In this paper, we propose new Metropolis-Hastings and simulated annealing algorithms on finite state space via modifying the energy landscape. The core idea of landscape modification relies on introducing a parameter $c$, in which the landscape is modified once the algorithm is above this threshold parameter. We illustrate the power and benefits of landscape modification by investigating its effect on the classical Curie-Weiss model with Glauber dynamics and external magnetic field in the subcritical regime. This leads to a landscape-modified mean-field equation, and with appropriate choice of $c$ the free energy landscape can be transformed from a double-well into a single-well, while the location of the global minimum is preserved on the convexified landscape. Consequently, running algorithms on the modified landscape can improve the convergence to the ground-state in the Curie-Weiss model. In the setting of simulated annealing, we demonstrate that landscape modification can yield improved mean tunneling time between global minima, and give convergence guarantee using an improved logarithmic cooling schedule with reduced critical height. Finally, we discuss connections between landscape modification and other acceleration techniques such as Catoni's energy transformation algorithm, preconditioning, importance sampling and quantum annealing.

翻译：在本文中,我们提出新的大都会-Hasting 和模拟anneal 算法,通过改变能源景观来改变有限的状态空间。地貌改变的核心理念依赖于引入一个参数$c$,一旦算法超过这一阈值参数,地貌景观就会被改变。我们通过调查地貌改变对古典Curie-Weiss模型的影响以及Grauber动态和次临界系统外磁场的影响来说明地貌变化的动力和好处。这导致一个地貌变化的中位方方,并且通过适当选择美元来改变自由能源景观,从一个双井变成一个单井,而全球最低值的位置则保留在凝固的地貌上。因此,在改变地貌时的算法可以改善地貌与Curi-Weis模型中地貌的趋同。在模拟的内脏变中,我们证明地貌改变能够改善全球迷宫之间的平均地道流时间,并且保证使用改进的对地冷计划,降低临界高度,从而实现趋同。最后,我们讨论地貌改变地貌和诸如Catimolimalimalimalimalimaling laction lagistration lagistration lagingsingsquimaking keductionsquistrationsmakeductionsmakedationsmakedationsultingsultings。