{"id":477370,"date":"2023-08-09T09:11:34","date_gmt":"2023-08-09T09:11:34","guid":{"rendered":""},"modified":"2023-09-05T11:14:34","modified_gmt":"2023-09-05T11:14:34","slug":"gradient-descent","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/gradient-descent\/","title":{"rendered":"Xu\u1ed1ng d\u1ed1c"},"content":{"rendered":"

Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n t\u1ed1i \u01b0u h\u00f3a l\u1eb7p l\u1ea1i th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ecm m\u1ee9c t\u1ed1i thi\u1ec3u c\u1ee5c b\u1ed9 ho\u1eb7c t\u1ed5ng th\u1ec3 c\u1ee7a h\u00e0m. \u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng ch\u1ee7 y\u1ebfu trong m\u00e1y h\u1ecdc v\u00e0 khoa h\u1ecdc d\u1eef li\u1ec7u, thu\u1eadt to\u00e1n n\u00e0y ho\u1ea1t \u0111\u1ed9ng t\u1ed1t nh\u1ea5t tr\u00ean c\u00e1c h\u00e0m kh\u00f3 t\u00ednh to\u00e1n ho\u1eb7c kh\u00f4ng th\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c gi\u00e1 tr\u1ecb t\u1ed1i thi\u1ec3u b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p ph\u00e2n t\u00edch.<\/p>\n

Ngu\u1ed3n g\u1ed1c v\u00e0 s\u1ef1 \u0111\u1ec1 c\u1eadp ban \u0111\u1ea7u c\u1ee7a vi\u1ec7c gi\u1ea3m \u0111\u1ed9 d\u1ed1c<\/h2>\n

Kh\u00e1i ni\u1ec7m gi\u1ea3m \u0111\u1ed9 d\u1ed1c b\u1eaft ngu\u1ed3n t\u1eeb nguy\u00ean t\u1eafc to\u00e1n h\u1ecdc c\u1ee7a ph\u00e9p t\u00ednh, \u0111\u1eb7c bi\u1ec7t l\u00e0 trong nghi\u00ean c\u1ee9u vi ph\u00e2n. Tuy nhi\u00ean, thu\u1eadt to\u00e1n ch\u00ednh th\u1ee9c m\u00e0 ch\u00fang ta bi\u1ebft ng\u00e0y nay \u0111\u00e3 \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 l\u1ea7n \u0111\u1ea7u ti\u00ean trong m\u1ed9t \u1ea5n ph\u1ea9m c\u1ee7a Vi\u1ec7n Khoa h\u1ecdc To\u00e1n h\u1ecdc Hoa K\u1ef3 v\u00e0o n\u0103m 1847, th\u1eadm ch\u00ed c\u00f2n c\u00f3 tr\u01b0\u1edbc c\u1ea3 nh\u1eefng m\u00e1y t\u00ednh hi\u1ec7n \u0111\u1ea1i.<\/p>\n

Vi\u1ec7c s\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3m \u0111\u1ed9 d\u1ed1c ban \u0111\u1ea7u ch\u1ee7 y\u1ebfu l\u00e0 trong l\u0129nh v\u1ef1c to\u00e1n h\u1ecdc \u1ee9ng d\u1ee5ng. V\u1edbi s\u1ef1 ra \u0111\u1eddi c\u1ee7a h\u1ecdc m\u00e1y v\u00e0 khoa h\u1ecdc d\u1eef li\u1ec7u, vi\u1ec7c s\u1eed d\u1ee5ng n\u00f3 \u0111\u00e3 m\u1edf r\u1ed9ng \u0111\u00e1ng k\u1ec3 nh\u1edd t\u00ednh hi\u1ec7u qu\u1ea3 c\u1ee7a n\u00f3 trong vi\u1ec7c t\u1ed1i \u01b0u h\u00f3a c\u00e1c h\u00e0m ph\u1ee9c t\u1ea1p v\u1edbi nhi\u1ec1u bi\u1ebfn s\u1ed1, m\u1ed9t k\u1ecbch b\u1ea3n ph\u1ed5 bi\u1ebfn trong c\u00e1c l\u0129nh v\u1ef1c n\u00e0y.<\/p>\n

