannot be modeled by such representations. Third, we establish sufficient conditions for average-reward policy evaluation in this setting. 1
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".