Joeyc_ 2022-09-04 19:56 采纳率: 0%
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刚接触机器学习,请教一下各位梯度下降得不到最优解的原因

刚接触机器学习,使用梯度下降算法解决线性回归问题,无论如何调整学习率和步数,都得不到代价函数(cost function)等于零的最优解,想向各位请教一下原因。

代码以及运行结果:

img

epoch= 0 w= 1.0933333333333333 cost= 4.666666666666667
epoch= 1 w= 1.1779555555555554 cost= 3.8362074074074086
epoch= 2 w= 1.2546797037037036 cost= 3.1535329869958857
epoch= 3 w= 1.3242429313580246 cost= 2.592344272332262
epoch= 4 w= 1.3873135910979424 cost= 2.1310222071581117
epoch= 5 w= 1.4444976559288012 cost= 1.7517949663820642
epoch= 6 w= 1.4963445413754464 cost= 1.440053319920117
epoch= 7 w= 1.5433523841804047 cost= 1.1837878313441108
epoch= 8 w= 1.5859728283235668 cost= 0.9731262101573632
epoch= 9 w= 1.6246153643467005 cost= 0.7999529948031382
epoch= 10 w= 1.659651263674342 cost= 0.6575969151946154
epoch= 11 w= 1.6914171457314033 cost= 0.5405738908195378
epoch= 12 w= 1.7202182121298057 cost= 0.44437576375991855
epoch= 13 w= 1.7463311789976905 cost= 0.365296627844598
epoch= 14 w= 1.7700069356245727 cost= 0.3002900634939416
epoch= 15 w= 1.7914729549662791 cost= 0.2468517784170642
epoch= 16 w= 1.8109354791694263 cost= 0.2029231330489788
epoch= 17 w= 1.8285815011136133 cost= 0.16681183417217407
epoch= 18 w= 1.8445805610096762 cost= 0.1371267415488235
epoch= 19 w= 1.8590863753154396 cost= 0.11272427607497944
epoch= 20 w= 1.872238313619332 cost= 0.09266436490145864
epoch= 21 w= 1.8841627376815275 cost= 0.07617422636521683
epoch= 22 w= 1.8949742154979183 cost= 0.06261859959338009
epoch= 23 w= 1.904776622051446 cost= 0.051475271914629306
epoch= 24 w= 1.9136641373266443 cost= 0.04231496130368814
epoch= 25 w= 1.9217221511761575 cost= 0.03478477885657844
epoch= 26 w= 1.9290280837330496 cost= 0.02859463421027894
epoch= 27 w= 1.9356521292512983 cost= 0.023506060193480772
epoch= 28 w= 1.9416579305211772 cost= 0.01932302619282764
epoch= 29 w= 1.9471031903392007 cost= 0.015884386331668398
epoch= 30 w= 1.952040225907542 cost= 0.01305767153735723
epoch= 31 w= 1.9565164714895047 cost= 0.010733986344664803
epoch= 32 w= 1.9605749341504843 cost= 0.008823813841374291
epoch= 33 w= 1.9642546069631057 cost= 0.007253567147113681
epoch= 34 w= 1.9675908436465492 cost= 0.005962754575689583
epoch= 35 w= 1.970615698239538 cost= 0.004901649272531298
epoch= 36 w= 1.9733582330705144 cost= 0.004029373553099482
epoch= 37 w= 1.975844797983933 cost= 0.0033123241439168096
epoch= 38 w= 1.9780992835054327 cost= 0.0027228776607060357
epoch= 39 w= 1.980143350378259 cost= 0.002238326453885249
epoch= 40 w= 1.9819966376762883 cost= 0.001840003826269386
epoch= 41 w= 1.983676951493168 cost= 0.0015125649231412608
epoch= 42 w= 1.9852004360204722 cost= 0.0012433955919298103
epoch= 43 w= 1.9865817286585614 cost= 0.0010221264385926248
epoch= 44 w= 1.987834100650429 cost= 0.0008402333603648631
epoch= 45 w= 1.9889695845897222 cost= 0.0006907091659248264
epoch= 46 w= 1.9899990900280147 cost= 0.0005677936325753796
epoch= 47 w= 1.9909325082920666 cost= 0.0004667516012495216
epoch= 48 w= 1.9917788075181404 cost= 0.000383690560742734
epoch= 49 w= 1.9925461188164473 cost= 0.00031541069384432885
epoch= 50 w= 1.9932418143935788 cost= 0.0002592816085930997
epoch= 51 w= 1.9938725783835114 cost= 0.0002131410058905752
