Adaptive Threshold-Driven Continuous Greedy Method for Scalable Submodular Optimization

• URL: http://arxiv.org/abs/2604.03419v1
• Date: Fri, 03 Apr 2026 19:32:39 GMT
• Title: Adaptive Threshold-Driven Continuous Greedy Method for Scalable Submodular Optimization
• Abstract summary: Submodular under matroid constraints is a fundamental problem in optimization with applications in sensing, data-marization, active learning, and resource allocation.<n>We propose textitATCG (underlineAdaptive underlineThresholded underlineThresholded underlineGreedy), expanding each agent's active set only when current candidates fail to capture sufficient marginal gain.<n>Experiments on a classbalanced prototype selection problem over a CIFAR-10 animal dataset show that textit
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Submodular maximization under matroid constraints is a fundamental problem in combinatorial optimization with applications in sensing, data summarization, active learning, and resource allocation. While the Sequential Greedy (SG) algorithm achieves only a $\frac{1}{2}$-approximation due to irrevocable selections, Continuous Greedy (CG) attains the optimal $\bigl(1-\frac{1}{e}\bigr)$-approximation via the multilinear relaxation, at the cost of a progressively dense decision vector that forces agents to exchange feature embeddings for nearly every ground-set element. We propose \textit{ATCG} (\underline{A}daptive \underline{T}hresholded \underline{C}ontinuous \underline{G}reedy), which gates gradient evaluations behind a per-partition progress ratio $η_i$, expanding each agent's active set only when current candidates fail to capture sufficient marginal gain, thereby directly bounding which feature embeddings are ever transmitted. Theoretical analysis establishes a curvature-aware approximation guarantee with effective factor $τ_{\mathrm{eff}}=\max\{τ,1-c\}$, interpolating between the threshold-based guarantee and the low-curvature regime where \textit{ATCG} recovers the performance of CG. Experiments on a class-balanced prototype selection problem over a subset of the CIFAR-10 animal dataset show that \textit{ATCG} achieves objective values comparable to those of the full CG method while substantially reducing communication overhead through adaptive active-set expansion.

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