keer_zu 发表于 2023-3-15 11:23

非线性优化: Levenberg-Marquardt法(LM法)

注意到关于LM法网上大部份资料内容比较混乱,主要是因为LM法是可以从两个不同的视角看的。一种是看作介于高斯牛顿和梯度下降法之间的一种算法,另一种是作为一种信赖域的算法来看,而两种视角下虽然最后结论比较相似,但公式推导的思路差别会比较大。
从历史上讲,LM法最初作为高斯牛顿法的改良而被提出,随后才有了信赖域法上应用。这里先从高斯牛顿法/梯度下降法混合的视角下来进行推导。
基础先来回顾一下高斯牛顿法的几个关键点(可参照非线性优化整理-2.高斯-牛顿法)高斯牛顿法的迭代公式为data:image/png;base64,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data:image/png;base64,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***7Fzk4pyl4JYYzCQ7G1SIJNK/X+oky+XIVcj6uRBcQ7z7KxyWhhZ8jqeZJFD/fwR9h7sY+Ft24wy0OOkxo+X1dK1Rc1Yp4JzSz2OM/vw/bQPxxvVebvqT9v1fo4d1cDRhDtn5TUhhBBCzJZk4J1lOqxx05fohE8ew9cTwT/UxGvfd2OdEFjH6f+vXjQcNG1yFJRF9L/RyKV81cUz/Xl48mWGIpybZH7qyYq6aYHLGYF3gb78DdZvzhwTmcp6jB8vaTxRw84cxckSQvQdLEKe4XqUC0MTH46f7yV4bTortOLc7JiQqTWVutjx4zJsP3uRfcdbeDpSRevLOyZ0ezWu+en85334rys4tr2JZ5MN840sTRJp48/jwU72tPRBuR0GIwyf7uR7p21s+2EDrlITYBA+eiBZ+GqYkZtAWgPDiJboov6VmXRhNWJcHj1GnCx7KLMasp8TA+B8cZJq6towHw8BqNisk501cYJ7d7F/2En9P3XhKYXI0Vdo3vsc0aFqSgb60Te38s6LJi4c2MO+tj0stL6ZszjZwhIbEIZglPhOR4E39+mNXCTGqB5NVESudGTffstj1VTnDaCnysC4DVDCwhlOJTZysZvmQz601Q00fX+yGgP3QrJhZvMq7CadaE8bzQdDaIqLpp/sxl2aO2AyldfS/hMlcX4dbCRyrZWf7y7hXMZ0hbmmKOPDI7Q1vV/4po5Om6UTOuUrfLqtHD67rQPK2AwFWUxoRE12pZ7g9i10fbLgMlFATH3+bUabAFKzDSjVeDaPD7ojR9to/P/yr1H7BHh0/GPGR900/4uPsAaODcvQBnrpvQncjHFhKA53NGLhWKI3zaAX3ynnxKnWZkwjdLybEDbqt1ROuafN6JSgM60DIIQQQnyBJAPvLNNhbbWnBd5m1Oc7eFNpofnAPr4Ti9Pxr/WoaTe98TNe9oXAtrWOylnotjxd0Yv9yRu+Yd5/rZlPn/ZQv/JulgwrzLgCO1kVp6p5PNw/NlXZ7RiRaxbspSa0IS/eqUwllrad9iyBNwDzrLh3v4ltSRvNB6LENCMj8NYIHfXhv61Su6918v10J07w4D72Hw9jeaaDdkeEJ38QoWRlBfaLXtq+HeVy60s0fCmAt0dDKbezcDBC/E86pI0h164HASeWmWT7r6aN72Y+t+Jhwsnaf/rVfk4c9RPBRsNDk9zS3ogl94eZuXkPCIPo0T20xNx0pVWgdjgroCdK5N1e4k+188tNNqJv/QP7ziRany7HNKqzdN8FMP11sm+GNoKWpQhUIeLn38cPOJ51556uaNbpaMMAFpSZzuG9wIKtHPoGvDQO9OG8y5nhSRlGoijih1FiqFgfXYal3MLul3dg1/z09uhYndU4Mq65iYY0M/Yn3DT93M6Kw35MG5woRCZMV5h1irI8EtOLWbCvLMl+DRvyc+w0KIqCpk3SCprvfbQw4Mw6533KhEbUZFfqTMHXv0Pw9cneMfOaaxDp8dKrKVTtqZswp/xCm51Vk00n9n/D4xu0AVOpFYsGYSD0VnNaN+7EVGjKnFIqtrixzBvh0vFeQlOdaq0gCo6db/KLtSNYlo4QCuqozhwV1YUQQggxK5KBd1ol4JzT5JiwbWqna3Ene17qpvG7URr+1UP1UjMMB/AdDIJSTcOmArrizbOgrlSpeLaDqqVT2NorfTS+dS53N3YjzLnjUdSVKuGLOsZnUbqbmpn7Rse4Ajmf3dLJNfsZjFX9ntQdg/iVGHNTN35//A0nekYyuprf4uM/AmR7DnJljIsjSvBkGFuZjeiQxgcHXiQUUqjd1059rinAkhVyp911EzO2Te38fLWOsijzyFBw7uzgzZvWSSsTa+Fe9r/uJXjdgnv3L9ixzoppMNkRv7SSHZsdiex6y3biO3dTs86NaUMFl77XTOR6HEbzuXFig4DyMKUzCLwT8xOn5CrepmIrnWRFxmfJ9Vgpybc9N4IceStObUf1uPG8xp9vjf678m9UzIwQv5LaMifffDTPPlMsOIEgI+i3yR143zHQBgP4I2aciy/ReWIsl6l9kgjhrp3aR+P/ybP9kJYRnak4nw4AZQunOX58zEKbi9onVCqO72ffwSDBg40ETzlp2LWT6vsh/W2yU/2DWs79IJX5rKXrjcRTWuQC3oNB6h+dGHgnGtKceFxu7IusuJ5vSD6Tdq2fUP06ZYT4h8CjdXgmZDNTFeHdNOzL1jCoETjqJaJU0bBpBO/B6U64lurVYMI0C40g6pZW6r6adoBf66dxvx/3zg4qR89RhfRqJsZFHy2Ho+D0UP1Y2msXqNR1dMCX7dgmXNPGfwZNXcHjZMyasMBB/b93UPlnMFsSU6GZ5hjE/hBDz5ijW50T4drvTBi6AbMaeAOYsZabiRx+muZDn+HypMa0Z5ExE4PiauVu1RYUQgghPi8KH+OdZHlsBx0/t9DyQy/ef3yO2O56LKdS067UT8gKjLqto99J/NP0aB2tjwLkD4AnWFxJ6yuVAGnzho/NL6qH+ummlqZvxghfNLP+5VdZf2g7bS80whsdo1XNu5ufJFuJtvGc2R82bvHZHSBygO9VtqFRTcd/VySeGwrQPZRr5Hau5/JkjGeZcbGfY0Nuap6/RXQIvrWtgWW3tuNraoZ97UXtGaDMidJ7WKdyS9pt/O0IfceHUTdMVrwvzoVjXoILqvD8qB7XEjPcAeaYUVeqiYaYZHbdUtqPaa0D+1MOIM6tldD32yjxTcnCZfo1oheBp2ZSyGz8+O7MRgnjup+22n0E1y7DOklgqP0plQ/LVb8guc7Yp+ir66jISCvHrqTy7qnpzCy4X3wTS0zHbFWzFjsbNRrQRIhrjOuODwb68EhiOrHDjWw8DKz2oCpxwhfDZIoPhpl0sj/z45MtUZjrsUTtA7t1ds6bOQrq5lbeXh3Eu3c/veEg3sYIFzZtY8cWF5OOACgy0/Ia6p/y01yUzGc2Blknai/E1XOcGADHrmqc87x4p70NI2jXAb6CMgvtH+ZSO2p6Q8rcRKOdxaaiZht2NBxg72u9ia9hztjZadyIEvlj8rfnjxHCfyzk3WNEwjHMo4F6es2QpBsBjjSOLygJYNvQxdubCv6Y4z/Cb0/Qe2NiVfPMAVv2TS9RH9qOr20PX7F05KziLoQQQoiZmXLgDWAqq6b9jYXs+6c2/HsTNVvtWxuozvODHTn+JNun1ZV5EqM3KnHOve9HWdeBOi8ZzMyx4NrZSvyPLVz6MEZ1cqxdKsuh/dZLW4+JWk89K9LugvTfH6ElvUq2oREOHKP/gxAXUmPvgPmPVVHztxVYIREIjM6Nmi77GO+7LzkG/6l21EXJcZvz7NT+Wxe0nED5UmLfRQO9XLNU4ixXsvdc0CL4B3RWbSgwc6nHCL7rw3soSBwrxsodySc+I3LKR+ehMJz8gHrPbmpzZhgtuF98h1VmJdkF2CD81j/QFqpk90860gIRM+rmqnGvsy5X4NDYlFmpCtHO5bmLBE5q3PhulVWPjN9u02IrDwP68rJZ29+mlfV0rMx8NE7098mjcfUybK**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**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***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***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**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***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**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**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**LSIiIiIiIpJDCrxFREREREREckiBt4iIiIiIiEgO/X9Nu8ARE+FjjQAAAABJRU5ErkJggg==

