MinMax4NI_OneRun.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b677a86b-802b-49c1-a8bd-73ae655eb687",
   "metadata": {},
   "source": [
    "## Example 2b: Nonconvex Minimax Problem with Constraints.\n",
    "We consider the following possibly nonconvex-nonconcave minimax problem:\n",
    "\\begin{equation}\n",
    "\\min_{u \\in \\mathbb{R}^{p_1}}\\max_{v\\in\\mathbb{R}^{p_2}}\\Big\\{ \\mathcal{L}(u,v) = f(u) + \\frac{1}{n}\\sum_{i=1}^n\\big[u^{\\top}A_iu + u^{\\top}L_iv - v^{\\top}B_iv + b_i^{\\top}u - c_i^{\\top}v\\big] - g(v) \\Big\\},\n",
    "\\end{equation}\n",
    "where $A_i \\in\\mathbb{R}^{p_1\\times p_1}$ and $B_i \\in \\mathbb{R}^{p_2\\times p_2}$ are symmetric matrices, $b_i\\in\\mathbb{R}^{p_1}$, $c_i \\in \\mathbb{R}^{p_2}$, and $L_i \\in \\mathbb{R}^{p_1\\times p_2}$ is a given matrix.\n",
    "Here, we add two terms $f(u)$ and $g(v)$ to possibly handle constraints or regularizers associated with $u$ and $v$, respectively.\n",
    "\n",
    "In this experiment, we consider the case where $f(u) = \\delta_{\\Delta_{p_1}}(u)$ is the indicator of the standard simplex in $\\mathbb{R}^{p_1}$, and $g(v) = \\delta_{\\Delta_{p_2}}(v)$ is the indicator of the standard simplex in $\\mathbb{R}^{p_2}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "32cb27db-072b-4b4c-a74f-c3190fb29a8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import linalg as la\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import scipy as sci\n",
    "import solvers.ni_solvers as solver\n",
    "import solvers.ami_solvers as acc_solver"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b0cab44-c08d-43a6-8d9c-43668d164e4f",
   "metadata": {},
   "source": [
    "## Resolvent operators\n",
    "Define the resovent operator of $T = [\\partial{f}, \\partial{g}]$, where $f$ and $g$ are the indicators of the standard simplexes in $\\mathbb{R}^{p_1}$ and $\\mathbb{R}^{p_2}$, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "1bc15e88-c2ac-44f0-8419-cbe0bb8a0977",
   "metadata": {},
   "outputs": [],
   "source": [
    "def projection_on_simplex(u, s=1):\n",
    "    n_u   = u.shape[0]\n",
    "    us    = np.sort(u)[::-1]\n",
    "    cssv  = np.cumsum(us) - s\n",
    "    ind   = np.arange(n_u) + 1\n",
    "    cond  = us - cssv / ind > 0\n",
    "    rho   = ind[cond][-1]\n",
    "    theta = cssv[cond][-1] / float(rho)\n",
    "    return np.maximum(u - theta, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "38b3bfec-f6d9-4fa1-b941-a0071168ebf5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def J_op_eval(data, x, eta):\n",
    "    p1, p2 = data.get(\"p1\"), data.get(\"p2\")\n",
    "    u, v   = x[0:p1], x[p1:p1+p2]\n",
    "    u_p    = projection_on_simplex(u)\n",
    "    v_p    = projection_on_simplex(v)\n",
    "    return np.concatenate((u_p, v_p), axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e13801fe-7f6b-48d6-8aba-bc627bec58db",
   "metadata": {},
   "source": [
    "## Linear Operator $G(x)$\n",
    "Define the perator $G(x) := [Au + Lv + b, -L^{\\top}u + Bv + c]$ for our experiments, where $A := \\frac{1}{n}\\sum_{i=1}^nA_i$, $B := \\frac{1}{n}\\sum_{i=1}^nB_i$, $L := \\frac{1}{n}\\sum_{i=1}^nL_i$, $b := \\frac{1}{n}\\sum_{i=1}^nb_i$, and $c := \\frac{1}{n}\\sum_{i=1}^nc_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "2730b330-8391-410d-a607-ccb231edd706",
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "-- Define the operator G for our methods\n",
    "-- Inputs: data, x=x(k), mb_id=the indices of minibatch-size, mb_size=the size of mini-batch.\n",
    "-- Output: G(x).\n",
    "\"\"\"\n",
    "def G_op_eval(data, x, mb_id, mb_size):\n",
    "    K = data.get(\"K\")\n",