Ti\u1ebft l\u1ed9 chi ti\u1ebft: Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c ch\u00ednh x\u00e1c l\u00e0 g\u00ec?<\/h2>\n

Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c l\u00e0 m\u1ed9t thu\u1eadt to\u00e1n t\u1ed1i \u01b0u h\u00f3a \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3m thi\u1ec3u m\u1ed9t s\u1ed1 h\u00e0m b\u1eb1ng c\u00e1ch di chuy\u1ec3n l\u1eb7p \u0111i l\u1eb7p l\u1ea1i theo h\u01b0\u1edbng gi\u1ea3m d\u1ea7n d\u1ed1c nh\u1ea5t nh\u01b0 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi gi\u00e1 tr\u1ecb \u00e2m c\u1ee7a \u0111\u1ed9 d\u1ed1c c\u1ee7a h\u00e0m. N\u00f3i m\u1ed9t c\u00e1ch \u0111\u01a1n gi\u1ea3n h\u01a1n, thu\u1eadt to\u00e1n t\u00ednh to\u00e1n \u0111\u1ed9 d\u1ed1c (ho\u1eb7c \u0111\u1ed9 d\u1ed1c) c\u1ee7a h\u00e0m t\u1ea1i m\u1ed9t \u0111i\u1ec3m nh\u1ea5t \u0111\u1ecbnh, sau \u0111\u00f3 th\u1ef1c hi\u1ec7n m\u1ed9t b\u01b0\u1edbc theo h\u01b0\u1edbng m\u00e0 \u0111\u1ed9 d\u1ed1c gi\u1ea3m d\u1ea7n nhanh nh\u1ea5t.<\/p>\n

Thu\u1eadt to\u00e1n b\u1eaft \u0111\u1ea7u b\u1eb1ng d\u1ef1 \u0111o\u00e1n ban \u0111\u1ea7u v\u1ec1 m\u1ee9c t\u1ed1i thi\u1ec3u c\u1ee7a h\u00e0m. K\u00edch th\u01b0\u1edbc c\u1ee7a c\u00e1c b\u01b0\u1edbc c\u1ea7n th\u1ef1c hi\u1ec7n \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi m\u1ed9t tham s\u1ed1 g\u1ecdi l\u00e0 t\u1ed1c \u0111\u1ed9 h\u1ecdc. N\u1ebfu t\u1ed1c \u0111\u1ed9 h\u1ecdc qu\u00e1 l\u1edbn, thu\u1eadt to\u00e1n c\u00f3 th\u1ec3 v\u01b0\u1ee3t qua m\u1ee9c t\u1ed1i thi\u1ec3u, trong khi n\u1ebfu t\u1ed1c \u0111\u1ed9 h\u1ecdc qu\u00e1 nh\u1ecf, qu\u00e1 tr\u00ecnh t\u00ecm m\u1ee9c t\u1ed1i thi\u1ec3u s\u1ebd tr\u1edf n\u00ean r\u1ea5t ch\u1eadm.<\/p>\n

Ho\u1ea1t \u0111\u1ed9ng b\u00ean trong: C\u00e1ch v\u1eadn h\u00e0nh c\u1ee7a Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c<\/h2>\n

Thu\u1eadt to\u00e1n gi\u1ea3m \u0111\u1ed9 d\u1ed1c tu\u00e2n theo m\u1ed9t lo\u1ea1t c\u00e1c b\u01b0\u1edbc \u0111\u01a1n gi\u1ea3n:<\/p>\n

    \n
  1. Kh\u1edfi t\u1ea1o m\u1ed9t gi\u00e1 tr\u1ecb cho c\u00e1c tham s\u1ed1 c\u1ee7a h\u00e0m.<\/li>\n
  2. T\u00ednh chi ph\u00ed (ho\u1eb7c t\u1ed5n th\u1ea5t) c\u1ee7a h\u00e0m v\u1edbi c\u00e1c tham s\u1ed1 hi\u1ec7n t\u1ea1i.<\/li>\n
  3. T\u00ednh gradient c\u1ee7a h\u00e0m t\u1ea1i c\u00e1c tham s\u1ed1 hi\u1ec7n t\u1ea1i.<\/li>\n
  4. C\u1eadp nh\u1eadt c\u00e1c tham s\u1ed1 theo h\u01b0\u1edbng gradient \u00e2m.<\/li>\n
  5. L\u1eb7p l\u1ea1i c\u00e1c b\u01b0\u1edbc 2-4 cho \u0111\u1ebfn khi thu\u1eadt to\u00e1n h\u1ed9i t\u1ee5 v\u1ec1 m\u1ee9c t\u1ed1i thi\u1ec3u.<\/li>\n<\/ol>\n

