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通过模拟退火逃避局部极小值：近似凸函数的优化
Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions |
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| 课程网址: |
https://videolectures.net/videos/colt2015_liang_convex_functions
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| 主讲教师: |
Tengyuan Liang
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| 开课单位: |
信息不详。欢迎您在右侧留言补充。
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| 开课时间: |
2025-02-04
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| 课程语种: |
英语
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| 中文简介: |
我们考虑了在$\mathbb{R}^n$中一个有界凸集上只用函数求值来优化一个近似凸函数的问题。将问题简化为使用Hit-and-Run方法从\emph{近似}对数凹分布中采样，查询复杂度为$\mathcal{O}^*(n^{4.5})$。在零阶随机凸优化的背景下，该方法通过诱导$\mathcal{O}(\epsilon/n)$ -近似对数凹分布，在$\mathcal{O}^*(n^{7.5}\epsilon^{-2})$噪声函数评估后产生$\epsilon$ -最小化器。我们还考虑了“非凸性量”在远离最小值的情况下可能很大，但向函数的最优值衰减的情况。随机漫步方法的其他应用包括经验风险最小化的私人计算、两阶段随机规划和在线学习的近似动态规划。
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| 课程简介: |
We consider the problem of optimizing an approximately convex function over a bounded convex set in $\mathbb{R}^n$ using only function evaluations. The problem is reduced to sampling from an \emph{approximately} log-concave distribution using the Hit-and-Run method, with query complexity of $\mathcal{O}^*(n^{4.5})$. In the context of zeroth order stochastic convex optimization, the proposed method produces an $\epsilon$-minimizer after $\mathcal{O}^*(n^{7.5}\epsilon^{-2})$ noisy function evaluations by inducing a $\mathcal{O}(\epsilon/n)$-approximately log concave distribution. We also consider the case when the ``amount of non-convexity'' can be large away from the minimum but decays towards the optimum of the function. Other applications of the random walk method include private computation of empirical risk minimizers, two-stage stochastic programming, and approximate dynamic programming for online learning.
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| 关 键 词: |
函数求值; 凸函数; 噪声函数
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| 课程来源: |
视频讲座网
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| 数据采集: |
2025-03-31：zsp
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| 最后编审: |
2025-03-31：zsp
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| 阅读次数: |
2
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图 书 馆