[RemyDegenne]

Adds the OnlineLearning roadmap, for F. Orabona, Online Learning: A Modern Introduction Using Convex Optimization (arXiv:1912.13213v10). It also makes companion edits to the Bandits, ReinforcementLearning and Generalization roadmaps, so that each tool has one owner.

Why. LMLExplore has the FTRL, mirror-descent and exponential-weights core that the Bandits roadmap's Layer 6 specifies. No roadmap asks for the rest of online learning with full information:

• adaptive and AdaGrad rates, online-to-batch conversions, the lower bounds of online linear optimization;
• optimism and delays, the Online Newton Step and Vovk–Azoury–Warmuth;
• the Aggregating Algorithm and universal portfolios;
• black-box reductions and parameter-free learning through coin betting;
• dynamic, strongly adaptive and tracking regret, and saddle points;
• the online-learning proofs of Rademacher, PAC-Bayes, non-convex and confidence-sequence results.

The roadmap asks for them at the generality of the literature:

• normed spaces with losses in the dual, and arbitrary types where no convexity is used;
• bounds for every loss sequence, hence against adaptive adversaries;
• priors as arbitrary probability measures;
• anytime rates first, tuned rates as corollaries.

Changes

• LMLRoadmaps/OnlineLearning/ (new): README.md with 17 layers following the book's chapters, Suggested.lean, and metadata.toml (math.OC).
• LMLRoadmaps/Bandits/:
  • the scope covers the online optimization of Layer 6 only; full information beyond it points to OnlineLearning;
  • new item 7.5: Tsallis-INF, with its adversarial bound and its bound under a self-bounding constraint [Ora, Theorems 9.2 and 9.17; Zimmert–Seldin 2021]. It uses OnlineLearning 6.1, the local-norm bound through the unconstrained step.
• LMLRoadmaps/ReinforcementLearning/: Layers 5.1–5.2 cite OnlineLearning 10.1 (the Gibbs variational formula) and 1.3 (the descent lemma, in a normed space) instead of specifying them.
• LMLRoadmaps/Generalization/: lists the three restatements of merged code that OnlineLearning items own: sum_apply_sub_le_ftrl, the FTRL bounds with a derivative hypothesis, and mixLoss/hedgePotential.

Points to check

• This touches four roadmap directories, against the one-directory-per-PR convention, at the code owner's request.
• The items were written from the book's text extraction, and garbled formulas were checked against the PDF. Where the book errs, the item states the corrected form:
  • Theorem 9.16's Lai–Robbins constant;
  • $\log(2^N-1)$ in Theorem 6.37;
  • the tuned $p$-norm bound of §6.7;
  • Theorem 7.35 for sets with empty interior;
  • the last hint in the proof of Theorem 7.47;
  • Theorem 13.11's equality, which is an inequality;
  • the concavity hypothesis of Theorem 13.14;
  • the additive constant of Theorem 14.15;
  • the factors $\lambda_X,\lambda_Y$ of Theorem 15.28.
• Some constants are derived here rather than taken from the book:
  • Layer 3's Hoeffding constants, sharper than the book's Azuma constants;
  • $\mathbb E|\sum_t\varepsilon_t|\ge\sqrt{n/3}$ in Layer 4.1, where the book uses Szarek's $\sqrt{n/2}$;
  • the split-sample PAC corollary of Layer 3.4;
  • the adaptive-rate bound of Layer 2.3;
  • the translation of Tsallis-INF to the Bandits roadmap's pseudo-regret.
• Some items are heavy and could be cut:
  • the binomial-tail lower bound (Layer 4.3, [Ora, Theorem 5.5]);
  • the digamma and Batir inequalities (Layer 11.3), which Theorem 10.1 needs in every dimension;
  • boosting (Layer 15.4).
• The README's scope excludes these parts of the book: group norms, scale-free FTRL and AdaFTRL, the dual analysis of FTRL, extensive-form games, and statistical learning theory beyond the reductions of Layer 16.
• The restatements of merged code (Layers 0.3, 5.2, 10.1) are owned by the items, following the Generalization roadmap's convention. Layer 10.1 comes after Generalization 1.13.

Suggested.lean builds, and so does the whole library (lake build).

Drafted with Claude Opus 5.5 at the request of the code owner.

🤖 Generated with Claude Code

https://claude.ai/code/session_0196ftMUWNxX7hzkApeYywka