epoch= 52 w= 1.994444471067717 cost= 0.00017521137977565514
epoch= 53 w= 1.9949629871013967 cost= 0.0001440315413480261
epoch= 54 w= 1.9954331083052663 cost= 0.0001184003283899171
epoch= 55 w= 1.9958593515301082 cost= 9.733033217332803e-05
epoch= 56 w= 1.9962458120539648 cost= 8.000985883901657e-05
epoch= 57 w= 1.9965962029289281 cost= 6.57716599593935e-05
epoch= 58 w= 1.9969138906555615 cost= 5.406722767150764e-05
epoch= 59 w= 1.997201927527709 cost= 4.444566413387458e-05
epoch= 60 w= 1.9974630809584561 cost= 3.65363112808981e-05
epoch= 61 w= 1.9976998600690001 cost= 3.0034471708953996e-05
epoch= 62 w= 1.9979145397958935 cost= 2.4689670610172655e-05
epoch= 63 w= 1.9981091827482769 cost= 2.0296006560253656e-05
epoch= 64 w= 1.9982856590251044 cost= 1.6684219437262796e-05
epoch= 65 w= 1.9984456641827613 cost= 1.3715169898293847e-05
epoch= 66 w= 1.9985907355257035 cost= 1.1274479219506377e-05
epoch= 67 w= 1.9987222668766378 cost= 9.268123006398985e-06
epoch= 68 w= 1.9988415219681517 cost= 7.61880902783969e-06
epoch= 69 w= 1.9989496465844576 cost= 6.262999634617916e-06
epoch= 70 w= 1.9990476795699081 cost= 5.1484640551938914e-06
epoch= 71 w= 1.9991365628100501 cost= 4.232266273994499e-06
epoch= 72 w= 1.999217150281112 cost= 3.479110977946351e-06
epoch= 73 w= 1.999290216254875 cost= 2.859983851026929e-06
epoch= 74 w= 1.9993564627377531 cost= 2.3510338359374262e-06
epoch= 75 w= 1.9994165262155628 cost= 1.932654303533636e-06
epoch= 76 w= 1.999470983768777 cost= 1.5887277332523938e-06
epoch= 77 w= 1.9995203586170245 cost= 1.3060048068548734e-06
epoch= 78 w= 1.9995651251461022 cost= 1.0735939958924364e-06
epoch= 79 w= 1.9996057134657994 cost= 8.825419799121559e-07
epoch= 80 w= 1.9996425135423248 cost= 7.254887315754342e-07
epoch= 81 w= 1.999675878945041 cost= 5.963839812987369e-07
epoch= 82 w= 1.999706130243504 cost= 4.902541385825727e-07
epoch= 83 w= 1.9997335580874436 cost= 4.0301069098738336e-07
epoch= 84 w= 1.9997584259992822 cost= 3.312926995781724e-07
epoch= 85 w= 1.9997809729060159 cost= 2.723373231729343e-07
epoch= 86 w= 1.9998014154347876 cost= 2.2387338352920307e-07
epoch= 87 w= 1.9998199499942075 cost= 1.8403387118941732e-07
epoch= 88 w= 1.9998367546614149 cost= 1.5128402140063082e-07
epoch= 89 w= 1.9998519908930161 cost= 1.2436218932547864e-07
epoch= 90 w= 1.9998658050763347 cost= 1.0223124683409346e-07
epoch= 91 w= 1.9998783299358769 cost= 8.403862850836479e-08
epoch= 92 w= 1.9998896858085284 cost= 6.908348768398496e-08
epoch= 93 w= 1.9998999817997325 cost= 5.678969725349543e-08
epoch= 94 w= 1.9999093168317574 cost= 4.66836551287917e-08
epoch= 95 w= 1.9999177805941268 cost= 3.8376039345125727e-08
epoch= 96 w= 1.9999254544053418 cost= 3.154680994333735e-08
epoch= 97 w= 1.9999324119941766 cost= 2.593287985380858e-08
epoch= 98 w= 1.9999387202080534 cost= 2.131797981222471e-08
epoch= 99 w= 1.9999444396553017 cost= 1.752432687141379e-08
epoch= 100 w= 1.9999496252874736 cost= 1.4405775547323328e-08

  • 写回答

1条回答 默认 最新

  • 万里鹏程转瞬至 人工智能领域优质创作者 2022-09-08 14:00
    关注

    你可以看到的你的权重w在不断趋近于最优解2啊,模型的梯度在w趋近于2时变得越来越小(w*x-y变得越来越小),对w的更新量也越来越小。你讲epoch设成2w应该就会无限的接近于2.

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