    "    b = data.get(\"b\")\n",
    "    return np.mean([K[i].dot(x) + b[i] for i in mb_id], axis=0)\n",
    "\"\"\"\n",
    "-- Define the operator G and also output the output components.\n",
    "\"\"\"\n",
    "def Gb_op_eval(data, x, mb_id, mb_size):\n",
    "    K   = data.get(\"K\")\n",
    "    b   = data.get(\"b\")\n",
    "    y_b = [K[i].dot(x) + b[i] for i in mb_id]\n",
    "    return np.mean(y_b, axis=0), y_b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c625072a-3c5a-415d-87ee-3e846fc5c4bc",
   "metadata": {},
   "source": [
    "## Synthetic Data\n",
    "We generate a synthetic data to test all algorithms. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "5202b1f1-b490-4f0e-b741-e0d5ce841399",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The Lipschitz constant: 0.5410093837361933\n"
     ]
    }
   ],
   "source": [
    "## the size of data\n",
    "n, p = 5000, 100\n",
    "\n",
    "# generate a symmetric matrix.\n",
    "p1 = int(p/2)\n",
    "p2 = p-p1\n",
    "K, b = [], []\n",
    "K_sum = []\n",
    "eig_min = -0.0\n",
    "\n",
    "#eig_min = -0.01 # default value\n",
    "for i in range(n):\n",
    "    # Generate KKT matrix\n",
    "    D1  = np.maximum(np.diag(np.random.randn(p1)), eig_min)\n",
    "    #D1  = D1/np.sum(D1, axis=1, keepdims=True)\n",
    "    Q1, _ = la.qr(np.random.randn(p1, p1))\n",
    "    Ai = np.matmul(np.matmul(Q1, D1), Q1.T)\n",
    "    \n",
    "    D2  = np.maximum(np.diag(np.random.randn(p2)), eig_min)\n",
    "    #D2  = D2/np.sum(D2, axis=1, keepdims=True)\n",
    "    Q2, _ = la.qr(np.random.randn(p2, p2))\n",
    "    Bi = np.matmul(np.matmul(Q2, D2), Q2.T)\n",
    "    \n",
    "    Li = np.random.randn(p1,p2)\n",
    "    #Li = Li/np.sum(Li, axis=1, keepdims=True)\n",
    "    \n",
    "    Ki = np.block([[Ai,  Li], [-Li, Bi]])\n",
    "    ##Ki = Ki/np.sum(Ki, axis=1, keepdims=True)\n",
    "    ##Ki = Ki/la.norm(Ki, ord=2)\n",
    "\n",
    "    \"\"\"\n",
    "    ## generate Ki\n",
    "    D   = np.maximum(np.diag(np.random.randn(p)), -0.01)\n",
    "    Q, _ = la.qr(np.random.randn(p, p))\n",
    "    Ki = np.matmul(np.matmul(Q, D), Q.T)\n",
    "    \"\"\"\n",
    "    \n",
    "    # generate bi.\n",
    "    bi = np.random.randn(p)\n",
    "    #bi = bi/np.sum(bi)\n",
    "    \n",
    "    K.append(Ki)\n",
    "    b.append(bi)\n",
    "    if i==0:\n",
    "        K_sum = Ki\n",
    "    else:\n",
    "        K_sum = K_sum + Ki\n",
    "K_sum = (1/n)*K_sum\n",
    "Lips = la.norm(K_sum, ord=2)    \n",
    "my_data = dict({\"K\": K, \"b\": b, \"n\": n, \"p\": p, \"p1\": p1, \"p2\": p2, \"L\": Lips})\n",
    "print(\"The Lipschitz constant:\", Lips)\n",
    "\n",
    "## general an initial point.\n",
    "x0 = np.random.randn(p)\n",
    "\n",
    "## set default parameters\n",
    "def_gamma = 0.75\n",
    "def_lr    = 0.5\n",
    "def_max_iters = 10000\n",
    "def_tol   = 1e-100\n",
    "def_n_max_epochs = 100\n",
    "def_mb_size = int(n**0.67)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42cf3bef-c019-4eb6-991e-f802aed903f9",
   "metadata": {},
   "source": [
    "## Set default parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "142cff96-80ca-4ff6-9d88-f92e3702a74c",
   "metadata": {},
   "outputs": [],
   "source": [
    "## set default parameters\n",
    "def_gamma        = 0.75\n",
    "def_lr           = 0.5\n",
    "def_max_iters    = 10000\n",
    "def_tol          = 1e-100\n",
    "def_n_max_epochs = 100\n",
    "def_mb_size      = 100 #int(n**0.67)\n",
    "my_is_term       = False ## using termination condition or not.\n",
    "my_verbose       = 1 # print output\n",
    "output_all       = []\n",
