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Empty file removed Completed/.gitkeep
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Expand Up @@ -22,8 +22,8 @@ In scope:
- Wald's identities, probability vectors on finite types, and the generic parts of
`LMLExplore/Bandits/Concentration.lean`.

Relation to the other roadmaps. The [Bandits](../Bandits/README.md) and
[Identification](../Identification/README.md) roadmaps specify the mathematics these developments
Relation to the other roadmaps. The [Bandits](../../LMLRoadmaps/Bandits/README.md) and
[Identification](../../LMLRoadmaps/Identification/README.md) roadmaps specify the mathematics these developments
contain, in the generality of the targets here (Bandits Layer 6 for online linear optimization,
Identification Layer 1.2 for exponential families); this roadmap restates the merged code in that
generality and moves it where its users are. It adds no target of those roadmaps.
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2 changes: 1 addition & 1 deletion LMLRoadmaps/Bandits/README.md
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Expand Up @@ -335,7 +335,7 @@ against `u` after `n` rounds is $\sum_{t<n}y_t(a_t-u)$. Strong convexity refers
(Mathlib's `StrongConvexOn`), and the norm of a loss is its operator norm, the dual norm. Losses
are minimized. Statements whose proofs do not use the dimension, such as the FTRL bounds of item 3,
are stated without it. The merged FTRL development of LMLExplore is restated in this generality by
the [Refactors](../Refactors/README.md) roadmap, Layer 0.1.
the [Refactors](../../Completed/Refactors/README.md) roadmap, Layer 0.1.

1. **Legendre functions.** For a convex function $F$ with domain $D$ (represent it as `F : E → ℝ`
with a convex set `D`, or as `E → EReal`; choose one representation and give conversions to
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2 changes: 1 addition & 1 deletion LMLRoadmaps/Identification/README.md
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Expand Up @@ -250,7 +250,7 @@ forms above, and that development may be adapted to them.
- Prove the Cramér–Chernoff bound
$P\big(\sum_{i<n}T(Y_i)\ge nx\big)\le\exp(-n\,d(x,\mu))$ for independent observations
$Y_i$ of law $\rho_{\eta(\mu)}$ and $x\ge\mu$ (and the lower tail), in the form of the
[Refactors](../Refactors/README.md) roadmap, Layer 0.3: for real random variables dominated
[Refactors](../../Completed/Refactors/README.md) roadmap, Layer 0.3: for real random variables dominated
by the member of mean $\mu$. That form contains the Bandits roadmap's Layer 1.4 bound.
- Prove the sub-Gaussian comparison: $d(\mu,\mu')\ge(\mu-\mu')^2/(2\sigma^2)$ when the family has
variance at most $\sigma^2$ on the segment.
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7 changes: 7 additions & 0 deletions README.md
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Expand Up @@ -20,6 +20,13 @@ propose or review one.

- [Bandit algorithms and their regret](LMLRoadmaps/Bandits/README.md)

## Completed roadmaps

Roadmaps the maintainers have declared complete, a judgment against the roadmap's `README.md`, are
archived under `Completed/`. Their Lean files stay checked against the current LMLExplore pin.

- [Refactors toward the generality of later layers](Completed/Refactors/README.md)

## Writing a roadmap

A roadmap is a specification for material we want in LMLExplore, written so that an AI contributor
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