    L\u00e0m n\u1ed5i b\u1eadt c\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c<\/h2>\n

    C\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a vi\u1ec7c gi\u1ea3m \u0111\u1ed9 d\u1ed1c bao g\u1ed3m:<\/p>\n

      \n
    1. \u0110\u1ed9 b\u1ec1n<\/strong>: N\u00f3 c\u00f3 th\u1ec3 x\u1eed l\u00fd c\u00e1c h\u00e0m c\u00f3 nhi\u1ec1u bi\u1ebfn, \u0111i\u1ec1u n\u00e0y l\u00e0m cho n\u00f3 ph\u00f9 h\u1ee3p v\u1edbi c\u00e1c v\u1ea5n \u0111\u1ec1 v\u1ec1 h\u1ecdc m\u00e1y v\u00e0 khoa h\u1ecdc d\u1eef li\u1ec7u.<\/li>\n
    2. Kh\u1ea3 n\u0103ng m\u1edf r\u1ed9ng<\/strong>: Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c c\u00f3 th\u1ec3 x\u1eed l\u00fd c\u00e1c t\u1eadp d\u1eef li\u1ec7u r\u1ea5t l\u1edbn b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng m\u1ed9t bi\u1ebfn th\u1ec3 c\u00f3 t\u00ean l\u00e0 Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c ng\u1eabu nhi\u00ean.<\/li>\n
    3. Uy\u1ec3n chuy\u1ec3n<\/strong>: Thu\u1eadt to\u00e1n c\u00f3 th\u1ec3 t\u00ecm c\u1ef1c ti\u1ec3u c\u1ee5c b\u1ed9 ho\u1eb7c c\u1ef1c ti\u1ec3u to\u00e0n c\u1ee5c, t\u00f9y thu\u1ed9c v\u00e0o h\u00e0m v\u00e0 \u0111i\u1ec3m kh\u1edfi t\u1ea1o.<\/li>\n<\/ol>\n

      C\u00e1c ki\u1ec3u gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c<\/h2>\n

      C\u00f3 ba lo\u1ea1i thu\u1eadt to\u00e1n gi\u1ea3m \u0111\u1ed9 d\u1ed1c ch\u00ednh, \u0111\u01b0\u1ee3c ph\u00e2n bi\u1ec7t b\u1eb1ng c\u00e1ch ch\u00fang s\u1eed d\u1ee5ng d\u1eef li\u1ec7u:<\/p>\n

        \n
      1. Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c h\u00e0ng lo\u1ea1t<\/strong>: D\u1ea1ng ban \u0111\u1ea7u, s\u1eed d\u1ee5ng to\u00e0n b\u1ed9 t\u1eadp d\u1eef li\u1ec7u \u0111\u1ec3 t\u00ednh to\u00e1n \u0111\u1ed9 d\u1ed1c \u1edf m\u1ed7i b\u01b0\u1edbc.<\/li>\n
      2. Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c ng\u1eabu nhi\u00ean (SGD)<\/strong>: Thay v\u00ec s\u1eed d\u1ee5ng t\u1ea5t c\u1ea3 d\u1eef li\u1ec7u cho t\u1eebng b\u01b0\u1edbc, SGD s\u1eed d\u1ee5ng m\u1ed9t \u0111i\u1ec3m d\u1eef li\u1ec7u ng\u1eabu nhi\u00ean.<\/li>\n
      3. Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c h\u00e0ng lo\u1ea1t nh\u1ecf<\/strong>: S\u1ef1 th\u1ecfa hi\u1ec7p gi\u1eefa Batch v\u00e0 SGD, Mini-Batch s\u1eed d\u1ee5ng m\u1ed9t t\u1eadp h\u1ee3p con d\u1eef li\u1ec7u cho m\u1ed7i b\u01b0\u1edbc.<\/li>\n<\/ol>\n