keer_zu 发表于 2023-3-15 11:24

LM法高斯牛顿法具有收敛快速但对初始点位置敏感的特点,梯度下降法则相反。
而LM法,也称作阻尼最小二乘法(Damped Least-squares),则结合了二者的特点,引入了阻尼因子<span class="MathJax" id="MathJax-Element-3399-Frame" tabindex="0" data-mathml="&#x03BC;" role="presentation" style="box-sizing: border-box; outline: 0px; display: inline; line-height: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">μ�来调节算法的特性。
原始版LM法的迭代公式为

keer_zu 发表于 2023-3-15 11:26


keer_zu 发表于 2023-3-15 11:26


keer_zu 发表于 2023-3-15 11:27

算法流程可以总结经典LM算法的迭代流程为

keer_zu 发表于 2023-3-15 11:31


keer_zu 发表于 2023-3-15 11:31


keer_zu 发表于 2023-3-15 11:31

结论
[*]LM法是一种非常高效的迭代算法,能适用于大多数的case
[*]该算法的许多变量决定了迭代的效率和结果的收敛性,而这些参数的理想值往往依目标函数不同而不同
[*]因为存在矩阵求逆这一运算,所以对于大型数据求解需要用一些特殊技巧。

keer_zu 发表于 2023-3-15 11:33

信赖域法
这里再补充一下信頼域法。
求解非线性优化的方法可以主要分为线性搜索和信赖域法(Trust Region Method)。
线性搜索核心思想是先确定搜索方向,然后确定步长进行迭代
信赖域法核心思想则是先确定最大距离,再确定方向。具体为每次迭代都会给出一个半径为Δ
Δ
的信赖域使得模型在该信頼域内足够精确。在该领域内求解问题得到一个步长h

,接着通过某一评价标准判断该步长的好坏来决定是否要接受该步长。如果接受则更新当前位置,否则则当前位置不变。而新信赖域的半径大小则依照判断预测的好坏,来增大或减小。
信赖域法的基本流程如下




页: [1]
查看完整版本: 非线性优化: Levenberg-Marquardt法(LM法)