发表机构
The Education University of Hong Kong（香港教育大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过限制局部信息传递并引入带信赖域的腔消息传递算法，在路由优化问题中揭示了非凸能量景观的三个特征区域，证明了该方法在识别崎岖能量景观特征方面的鲁棒性。
AI 中文摘要
非凸优化问题的能量景观是高维表面，难以揭示、可视化或分析。消息传递算法，或等价地统计物理中的腔方法，可能因能量景观的崎岖性导致消息不收敛而无法识别局部最小值。在此，我们旨在通过限制局部消息中传递的信息量来揭示这些复杂能量景观的特征，从而提高消息对局部最小值的收敛性。通过研究一个其凸性由单一参数控制的路由优化问题，我们引入了一种带信赖域的腔消息传递算法，并在同一问题实例的多次独立实现中采样了崎岖能量景观的收敛局部最小值集合。我们观察到具有不同能量景观特征的三个区域：（1）最大崎岖区域，低能量最小值的多样性达到峰值；（2）中间区域，低能量解具有层次化的多簇组织；（3）平滑区域，由单一最小值主导。额外测试表明，如果信赖域大小较小或适中，收敛能量对其大小基本不敏感，这证明了所提方法在识别崎岖能量景观特征方面的鲁棒性。
英文摘要
Energy landscapes of non-convex optimization problems are high-dimensional surfaces that are difficult to reveal, visualize, or analyze. Message-passing algorithms, or equivalently cavity approaches in statistical physics, may fail to identify local minima as messages do not converge owing to the ruggedness of the energy landscapes. Here we aim to reveal the characteristics of these complex energy landscapes by limiting the amount of information passed in local messages, improving the convergence of messages for local minima. By studying a routing optimization problem with its convexity governed by a single parameter, we introduce a cavity message-passing algorithm with a trust region, and sample ensembles of converged local minima of rugged energy landscapes across many independent realizations of the same problem instances. We observe three regimes with different characteristics of the energy landscapes: (1) a maximally rugged regime with a peak in the diversity of low-energy minima; (2) an intermediate regime with a hierarchical multi-cluster organization of low-energy solutions; and (3) a smooth regime dominated by a single minimum. Additional tests show that the converged energies are largely insensitive to the size of the trust region if the size is small or moderate, demonstrating the robustness of the proposed approach in identifying characteristics of rugged energy landscapes.
Comments12 pages, 13 figures
