论文标题
兰格文扩散的状态依赖温度控制
State-Dependent Temperature Control for Langevin Diffusions
论文作者
论文摘要
我们研究了非凸优化的背景下兰格文扩散的温度控制问题。对此类问题的经典最佳控制是Bang-Bang类型，该类型对错误过于敏感。一种补救措施是允许扩散探索其他温度值，从而使Bang-Bang控件平滑。我们通过随机宽松的控制配方来实现这一目标，该配方融合了温度控制的随机化并正规化其熵。我们得出了一种依赖状态的，截断的指数分布，该分布可用于在langevin算法中的样本温度，以HJB偏微分方程的解决方案。我们在一维基线示例上进行了数值实验，其中可以轻松地求解HJB方程，以将算法的性能与其他三种可用算法进行比较，以查找全局最佳。
We study the temperature control problem for Langevin diffusions in the context of non-convex optimization. The classical optimal control of such a problem is of the bang-bang type, which is overly sensitive to errors. A remedy is to allow the diffusions to explore other temperature values and hence smooth out the bang-bang control. We accomplish this by a stochastic relaxed control formulation incorporating randomization of the temperature control and regularizing its entropy. We derive a state-dependent, truncated exponential distribution, which can be used to sample temperatures in a Langevin algorithm, in terms of the solution to an HJB partial differential equation. We carry out a numerical experiment on a one-dimensional baseline example, in which the HJB equation can be easily solved, to compare the performance of the algorithm with three other available algorithms in search of a global optimum.