    "n_number_of_algs = 7"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ac76087-86b8-43c3-b10b-39ca95b0ae22",
   "metadata": {},
   "source": [
    "## Test all algorithms\n",
    "Now, we test all the algorithms implmented above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "defe9b5e-dd0d-4094-992e-f04fa731e491",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solver: Optimistic Gradient Method for Monotone Inclusions ...\n",
      "========================================== \n",
      "  Epoch  |     Error     | ||G_eta(x)||  \n",
      " ------------------------------------------\n",
      "   0     |   8.886e+00   |   1.000e+00   |\n",
      "   1     |   1.760e-01   |   3.596e-02   |\n",
      "   2     |   1.364e-01   |   3.268e-02   |\n",
      "   3     |   9.753e-02   |   2.722e-02   |\n",
      "   4     |   8.584e-02   |   2.326e-02   |\n",
      "   5     |   7.246e-02   |   1.973e-02   |\n",
      "   6     |   6.184e-02   |   1.679e-02   |\n",
      "   7     |   5.263e-02   |   1.431e-02   |\n",
      "   8     |   4.493e-02   |   1.212e-02   |\n",
      "   9     |   3.839e-02   |   1.004e-02   |\n",
      "   10    |   3.189e-02   |   8.406e-03   |\n",
      "   11    |   2.653e-02   |   7.069e-03   |\n",
      "   12    |   2.245e-02   |   6.000e-03   |\n",
      "   13    |   1.903e-02   |   5.131e-03   |\n",
      "   14    |   1.632e-02   |   4.400e-03   |\n",
      "   15    |   1.402e-02   |   3.769e-03   |\n",
      "   16    |   1.200e-02   |   3.178e-03   |\n",
      "   17    |   1.031e-02   |   2.510e-03   |\n",
      "   18    |   8.000e-03   |   2.030e-03   |\n",
      "   19    |   6.427e-03   |   1.725e-03   |\n",
      "   20    |   5.502e-03   |   1.481e-03   |\n",
      "   21    |   4.739e-03   |   1.273e-03   |\n",
      "   22    |   4.080e-03   |   1.095e-03   |\n",
      "   23    |   3.516e-03   |   9.429e-04   |\n",
      "   24    |   3.032e-03   |   8.123e-04   |\n",
      "   25    |   2.617e-03   |   7.003e-04   |\n",
      "   26    |   2.260e-03   |   6.042e-04   |\n",
      "   27    |   1.952e-03   |   5.216e-04   |\n",
      "   28    |   1.688e-03   |   4.506e-04   |\n",
      "   29    |   1.460e-03   |   3.895e-04   |\n",
      "   30    |   1.264e-03   |   3.369e-04   |\n",
      "   31    |   1.095e-03   |   2.915e-04   |\n",
      "   32    |   9.487e-04   |   2.524e-04   |\n",
      "   33    |   8.225e-04   |   2.187e-04   |\n",
      "   34    |   7.134e-04   |   1.896e-04   |\n",
      "   35    |   6.191e-04   |   1.644e-04   |\n",
      "   36    |   5.375e-04   |   1.426e-04   |\n",
      "   37    |   4.669e-04   |   1.238e-04   |\n",
      "   38    |   4.057e-04   |   1.075e-04   |\n",
      "   39    |   3.527e-04   |   9.342e-05   |\n",
      "   40    |   3.067e-04   |   8.120e-05   |\n",
      "   41    |   2.668e-04   |   7.060e-05   |\n",
      "   42    |   2.322e-04   |   6.141e-05   |\n",
      "   43    |   2.021e-04   |   5.344e-05   |\n",
      "   44    |   1.760e-04   |   4.651e-05   |\n",
      "   45    |   1.533e-04   |   4.050e-05   |\n",
      "   46    |   1.336e-04   |   3.528e-05   |\n",
      "   47    |   1.164e-04   |   3.073e-05   |\n",
      "   48    |   1.015e-04   |   2.678e-05   |\n",
      "   49    |   8.852e-05   |   2.335e-05   |\n",
      "   50    |   7.721e-05   |   2.036e-05   |\n",
      "   51    |   6.737e-05   |   1.776e-05   |\n",
      "   52    |   5.878e-05   |   1.549e-05   |\n",
      "   53    |   5.131e-05   |   1.352e-05   |\n",
      "   54    |   4.479e-05   |   1.180e-05   |\n",
      "   55    |   3.911e-05   |   1.030e-05   |\n",
      "   56    |   3.415e-05   |   8.990e-06   |\n",