        \u00c1p d\u1ee5ng gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c: C\u00e1c v\u1ea5n \u0111\u1ec1 v\u00e0 gi\u1ea3i ph\u00e1p<\/h2>\n

        Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong h\u1ecdc m\u00e1y cho c\u00e1c t\u00e1c v\u1ee5 nh\u01b0 h\u1ed3i quy tuy\u1ebfn t\u00ednh, h\u1ed3i quy logistic v\u00e0 m\u1ea1ng l\u01b0\u1edbi th\u1ea7n kinh. Tuy nhi\u00ean, c\u00f3 m\u1ed9t s\u1ed1 v\u1ea5n \u0111\u1ec1 c\u00f3 th\u1ec3 ph\u00e1t sinh:<\/p>\n

          \n
        1. T\u1ed1i thi\u1ec3u \u0111\u1ecba ph\u01b0\u01a1ng<\/strong>: Thu\u1eadt to\u00e1n c\u00f3 th\u1ec3 b\u1ecb k\u1eb9t \u1edf m\u1ee9c t\u1ed1i thi\u1ec3u c\u1ee5c b\u1ed9 khi t\u1ed3n t\u1ea1i m\u1ee9c t\u1ed1i thi\u1ec3u to\u00e0n c\u1ea7u. Gi\u1ea3i ph\u00e1p: kh\u1edfi t\u1ea1o nhi\u1ec1u l\u1ea7n c\u00f3 th\u1ec3 gi\u00fap kh\u1eafc ph\u1ee5c v\u1ea5n \u0111\u1ec1 n\u00e0y.<\/li>\n
        2. H\u1ed9i t\u1ee5 ch\u1eadm<\/strong>: N\u1ebfu t\u1ed1c \u0111\u1ed9 h\u1ecdc qu\u00e1 nh\u1ecf, thu\u1eadt to\u00e1n c\u00f3 th\u1ec3 r\u1ea5t ch\u1eadm. Gi\u1ea3i ph\u00e1p: t\u1ed1c \u0111\u1ed9 h\u1ecdc th\u00edch \u1ee9ng c\u00f3 th\u1ec3 gi\u00fap t\u0103ng t\u1ed1c \u0111\u1ed9 h\u1ed9i t\u1ee5.<\/li>\n
        3. V\u01b0\u1ee3t qu\u00e1<\/strong>: N\u1ebfu t\u1ed1c \u0111\u1ed9 h\u1ecdc qu\u00e1 l\u1edbn, thu\u1eadt to\u00e1n c\u00f3 th\u1ec3 b\u1ecf l\u1ee1 m\u1ee9c t\u1ed1i thi\u1ec3u. Gi\u1ea3i ph\u00e1p: m\u1ed9t l\u1ea7n n\u1eefa, t\u1ed1c \u0111\u1ed9 h\u1ecdc t\u1eadp th\u00edch \u1ee9ng l\u00e0 m\u1ed9t bi\u1ec7n ph\u00e1p \u0111\u1ed1i ph\u00f3 t\u1ed1t.<\/li>\n<\/ol>\n

          So s\u00e1nh v\u1edbi c\u00e1c thu\u1eadt to\u00e1n t\u1ed1i \u01b0u h\u00f3a t\u01b0\u01a1ng t\u1ef1<\/h2>\n\n\n\n\n\n\n\n\n
          Thu\u1eadt to\u00e1n<\/th>\nT\u1ed1c \u0111\u1ed9<\/th>\nR\u1ee7i ro t\u1ed1i thi\u1ec3u c\u1ee5c b\u1ed9<\/th>\nT\u00ednh to\u00e1n chuy\u00ean s\u00e2u<\/th>\n<\/tr>\n<\/thead>\n
          Xu\u1ed1ng d\u1ed1c<\/td>\nTrung b\u00ecnh<\/td>\nCao<\/td>\n\u0110\u00fang<\/td>\n<\/tr>\n
          Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c ng\u1eabu nhi\u00ean<\/td>\nNhanh<\/td>\nTh\u1ea5p<\/td>\nKH\u00d4NG<\/td>\n<\/tr>\n
          Ph\u01b0\u01a1ng ph\u00e1p Newton<\/td>\nCh\u1eadm<\/td>\nTh\u1ea5p<\/td>\n\u0110\u00fang<\/td>\n<\/tr>\n
          Thu\u1eadt to\u00e1n di truy\u1ec1n<\/td>\nBi\u1ebfn \u0111\u1ed5i<\/td>\nTh\u1ea5p<\/td>\n\u0110\u00fang<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          Tri\u1ec3n v\u1ecdng t\u01b0\u01a1ng lai v\u00e0 s\u1ef1 ph\u00e1t tri\u1ec3n c\u00f4ng ngh\u1ec7<\/h2>\n

