Cooperative multi-agent reinforcement learning (MARL) faces significant challenges in maintaining robust coordination under noisy observations. Although observation disturbances are often introduced independently across agents, their downstream effects on cooperative decision-making can become structured through underlying cooperation structures. We characterize this phenomenon as structured noise effects, where noise-induced decision effects exhibit local correlation among agents with stronger task-related dependencies while remaining globally heterogeneous across different agents and local structures. Existing robust MARL methods, however, rarely explicitly characterize or exploit such structure-dependent noise effects. To address this limitation, we propose SIGMA, a hierarchical collaboration framework that exploits cooperation structures to learn robust representations under noisy observations. SIGMA first organizes agents into adaptive local structures through density-based grouping and performs intra-group consensus aggregation to preserve shared task-relevant information while smoothing agent-specific representation deviations. Inter-group attention then adaptively integrates information across different groups to preserve global coordination while accommodating their heterogeneous contributions. Experiments on noisy-observation tasks in StarCraft II empirically validate the structured noise effects and demonstrate that SIGMA consistently improves robustness under observation noise while maintaining competitive performance in noise-free environments.
Kernel methods are typically formulated under the assumption of exact, noise-free access to the Gram matrix. However, in emerging settings such as quantum machine learning, each kernel entry must be inferred from noisy observations, and its accuracy depends on how a limited measurement budget is allocated. Despite this, existing approaches overwhelmingly rely on uniform allocation, which equalizes estimator variance but ignores the highly non-uniform dependence of kernelized classifiers on the Gram matrix. In this work, we introduce an adaptive measurement-allocation strategy for learning kernelized Support Vector Machines (SVMs) from noisy Bernoulli observations. Our approach combines two complementary principles: (i) geometric sensitivity, capturing how perturbations of individual kernel entries affect the classifier margin, and (ii) active-set instability, quantifying the probability of discrete changes in support-vector membership induced by measurement noise. These signals define a task-aware allocation scheme that concentrates measurements on the most decision-critical regions of the kernel matrix. We provide a theoretical analysis showing that the benefit of adaptive allocation is governed by the heterogeneity of the induced kernel importance structure, leading to distinct regimes in which adaptive or uniform strategies are preferable. Empirical evaluations on synthetic datasets demonstrate that adaptive allocation significantly improves support-vector recovery, margin estimation, and decision-function accuracy under fixed measurement budgets. A dual-coefficient stability criterion further enables early stopping, achieving near-optimal performance while using only a fraction of the measurement cost. Additional experiments on quantum kernels derived from real-world data reveal a regime-dependent behavior aligned with known phenomena such as kernel concentration. Together...