      "   57    |   2.983e-05   |   7.850e-06   |\n",
      "   58    |   2.606e-05   |   6.856e-06   |\n",
      "   59    |   2.277e-05   |   5.989e-06   |\n",
      "   60    |   1.989e-05   |   5.232e-06   |\n",
      "   61    |   1.739e-05   |   4.572e-06   |\n",
      "   62    |   1.520e-05   |   3.995e-06   |\n",
      "   63    |   1.328e-05   |   3.492e-06   |\n",
      "   64    |   1.161e-05   |   3.052e-06   |\n",
      "   65    |   1.015e-05   |   2.668e-06   |\n",
      "   66    |   8.876e-06   |   2.332e-06   |\n",
      "   67    |   7.761e-06   |   2.039e-06   |\n",
      "   68    |   6.787e-06   |   1.783e-06   |\n",
      "   69    |   5.936e-06   |   1.559e-06   |\n",
      "   70    |   5.191e-06   |   1.364e-06   |\n",
      "   71    |   4.540e-06   |   1.193e-06   |\n",
      "   72    |   3.971e-06   |   1.043e-06   |\n",
      "   73    |   3.474e-06   |   9.123e-07   |\n",
      "   74    |   3.039e-06   |   7.980e-07   |\n",
      "   75    |   2.658e-06   |   6.980e-07   |\n",
      "   76    |   2.325e-06   |   6.106e-07   |\n",
      "   77    |   2.034e-06   |   5.342e-07   |\n",
      "   78    |   1.780e-06   |   4.673e-07   |\n",
      "   79    |   1.557e-06   |   4.088e-07   |\n",
      "   80    |   1.362e-06   |   3.576e-07   |\n",
      "   81    |   1.192e-06   |   3.129e-07   |\n",
      "   82    |   1.042e-06   |   2.737e-07   |\n",
      "   83    |   9.120e-07   |   2.395e-07   |\n",
      "   84    |   7.979e-07   |   2.095e-07   |\n",
      "   85    |   6.980e-07   |   1.833e-07   |\n",
      "   86    |   6.107e-07   |   1.603e-07   |\n",
      "   87    |   5.342e-07   |   1.403e-07   |\n",
      "   88    |   4.674e-07   |   1.227e-07   |\n",
      "   89    |   4.089e-07   |   1.074e-07   |\n",
      "   90    |   3.577e-07   |   9.392e-08   |\n",
      "   91    |   3.129e-07   |   8.216e-08   |\n",
      "   92    |   2.737e-07   |   7.187e-08   |\n",
      "   93    |   2.394e-07   |   6.287e-08   |\n",
      "   94    |   2.094e-07   |   5.500e-08   |\n",
      "   95    |   1.832e-07   |   4.811e-08   |\n",
      "   96    |   1.602e-07   |   4.208e-08   |\n",
      "   97    |   1.402e-07   |   3.681e-08   |\n",
      "   98    |   1.226e-07   |   3.220e-08   |\n",
      "   99    |   1.072e-07   |   2.816e-08   |\n",
      "========================================== \n",
      "\n",
      "Solver status (OG):      Exceed the maximum number of epochs. Increase it to run further ...\n",
      "Solver: Accelerated Optimistic Gradient Method for Monotone Inclusions ...\n",
      "========================================== \n",
      "  Epoch  |     Error     |   ||G(x)||    \n",
      " ------------------------------------------\n",
      "   0     |   7.049e+00   |   1.000e+00   |\n",
      "   1     |   1.516e+00   |   2.315e-01   |\n",
      "   2     |   4.332e-01   |   6.958e-02   |\n",
      "   3     |   1.697e-01   |   2.731e-02   |\n",
      "   4     |   8.147e-02   |   1.288e-02   |\n",
      "   5     |   3.987e-02   |   6.332e-03   |\n",
      "   6     |   1.978e-02   |   3.200e-03   |\n",
      "   7     |   1.031e-02   |   1.699e-03   |\n",
      "   8     |   5.520e-03   |   9.322e-04   |\n",
      "   9     |   3.058e-03   |   5.292e-04   |\n",
      "   10    |   1.751e-03   |   3.104e-04   |\n",
      "   11    |   1.027e-03   |   1.868e-04   |\n",
      "   12    |   6.165e-04   |   1.150e-04   |\n",
      "   13    |   3.776e-04   |   7.230e-05   |\n",
      "   14    |   2.357e-04   |   4.634e-05   |\n",
      "   15    |   1.498e-04   |   3.024e-05   |\n",
      "   16    |   9.671e-05   |   2.006e-05   |\n",
      "   17    |   6.339e-05   |   1.351e-05   |\n",
