论文标题
非本地优化：通过放松对优化问题施加结构
Non-local Optimization: Imposing Structure on Optimization Problems by Relaxation
论文作者
论文摘要
In stochastic optimization, particularly in evolutionary computation and reinforcement learning, the optimization of a function $f: Ω\to \mathbb{R}$ is often addressed through optimizing a so-called relaxation $θ\in Θ\mapsto \mathbb{E}_θ(f)$ of $f$, where $Θ$ resembles the parameters of a family of probability measures on $ω$。我们通过测量理论和傅立叶分析研究了这种放松的结构，使我们能够阐明许多相关的随机优化方法的成功。我们得出的主要结构特征并允许快速可靠的放松优化是$ f $的最佳值，梯度的Lipschitzness和凸度的一致性。我们强调$ f $本身不是可区分或凸的设置，例如在（随机）干扰的情况下。
In stochastic optimization, particularly in evolutionary computation and reinforcement learning, the optimization of a function $f: Ω\to \mathbb{R}$ is often addressed through optimizing a so-called relaxation $θ\in Θ\mapsto \mathbb{E}_θ(f)$ of $f$, where $Θ$ resembles the parameters of a family of probability measures on $Ω$. We investigate the structure of such relaxations by means of measure theory and Fourier analysis, enabling us to shed light on the success of many associated stochastic optimization methods. The main structural traits we derive and that allow fast and reliable optimization of relaxations are the consistency of optimal values of $f$, Lipschitzness of gradients, and convexity. We emphasize settings where $f$ itself is not differentiable or convex, e.g., in the presence of (stochastic) disturbance.
