[RemyDegenne]

Adds LMLRoadmaps/Identification/, a roadmap for identification in stochastic bandits (pure exploration), with best arm identification as the main case. It covers fixed confidence and fixed budget, general identification tasks with multiple correct answers, and linear identification. It is written at the generality of the research literature, so that papers in the area can be formalized on top of it. It is built on LML's IdentAlg framework and on the Bandits roadmap material already in LMLExplore (binary relative entropy, Bretagnolle–Huber, Ville's inequality, mixtures of supermartingales, sub-Gaussian supermartingales, KL Chernoff bounds, design operators).

Layers
0. Identification algorithms: constructions, canonical runs, δ-correct and δ-PAC algorithms, expected sample complexity, Wald identities at the stopping time, fixed-budget algorithms

1. Identification tasks (arbitrary models, set-valued correct answers; best arm, top-m, ε-best arm, thresholding, Any Low Arm, half-space) and natural exponential families as tilts of a base measure (KL closed form, Cramér–Chernoff bounds, Gaussian/Bernoulli/Poisson/exponential instances); Gaussian arms with unknown variances
2. Divergence decomposition at stopping times, transportation lemma, fixed-confidence lower bound E[τ] ≥ T* kl(δ, 1-δ) (single and multiple answers), fixed-budget two-model lower bounds
3. The pure exploration game: concavity, Sion minimax form, Berge continuity and upper hemicontinuity of optimal allocations, closed forms for best arm identification, Top Two allocations, Gaussian closed forms
4. Deviation inequalities for exponential families (Kaufmann–Koolen mixture thresholds, union-bound thresholds), GLR stopping rules δ-correct for every sampling rule, generic asymptotic and non-asymptotic sample-complexity reductions
5. Tracking lemmas, Track-and-Stop (C- and D-tracking), Sticky Track-and-Stop
6. AdaHedge and FTPL, pure exploration by solving games, Top Two algorithms (TTTS, T3C, TTUCB, EB-TCε), Frank–Wolfe sampling
7. Successive elimination, median elimination, LUCB and KL-LUCB, PAC lower bounds
8. Successive rejects, sequential halving, large deviations under static allocations, the Carpentier–Locatelli lower bound, the results of Degenne (COLT 2023) on the existence of a complexity
9. Linear identification: characteristic time with design operators, RAGE, GLRT with self-normalized thresholds, LinGame and lazy Track-and-Stop

Generality beyond the papers

• arbitrary model types, observation spaces and answer types;
• set-valued correct answers throughout;
• ℝ≥0∞-valued divergences and game quantities, with no absolute-continuity assumptions in the change of measure;
• exponential families stated through Mathlib's Measure.tilted and cgf;
• every result is stated for general tasks, with best arm identification as a corollary.

Suggested.lean compiles against the pinned LMLExplore dependencies (6 admitted declarations: the game quantities with their concavity, the exponential-family KL formula, the transportation lemma, the lower bound, and Track-and-Stop with its asymptotic optimality).

Points for review

• The divergence-order convention: true model first for fixed confidence, alternative first for fixed-budget exponents (they differ outside the Gaussian case).
• The scope boundary: nonparametric identification with K_inf/KL_inf (including the bounded-arm Top Two theorem of Jourdan et al. 2022), MDPs, combinatorial, dueling and multi-fidelity identification, and Bayesian guarantees are out.
• Constants whose theorem numbers could not be confirmed against the sources are cited without a number (successive rejects, sequential halving, Carpentier–Locatelli); the explicit form of the Kaufmann–Koolen function C^exp is left to an O(log) estimate with explicit constants.

The roadmap was drafted with Claude Opus 5.5, which also ran a literature survey of the area to check the citations and theorem numbers.

🤖 Generated with Claude Code

https://claude.ai/code/session_0196ftMTTvboLE9rrbLUFss1