      "   18    |   4.216e-05   |   9.225e-06   |\n",
      "   19    |   2.842e-05   |   6.385e-06   |\n",
      "   20    |   1.940e-05   |   4.475e-06   |\n",
      "   21    |   1.341e-05   |   3.174e-06   |\n",
      "   22    |   9.377e-06   |   2.276e-06   |\n",
      "   23    |   6.627e-06   |   1.649e-06   |\n",
      "   24    |   4.732e-06   |   1.207e-06   |\n",
      "   25    |   3.412e-06   |   8.911e-07   |\n",
      "   26    |   2.482e-06   |   6.639e-07   |\n",
      "   27    |   1.822e-06   |   4.987e-07   |\n",
      "   28    |   1.349e-06   |   3.776e-07   |\n",
      "   29    |   1.006e-06   |   2.880e-07   |\n",
      "   30    |   7.560e-07   |   2.212e-07   |\n",
      "   31    |   5.722e-07   |   1.711e-07   |\n",
      "   32    |   4.360e-07   |   1.331e-07   |\n",
      "   33    |   3.344e-07   |   1.042e-07   |\n",
      "   34    |   2.581e-07   |   8.208e-08   |\n",
      "   35    |   2.003e-07   |   6.500e-08   |\n",
      "   36    |   1.564e-07   |   5.174e-08   |\n",
      "   37    |   1.228e-07   |   4.140e-08   |\n",
      "   38    |   9.685e-08   |   3.328e-08   |\n",
      "   39    |   7.679e-08   |   2.688e-08   |\n",
      "   40    |   6.117e-08   |   2.181e-08   |\n",
      "   41    |   4.896e-08   |   1.777e-08   |\n",
      "   42    |   3.935e-08   |   1.454e-08   |\n",
      "   43    |   3.177e-08   |   1.194e-08   |\n",
      "   44    |   2.575e-08   |   9.844e-09   |\n",
      "   45    |   2.095e-08   |   8.145e-09   |\n",
      "   46    |   1.711e-08   |   6.763e-09   |\n",
      "   47    |   1.403e-08   |   5.635e-09   |\n",
      "   48    |   1.154e-08   |   4.710e-09   |\n",
      "   49    |   9.525e-09   |   3.950e-09   |\n",
      "   50    |   7.888e-09   |   3.322e-09   |\n",
      "   51    |   6.553e-09   |   2.802e-09   |\n",
      "   52    |   5.461e-09   |   2.370e-09   |\n",
      "   53    |   4.564e-09   |   2.011e-09   |\n",
      "   54    |   3.825e-09   |   1.710e-09   |\n",
      "   55    |   3.215e-09   |   1.458e-09   |\n",
      "   56    |   2.710e-09   |   1.247e-09   |\n",
      "   57    |   2.290e-09   |   1.068e-09   |\n",
      "   58    |   1.940e-09   |   9.174e-10   |\n",
      "   59    |   1.647e-09   |   7.898e-10   |\n",
      "   60    |   1.402e-09   |   6.814e-10   |\n",
      "   61    |   1.196e-09   |   5.892e-10   |\n",
      "   62    |   1.023e-09   |   5.105e-10   |\n",
      "   63    |   8.768e-10   |   4.432e-10   |\n",
      "   64    |   7.530e-10   |   3.855e-10   |\n",
      "   65    |   6.480e-10   |   3.360e-10   |\n",
      "   66    |   5.589e-10   |   2.934e-10   |\n",
      "   67    |   4.829e-10   |   2.566e-10   |\n",
      "   68    |   4.180e-10   |   2.249e-10   |\n",
      "   69    |   3.626e-10   |   1.974e-10   |\n",
      "   70    |   3.150e-10   |   1.736e-10   |\n",
      "   71    |   2.742e-10   |   1.529e-10   |\n",
      "   72    |   2.391e-10   |   1.349e-10   |\n",
      "   73    |   2.088e-10   |   1.191e-10   |\n",
      "   74    |   1.827e-10   |   1.054e-10   |\n",
      "   75    |   1.601e-10   |   9.342e-11   |\n",
      "   76    |   1.405e-10   |   8.290e-11   |\n",
      "   77    |   1.235e-10   |   7.367e-11   |\n",
      "   78    |   1.087e-10   |   6.556e-11   |\n",
      "   79    |   9.583e-11   |   5.842e-11   |\n",
      "   80    |   8.460e-11   |   5.212e-11   |\n",
      "   81    |   7.479e-11   |   4.657e-11   |\n",
      "   82    |   6.621e-11   |   4.166e-11   |\n",
      "   83    |   5.869e-11   |   3.731e-11   |\n",
      "   84    |   5.210e-11   |   3.345e-11   |\n",
      "   85    |   4.630e-11   |   3.003e-11   |\n",
