arXiv:2606.14690v1 Announce Type: new 
Abstract: We study a \emph{max-risk} objective for active learning in a multi-group mean estimation $d$-armed bandits: a learner adaptively allocates a budget of $T$ samples across $d$ groups to minimize the worst-case uncertainty index $\max_{k\in[d]}\sigma_k^2/n_k$, where $\sigma_k$ is the standard deviation of the distribution of arm $d$, and $n_k$ is the number of times arm $d$ is sampled. We develop a local minimax framework and prove the first general lower bound for this objective, valid for any finite-variance hypothesis class. The bound separates difficulty into three orthogonal factors: a \emph{budget} term, a \emph{heteroscedasticity} index measuring how unevenly the uncertainty is spread across arms, and a model-dependent complexity measure, the \emph{Variance Local Curvature} ($\mathrm{VLC}$), which captures how much information a local change of variance creates inside the hypothesis class. For smooth classes, the $\mathrm{VLC}$ is a reparametrization of a variance--Fisher information, with closed-form values for common families. Benchmarking against the strongest available upper bound shows near-optimality up to logarithmic factors in broad regimes, and pinpoints a systematic gap in highly heterogeneous instances. Our proof introduces two key ingredients: a loss-induced $\ell_1$ geometry on the decision space, and a representation-based instance generator that reduces hard-instance construction to an explicit random matrix calculation.

دراسة جديدة نشرت على arXiv تستكشف هدف المخاطر القصوى للتعلم النشط في تقدير المتوسطات متعددة المجموعات، مع التركيز على كيفية تخصيص المتعلم لميزانية من العينات عبر مجموعات متعددة لتقليل عدم اليقين. تقدم البحث إطارًا محليًا للحد الأدنى وتثبت حدًا أدنى عامًا لهذا الهدف، قابل للتطبيق على أي فئة فرضية ذات تباين محدود.

Un nuevo estudio publicado en arXiv explora un objetivo de riesgo máximo para el aprendizaje activo en la estimación de medias en múltiples grupos, centrándose en cómo un aprendiz puede asignar un presupuesto de muestras entre varios grupos para minimizar la incertidumbre. La investigación introduce un marco minimax local y establece un límite inferior general para este objetivo, aplicable a cualquier clase de hipótesis de varianza finita.

Une nouvelle étude publiée sur arXiv examine un objectif de risque maximal pour l'apprentissage actif dans l'estimation de la moyenne multi-groupe, en se concentrant sur la manière dont un apprenant peut allouer un budget d'échantillons à travers plusieurs groupes pour minimiser l'incertitude. La recherche introduit un cadre minimax local et établit une borne inférieure générale pour cet objectif, applicable à toute classe d'hypothèses à variance finie.

A new study published on arXiv explores a max-risk objective for active learning in multi-group mean estimation, focusing on how a learner can allocate a budget of samples across multiple groups to minimize uncertainty. The research introduces a local minimax framework and establishes a general lower bound for this objective, which is applicable to any finite-variance hypothesis class.