Bounding Performance Loss in Approximate MDP Homomorphisms
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Bibliographic record
Abstract
We define a metric for measuring behavior similarity between states in a Markov decision process (MDP), which takes action similarity into account. We show that the kernel of our metric corresponds exactly to the classes of states defined by MDP homomorphisms (Ravindran & Barto, 2003). We prove that the differ-ence in the optimal value function of different states can be upper-bounded by the value of this metric, and that the bound is tighter than previous bounds pro-vided by bisimulation metrics (Ferns et al. 2004, 2005). Our results hold both for discrete and for continuous actions. We provide an algorithm for constructing approximate homomorphisms, by using this metric to identify states that can be grouped together, as well as actions that can be matched. Previous research on this topic is based mainly on heuristics. 1
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 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