$\R^d$中的快速模拟退火算法及其在极大似然估计中的应用
Fast simulated annealing in $\R^d$ and an application to maximum likelihood estimation
摘要：
使用经典模拟退火来最大化在$\R^d$的子集上定义的函数$ψ$，概率$\p(ψ(θ\_n)\leq ψ\_{\max}-ε)$随着$n$增加以对数速率趋于零;这里$θ\_n$是模拟退火算法的$n$阶段中的状态，并且$ψ\_{\max}$是$ψ$的最大值。我们提出了一个修改后的计划，这个概率是为了$n^{-1/3}\log n$，因此消失在一个代数率。为了获得更快的速率，经典模拟退火的指数衰减的接受概率被替换为更重尾的函数，并且系统被更快地冷却。我们还展示了该算法如何可能被应用到功能，不能准确计算，但只能近似，并给出一个例子，最大化的日志-似然函数的状态空间模型。
英文摘要：
Using classical simulated annealing to maximise a function $ψ$ defined on a subset of $\R^d$, the probability $\p(ψ(θ\_n)\leq ψ\_{\max}-ε)$ tends to zero at a logarithmic rate as $n$ increases; here $θ\_n$ is the state in the $n$-th stage of the simulated annealing algorithm and $ψ\_{\max}$ is the maximal value of $ψ$. We propose a modified scheme for which this probability is of order $n^{-1/3}\log n$, and hence vanishes at an algebraic rate. To obtain this faster rate, the exponentially decaying acceptance probability of classical simulated annealing is replaced by a more heavy-tailed function, and the system is cooled faster. We also show how the algorithm may be applied to functions that cannot be computed exactly but only approximated, and give an example of maximising the log-likelihood function for a state-space model.
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。
