On-the-Fly Algorithms for Bisimulation Metrics
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Bibliographic record
Abstract
We study the problem of determining approximate equivalences in Markov Decision Processes with rewards using bisimulation metrics. We provide an extension of the framework previously introduced in Ferns et al. (2004), which computes iteratively improving approximations to bisimulation metrics using exhaustive pairwise state comparisons. The similarity between states is determined using the Earth Mover's Distance, as extensively studied in optimization and machine learning. We address two computational limitations of the above framework: first, all pairs of states have to be compared at every iteration, and second, convergence is proven only under exact computations. We extend their work to incorporate "on-the-fly" methods, which allow computational effort to focus first on pairs of states where the impact is expected to be greater. We prove that a method similar to asynchronous dynamic programming converges to the correct value of the bisimulation metric. The second relaxation is based on applying heuristics to obtain approximate state comparisons, building on recent work on improved algorithms for computing Earth Mover's Distance. Finally, we show how this approach can be used to generate new algorithmic strategies, based on existing prioritized sweeping algorithms used for prediction and control in MDPs.
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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 | 0.001 | 0.001 |
| 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 | 0.001 |
| 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