      "   86    |   4.120e-11   |   2.699e-11   |\n",
      "   87    |   3.671e-11   |   2.429e-11   |\n",
      "   88    |   3.274e-11   |   2.188e-11   |\n",
      "   89    |   2.924e-11   |   1.973e-11   |\n",
      "   90    |   2.614e-11   |   1.781e-11   |\n",
      "   91    |   2.340e-11   |   1.609e-11   |\n",
      "   92    |   2.097e-11   |   1.456e-11   |\n",
      "   93    |   1.881e-11   |   1.318e-11   |\n",
      "   94    |   1.689e-11   |   1.195e-11   |\n",
      "   95    |   1.518e-11   |   1.084e-11   |\n",
      "   96    |   1.366e-11   |   9.843e-12   |\n",
      "   97    |   1.231e-11   |   8.947e-12   |\n",
      "   98    |   1.110e-11   |   8.139e-12   |\n",
      "   99    |   1.002e-11   |   7.411e-12   |\n",
      "========================================== \n",
      "\n",
      "Solver status (AOG):     Exceed the maximum number of epochs. Increase it to run further ...\n",
      "Solver: SAGA-Root-Finding Algorithm for Monotone Inclusions ...\n",
      "========================================== \n",
      "  Iters  |     Error     |   ||G(x)||    \n",
      " ------------------------------------------\n",
      "   1     |   4.582e+00   |   1.000e+00   |\n",
      "   2     |   3.125e-01   |   6.820e-02   |\n",
      "   3     |   2.713e-01   |   5.921e-02   |\n",
      "   4     |   1.990e-01   |   4.343e-02   |\n",
      "   5     |   1.295e-01   |   2.827e-02   |\n",
      "   6     |   9.141e-02   |   1.995e-02   |\n",
      "   7     |   6.171e-02   |   1.347e-02   |\n",
      "   8     |   5.219e-02   |   1.139e-02   |\n",
      "   9     |   3.600e-02   |   7.857e-03   |\n",
      "   10    |   2.193e-02   |   4.786e-03   |\n",
      "   11    |   1.907e-02   |   4.163e-03   |\n",
      "   12    |   1.583e-02   |   3.456e-03   |\n",
      "   13    |   9.500e-03   |   2.074e-03   |\n",
      "   14    |   6.108e-03   |   1.333e-03   |\n",
      "   15    |   5.146e-03   |   1.123e-03   |\n",
      "   16    |   3.398e-03   |   7.417e-04   |\n",
      "   17    |   2.238e-03   |   4.886e-04   |\n",
      "   18    |   1.708e-03   |   3.728e-04   |\n",
      "   19    |   1.439e-03   |   3.142e-04   |\n",
      "   20    |   9.904e-04   |   2.162e-04   |\n",
      "   21    |   6.835e-04   |   1.492e-04   |\n",
      "   22    |   6.477e-04   |   1.414e-04   |\n",
      "   23    |   4.102e-04   |   8.953e-05   |\n",
      "   24    |   2.672e-04   |   5.832e-05   |\n",
      "   25    |   1.748e-04   |   3.816e-05   |\n",
      "   26    |   1.458e-04   |   3.183e-05   |\n",
      "   27    |   1.152e-04   |   2.515e-05   |\n",
      "   28    |   7.355e-05   |   1.605e-05   |\n",
      "   29    |   5.607e-05   |   1.224e-05   |\n",
      "   30    |   4.406e-05   |   9.618e-06   |\n",
      "   31    |   2.965e-05   |   6.472e-06   |\n",
      "   32    |   2.114e-05   |   4.613e-06   |\n",
      "   33    |   1.464e-05   |   3.195e-06   |\n",
      "   34    |   1.045e-05   |   2.280e-06   |\n",
      "   35    |   7.134e-06   |   1.557e-06   |\n",
      "   36    |   8.225e-06   |   1.795e-06   |\n",
      "   37    |   5.133e-06   |   1.120e-06   |\n",
      "   38    |   3.292e-06   |   7.185e-07   |\n",
      "   39    |   2.189e-06   |   4.778e-07   |\n",
      "   40    |   2.041e-06   |   4.455e-07   |\n",
      "   41    |   1.261e-06   |   2.752e-07   |\n",
      "   42    |   8.725e-07   |   1.904e-07   |\n",
      "   43    |   6.991e-07   |   1.526e-07   |\n",
      "   44    |   4.526e-07   |   9.879e-08   |\n",
      "   45    |   3.284e-07   |   7.167e-08   |\n",
      "   46    |   2.417e-07   |   5.276e-08   |\n",
      "   47    |   1.850e-07   |   4.038e-08   |\n",
