RemarkRemark: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Ensemble disagreement is not calibrated uncertainty by definition

Remark

For an ensemble of $m \geq 2$ learned transition rows ${\hat{P}}_{1} (\cdot ∣ s, a), \dots, {\hat{P}}_{m} (\cdot ∣ s, a)$ , define the pairwise disagreement score by

$u (s, a) = \frac{2}{m (m - 1)} \sum_{1 \leq i < j \leq m} TV ({\hat{P}}_{i} (\cdot ∣ s, a), {\hat{P}}_{j} (\cdot ∣ s, a)) .$

This statistic measures dispersion among the fitted models. By itself it does not specify a probability law for the true model error $TV (P (\cdot ∣ s, a), {\hat{P}}_{i} (\cdot ∣ s, a))$ , nor does it assert a calibrated coverage frequency for any error threshold. Calibration requires additional assumptions and a separately proved or empirically checked calibration condition.

Remark references

The true and learned transition rows and their total-variation errors.

Levine, Kumar, Tucker, and Fu, Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems.

Depends on

Finite learned transition and reward models

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Sergey Levine, Aviral Kumar, George Tucker, and Justin Fu, Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems (standard reference, not scraped)