随机化Kaczmarz中的自适应行选择与异步性
Adaptive Row Selection Meets Asynchrony in Randomized Kaczmarz
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中文总结 AI 辅助
研究随机化Kaczmarz中自适应行选择与异步性，通过在96核节点上339次运行测量实际延迟，发现稳定性受边界$\ell^*(T)$等影响，阈值贪婪选择在高线程数不稳定，欠松弛可恢复边界，不一致读取更优，还验证实现并概述分布式两级采样器。
中文摘要 AI 辅助
随机化Kaczmarz适用于大型稀疏最小二乘和断层扫描重建，自适应行选择可减少迭代次数。但在共享内存机器上部署自适应选择意味着从无锁工作线程同时修改的残差中采样，常使用陈旧数据。本文首次对该机制进行系统研究：在异步执行下的残差加权和贪婪Kaczmarz，在一个96核节点上进行339次运行并测量实际（非注入）延迟。有四个发现可直接应用于实践：稳定性由采样积极性和线程数之间的边界$\ell^*(T)$决定；阈值贪婪选择在高线程数时不稳定；欠松弛以可预测成本恢复边界；一致快照读取存在罕见的、依赖调度的发散，实时（不一致）读取未出现且成本更低，使不一致读取成为正确默认选择。我们根据已发表的顺序结果验证了实现，并概述了这些测量结果所推动的分布式两级采样器。
英文摘要
Randomized Kaczmarz is a natural fit for large sparse least-squares and tomographic reconstruction, and adaptive row selection can reduce iteration counts. However, deploying adaptive selection on a shared-memory machine means sampling from a residual that lock-free workers are concurrently modifying, often using stale data. We present the first systematic study of this regime: residual-weighted and greedy Kaczmarz under asynchronous execution, measured across 339 runs on a 96-core node with realized (not injected) delays. Four findings carry directly to practice. (i) Stability is governed by a boundary $\ell^*(T)$ between sampling aggressiveness and thread count; below it, more aggressive sampling is strictly better, so one should tune to just inside the cliff. (ii) Threshold-greedy selection (the standard accelerated rule) is unstable at high thread counts, diverging almost immediately. (iii) Under-relaxation buys back the cliff at a predictable cost, giving a usable safety knob. (iv) Consistent-snapshot reads admit a rare, scheduling-dependent divergence that live (inconsistent) reads never exhibited; live reads also cost less per step, making them the right default. We validate the implementation against published sequential results and outline the distributed two-level sampler these measurements motivate.