      "   48    |   1.179e-07   |   2.573e-08   |\n",
      "   49    |   1.130e-07   |   2.466e-08   |\n",
      "   50    |   7.632e-08   |   1.666e-08   |\n",
      "   51    |   5.200e-08   |   1.135e-08   |\n",
      "   52    |   3.816e-08   |   8.329e-09   |\n",
      "   53    |   2.687e-08   |   5.865e-09   |\n",
      "   54    |   1.842e-08   |   4.021e-09   |\n",
      "   55    |   1.421e-08   |   3.102e-09   |\n",
      "   56    |   9.326e-09   |   2.036e-09   |\n",
      "   57    |   6.248e-09   |   1.364e-09   |\n",
      "   58    |   5.358e-09   |   1.170e-09   |\n",
      "   59    |   3.839e-09   |   8.378e-10   |\n",
      "   60    |   3.220e-09   |   7.028e-10   |\n",
      "   61    |   2.399e-09   |   5.237e-10   |\n",
      "   62    |   1.359e-09   |   2.966e-10   |\n",
      "   63    |   1.219e-09   |   2.661e-10   |\n",
      "   64    |   8.679e-10   |   1.894e-10   |\n",
      "   65    |   6.051e-10   |   1.321e-10   |\n",
      "   66    |   4.367e-10   |   9.531e-11   |\n",
      "   67    |   3.274e-10   |   7.147e-11   |\n",
      "   68    |   1.998e-10   |   4.360e-11   |\n",
      "   69    |   1.356e-10   |   2.959e-11   |\n",
      "   70    |   1.026e-10   |   2.240e-11   |\n",
      "   71    |   8.701e-11   |   1.899e-11   |\n",
      "   72    |   6.766e-11   |   1.477e-11   |\n",
      "   73    |   4.521e-11   |   9.867e-12   |\n",
      "   74    |   3.537e-11   |   7.719e-12   |\n",
      "   75    |   2.245e-11   |   4.899e-12   |\n",
      "   76    |   1.726e-11   |   3.766e-12   |\n",
      "   77    |   1.048e-11   |   2.288e-12   |\n",
      "   78    |   9.973e-12   |   2.177e-12   |\n",
      "   79    |   6.135e-12   |   1.339e-12   |\n",
      "   80    |   5.086e-12   |   1.110e-12   |\n",
      "   81    |   3.547e-12   |   7.743e-13   |\n",
      "   82    |   2.310e-12   |   5.041e-13   |\n",
      "   83    |   1.723e-12   |   3.762e-13   |\n",
      "   84    |   1.604e-12   |   3.501e-13   |\n",
      "   85    |   9.934e-13   |   2.168e-13   |\n",
      "   86    |   7.407e-13   |   1.617e-13   |\n",
      "   87    |   5.150e-13   |   1.124e-13   |\n",
      "   88    |   4.483e-13   |   9.784e-14   |\n",
      "   89    |   2.929e-13   |   6.393e-14   |\n",
      "   90    |   1.895e-13   |   4.137e-14   |\n",
      "   91    |   1.394e-13   |   3.042e-14   |\n",
      "   92    |   1.051e-13   |   2.293e-14   |\n",
      "   93    |   8.169e-14   |   1.783e-14   |\n",
      "   94    |   5.753e-14   |   1.256e-14   |\n",
      "   95    |   3.482e-14   |   7.599e-15   |\n",
      "   96    |   3.551e-14   |   7.751e-15   |\n",
      "   97    |   1.998e-14   |   4.362e-15   |\n",
      "   98    |   1.480e-14   |   3.230e-15   |\n",
      "   99    |   1.128e-14   |   2.461e-15   |\n",
      "  100    |   7.864e-15   |   1.716e-15   |\n",
      "========================================== \n",
      "\n",
      "Solver status (SagaVrRF): Exceed the maximum number of epochs. Increase it to run further ...\n",
      "Solver: Variance-Reduced Forward-Reflected-Backward Splitting (Alacaoglu et al 2021) ...\n",
      "========================================== \n",
      "  Epoch  |     Error     | ||G_eta(x)||  \n",
      " ------------------------------------------\n",
      "   1     |   8.885e+00   |   1.000e+00   |\n",
      "   2     |   9.897e-02   |   1.114e-02   |\n",
      "   3     |   5.867e-03   |   6.603e-04   |\n",
      "   4     |   2.706e-03   |   3.046e-04   |\n",
      "   5     |   2.058e-03   |   2.316e-04   |\n",
      "   6     |   1.652e-03   |   1.859e-04   |\n",
      "   7     |   6.693e-04   |   7.533e-05   |\n",