          Thu\u1eadt to\u00e1n gi\u1ea3m \u0111\u1ed9 d\u1ed1c \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong h\u1ecdc m\u00e1y, nh\u01b0ng nh\u1eefng ti\u1ebfn b\u1ed9 c\u00f4ng ngh\u1ec7 v\u00e0 nghi\u00ean c\u1ee9u \u0111ang di\u1ec5n ra h\u1ee9a h\u1eb9n s\u1ebd c\u00f2n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng nhi\u1ec1u h\u01a1n n\u1eefa. S\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a \u0111i\u1ec7n to\u00e1n l\u01b0\u1ee3ng t\u1eed c\u00f3 kh\u1ea3 n\u0103ng c\u00e1ch m\u1ea1ng h\u00f3a hi\u1ec7u qu\u1ea3 c\u1ee7a c\u00e1c thu\u1eadt to\u00e1n gi\u1ea3m \u0111\u1ed9 d\u1ed1c v\u00e0 c\u00e1c bi\u1ebfn th\u1ec3 n\u00e2ng cao li\u00ean t\u1ee5c \u0111\u01b0\u1ee3c ph\u00e1t tri\u1ec3n \u0111\u1ec3 c\u1ea3i thi\u1ec7n hi\u1ec7u qu\u1ea3 v\u00e0 tr\u00e1nh c\u00e1c c\u1ef1c ti\u1ec3u c\u1ee5c b\u1ed9.<\/p>\n

          S\u1ef1 giao nhau c\u1ee7a m\u00e1y ch\u1ee7 proxy v\u00e0 \u0111\u1ed9 d\u1ed1c gi\u1ea3m d\u1ea7n<\/h2>\n

          M\u1eb7c d\u00f9 gradient Descent th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong khoa h\u1ecdc d\u1eef li\u1ec7u v\u00e0 h\u1ecdc m\u00e1y nh\u01b0ng n\u00f3 kh\u00f4ng th\u1ec3 \u00e1p d\u1ee5ng tr\u1ef1c ti\u1ebfp cho ho\u1ea1t \u0111\u1ed9ng c\u1ee7a m\u00e1y ch\u1ee7 proxy. Tuy nhi\u00ean, m\u00e1y ch\u1ee7 proxy th\u01b0\u1eddng l\u00e0 m\u1ed9t ph\u1ea7n c\u1ee7a vi\u1ec7c thu th\u1eadp d\u1eef li\u1ec7u cho m\u00e1y h\u1ecdc, n\u01a1i c\u00e1c nh\u00e0 khoa h\u1ecdc d\u1eef li\u1ec7u thu th\u1eadp d\u1eef li\u1ec7u t\u1eeb nhi\u1ec1u ngu\u1ed3n kh\u00e1c nhau trong khi v\u1eabn duy tr\u00ec t\u00ednh \u1ea9n danh c\u1ee7a ng\u01b0\u1eddi d\u00f9ng. Trong nh\u1eefng tr\u01b0\u1eddng h\u1ee3p n\u00e0y, d\u1eef li\u1ec7u \u0111\u01b0\u1ee3c thu th\u1eadp c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u1ed1i \u01b0u h\u00f3a b\u1eb1ng thu\u1eadt to\u00e1n gi\u1ea3m \u0111\u1ed9 d\u1ed1c.<\/p>\n

          Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n

          \u0110\u1ec3 bi\u1ebft th\u00eam th\u00f4ng tin v\u1ec1 Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c, b\u1ea1n c\u00f3 th\u1ec3 truy c\u1eadp c\u00e1c t\u00e0i nguy\u00ean sau:<\/p>\n

            \n
          1. Gi\u1ea3m d\u1ea7n \u0111\u1ed9 d\u1ed1c t\u1eeb \u0111\u1ea7u<\/a> \u2013 H\u01b0\u1edbng d\u1eabn to\u00e0n di\u1ec7n v\u1ec1 c\u00e1ch th\u1ef1c hi\u1ec7n gi\u1ea3m \u0111\u1ed9 d\u1ed1c.<\/li>\n
          2. T\u00ecm hi\u1ec3u to\u00e1n h\u1ecdc v\u1ec1 \u0111\u1ed9 d\u1ed1c gi\u1ea3m d\u1ea7n<\/a> \u2013 M\u1ed9t kh\u00e1m ph\u00e1 to\u00e1n h\u1ecdc chi ti\u1ebft v\u1ec1 \u0111\u1ed9 d\u1ed1c gi\u1ea3m d\u1ea7n.<\/li>\n
          3. SGDRegressor c\u1ee7a Scikit-Learn<\/a> \u2013 \u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a Stochastic gradient Descent trong th\u01b0 vi\u1ec7n Scikit-Learn c\u1ee7a Python.<\/li>\n<\/ol>","protected":false},"featured_media":468485,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-477370","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about Gradient Descent: The Core of Optimizing Complex Functions<\/mark>","faq_items":[{"question":"What is Gradient Descent?","answer":"

            Gradient Descent is an optimization algorithm used to find the minimum of a function. It is often used in machine learning and data science to optimize complex functions that are difficult or impossible to solve analytically.<\/p>"},{"question":"When was Gradient Descent first mentioned?","answer":"

            The concept of gradient descent, rooted in calculus, was first described formally in a publication by the American Institute of Mathematical Sciences in 1847.<\/p>"},{"question":"How does Gradient Descent work?","answer":"

            Gradient Descent works by taking iterative steps in the direction of the steepest descent of a function. It starts with an initial guess for the minimum of the function, computes the gradient of the function at that point, and then takes a step in the direction where the gradient is descending most rapidly.<\/p>"},{"question":"What are the key features of Gradient Descent?","answer":"

            The key features of Gradient Descent include its robustness (it can handle functions with many variables), scalability (it can deal with large datasets using a variant called Stochastic Gradient Descent), and flexibility (it can find either local or global minima, depending on the function and initialization point).<\/p>"},{"question":"What types of Gradient Descent exist?","answer":"

            Three main types of gradient descent algorithms exist: Batch Gradient Descent, which uses the entire dataset to compute the gradient at each step; Stochastic Gradient Descent (SGD), which uses one random data point at each step; and Mini-Batch Gradient Descent, which uses a subset of the data at each step.<\/p>"},{"question":"Where is Gradient Descent used and what problems can arise?","answer":"

            Gradient Descent is commonly used in machine learning for tasks like linear regression, logistic regression, and neural networks. However, issues can arise, such as getting stuck in local minima, slow convergence if the learning rate is too small, or overshooting the minimum if the learning rate is too large.<\/p>"},{"question":"How does Gradient Descent compare to other optimization algorithms?","answer":"

            Gradient Descent is generally more robust than other methods like Newton's Method and Genetic Algorithms but can risk getting stuck in local minima and can be computationally intensive. Stochastic Gradient Descent mitigates some of these issues by being faster and less likely to get stuck in local minima.<\/p>"},{"question":"What are the future prospects for Gradient Descent?","answer":"

            Ongoing research and technological advancements, including the development of quantum computing, promise even greater utilization of gradient descent. Advanced variants are continually being developed to improve efficiency and avoid local minima.<\/p>"},{"question":"How can Gradient Descent be associated with proxy servers?","answer":"

            While Gradient Descent is not directly applicable to the operations of proxy servers, proxy servers often form part of data collection for machine learning. In these scenarios, the collected data might be optimized using gradient descent algorithms.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/477370","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/477370\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/468485"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=477370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}