加权相互作用Langevin扩散：一种加速抽样优化方法
Reweighted Interacting Langevin Diffusions: an Accelerated Sampling Methodfor Optimization
摘要：
我们提出了一种新的技术来加速解决困难的优化问题的采样方法。我们的方法研究后验分布采样和优化与朗之万动力学之间的内在联系，然后我们提出了一个相互作用的粒子计划，近似一个加权相互作用朗之万扩散系统（RILD）。通过在经典的Langevin算子中加入一个乘性源项来设计底层系统，从而获得更高的收敛速度和更集中的不变测度。我们分析了算法的收敛速度，并与已有的结果相比，在渐近的情况下，改进。我们还设计了各种测试来验证我们的理论结果，显示出加速收敛和突破可疑的局部极小值的障碍，特别是在高维非凸设置的优势。我们的算法和分析揭示了结合梯度和遗传算法使用偏微分方程（PDE）与可证明的保证。
英文摘要：
We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and then we propose an interacting particle scheme that approximates a Reweighted Interacting Langevin Diffusion system (RILD). The underlying system is designed by adding a multiplicative source term into the classical Langevin operator, leading to a higher convergence rate and a more concentrated invariant measure. We analyze the convergence rate of our algorithm and the improvement compared to existing results in the asymptotic situation. We also design various tests to verify our theoretical results, showing the advantages of accelerating convergence and breaking through barriers of suspicious local minimums, especially in high-dimensional non-convex settings. Our algorithms and analysis shed some light on combining gradient and genetic algorithms using Partial Differential Equations (PDEs) with provable guarantees.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
