[RemyDegenne]

Adds LMLRoadmaps/Bandits/: the regret theory of stochastic, adversarial and linear bandits, following Lattimore and Szepesvári, Bandit Algorithms (2020), and built on LML's interaction framework and existing bandit results.

Layers
0. Bandit instances, binary relative entropy and the KL-UCB level, weight-based and index policies, regret notions

1. Ville's inequality, time-uniform and KL-form concentration, Gaussian tails
2. Minimax bound for LML's UCB, asymptotically optimal UCB, MOSS
3. KL-UCB for rewards in [0, 1]
4. Divergence decomposition, Bretagnolle–Huber, minimax and Lai–Robbins lower bounds, asymptotic optimality, adversarial lower bound
5. Frequentist Gaussian Thompson sampling
6. Legendre functions, Bregman projections, FTRL and mirror descent
7. Exp3, Exp3-IX, Exp4
8. Design operators, elliptical potential, self-normalized bound, Kiefer–Wolfowitz
9. Linear bandit environments (contextual features), OFUL, phased elimination, linear lower bounds
10. Exp3 with optimal-design exploration, mirror descent on the unit ball

Generality beyond the book

• any finite arm type;
• σ²-sub-Gaussian rewards with rescaled constants;
• KL-UCB for any rewards in [0, 1];
• a minimax lower bound for families with quadratic KL (giving the Gaussian, Bernoulli and adversarial cases);
• Lai–Robbins over arbitrary distribution classes;
• inner product spaces instead of ℝ^d;
• Kiefer–Wolfowitz for compact and non-spanning sets.

Suggested.lean compiles against the pinned LMLExplore dependencies (24 admitted signatures).

Points for review

• The constants rescaled with σ² (Layers 2, 5, 8, 9) and the general lower-bound family of Layer 4.3.
• The reward/loss convention: rewards and maximization for finitely many arms; losses for online linear optimization and adversarial linear bandits.
• The scope boundary: pure exploration, MDPs, combinatorial, non-stationary and sparse bandits are out.

AI assistance: the scope was chosen by the author. Claude Opus 5.5, in Claude Code, surveyed LML, Mathlib and Tau Ceti for existing material, extracted the theorem statements from the book, and drafted README.md and Suggested.lean. The author has not yet reviewed every constant.

🤖 Generated with Claude Code