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Compositional design spaces in materials engineering, particularly for alloys and multi-component systems, present exceptionally high-dimensional and sparsely populated landscapes that challenge conventional discovery workflows. A typical five-element alloy system sampled at 10% concentration increments can encompass millions of possible compositions, rendering exhaustive evaluation infeasible. Active learning has emerged as an essential paradigm for navigating these spaces efficiently, yet standard implementations often fail to address the simultaneous demands of multiple conflicting objectives—such as balancing mechanical strength against ductility, electrical conductivity against thermal stability, or performance against material cost—while properly accounting for uncertainty and practical constraints. This conceptual framework introduces an uncertainty-aware active learning approach tailored specifically for compositional design spaces with multiple objectives. The framework comprises four core components: robust uncertainty quantification that distinguishes epistemic from aleatoric contributions across heterogeneous composition regions, multi-objective acquisition functions grounded in Pareto optimization to explicitly explore trade-offs, systematic constraint handling for both hard thermodynamic limits and soft economic or manufacturability requirements, and adaptive sequential sampling strategies that prioritize informative candidates under limited evaluation budgets. The key innovation lies in a Pareto-based acquisition mechanism that integrates uncertainty estimates to balance exploration of uncertain regions, exploitation of promising trade-offs, and navigation of sparse high-dimensional manifolds. By embedding these elements into a unified conceptual structure, the framework provides design principles that enable more reliable, interpretable, and scalable materials discovery. It shifts the focus from single-objective optimization to holistic decision-making under uncertainty, ensuring that active learning not only accelerates identification of high-performing compositions but also respects real-world engineering constraints inherent to multi-component systems. The proposed approach is expected to guide both computational and experimental campaigns in alloy design, high-entropy materials, and mixed ionic conductors, ultimately fostering more sustainable and high-performance materials.