      "   8     |   5.440e-04   |   6.123e-05   |\n",
      "   9     |   4.258e-04   |   4.793e-05   |\n",
      "   10    |   2.865e-04   |   3.225e-05   |\n",
      "   11    |   2.006e-04   |   2.258e-05   |\n",
      "   12    |   1.546e-04   |   1.740e-05   |\n",
      "   13    |   1.137e-04   |   1.280e-05   |\n",
      "   14    |   1.067e-04   |   1.201e-05   |\n",
      "   15    |   6.944e-05   |   7.815e-06   |\n",
      "   16    |   6.884e-05   |   7.748e-06   |\n",
      "   17    |   5.602e-05   |   6.305e-06   |\n",
      "   18    |   3.657e-05   |   4.116e-06   |\n",
      "   19    |   2.373e-05   |   2.671e-06   |\n",
      "   20    |   1.815e-05   |   2.043e-06   |\n",
      "   21    |   1.132e-05   |   1.274e-06   |\n",
      "   22    |   1.230e-05   |   1.385e-06   |\n",
      "   23    |   7.428e-06   |   8.360e-07   |\n",
      "   24    |   6.752e-06   |   7.599e-07   |\n",
      "   25    |   7.857e-06   |   8.843e-07   |\n",
      "   26    |   4.477e-06   |   5.039e-07   |\n",
      "   27    |   4.099e-06   |   4.614e-07   |\n",
      "   28    |   2.927e-06   |   3.294e-07   |\n",
      "   29    |   2.558e-06   |   2.879e-07   |\n",
      "   30    |   2.282e-06   |   2.568e-07   |\n",
      "   31    |   1.425e-06   |   1.604e-07   |\n",
      "   32    |   1.094e-06   |   1.231e-07   |\n",
      "   33    |   8.706e-07   |   9.799e-08   |\n",
      "   34    |   5.010e-07   |   5.639e-08   |\n",
      "   35    |   5.029e-07   |   5.661e-08   |\n",
      "   36    |   3.533e-07   |   3.976e-08   |\n",
      "   37    |   2.584e-07   |   2.908e-08   |\n",
      "   38    |   2.069e-07   |   2.329e-08   |\n",
      "   39    |   1.603e-07   |   1.804e-08   |\n",
      "   40    |   1.214e-07   |   1.366e-08   |\n",
      "   41    |   8.990e-08   |   1.012e-08   |\n",
      "   42    |   6.028e-08   |   6.784e-09   |\n",
      "   43    |   5.161e-08   |   5.808e-09   |\n",
      "   44    |   5.245e-08   |   5.904e-09   |\n",
      "   45    |   3.365e-08   |   3.787e-09   |\n",
      "   46    |   3.050e-08   |   3.433e-09   |\n",
      "   47    |   1.974e-08   |   2.221e-09   |\n",
      "   48    |   1.674e-08   |   1.884e-09   |\n",
      "   49    |   1.488e-08   |   1.675e-09   |\n",
      "   50    |   1.018e-08   |   1.146e-09   |\n",
      "   51    |   7.788e-09   |   8.765e-10   |\n",
      "   52    |   7.031e-09   |   7.914e-10   |\n",
      "   53    |   7.888e-09   |   8.878e-10   |\n",
      "   54    |   3.469e-09   |   3.904e-10   |\n",
      "   55    |   2.822e-09   |   3.176e-10   |\n",
      "   56    |   2.204e-09   |   2.481e-10   |\n",
      "   57    |   1.765e-09   |   1.987e-10   |\n",
      "   58    |   1.308e-09   |   1.472e-10   |\n",
      "   59    |   1.487e-09   |   1.674e-10   |\n",
      "   60    |   1.165e-09   |   1.311e-10   |\n",
      "   61    |   6.757e-10   |   7.604e-11   |\n",
      "   62    |   6.079e-10   |   6.841e-11   |\n",
      "   63    |   4.198e-10   |   4.725e-11   |\n",
      "   64    |   3.335e-10   |   3.753e-11   |\n",
      "   65    |   2.229e-10   |   2.508e-11   |\n",
      "   66    |   2.507e-10   |   2.822e-11   |\n",
      "   67    |   1.609e-10   |   1.811e-11   |\n",
      "   68    |   1.146e-10   |   1.290e-11   |\n",
      "   69    |   1.175e-10   |   1.322e-11   |\n",
      "   70    |   7.919e-11   |   8.913e-12   |\n",
      "   71    |   6.168e-11   |   6.942e-12   |\n",
      "   72    |   4.217e-11   |   4.747e-12   |\n",
      "   73    |   4.574e-11   |   5.148e-12   |\n",
      "   74    |   4.821e-11   |   5.425e-12   |\n",
      "   75    |   4.856e-11   |   5.466e-12   |\n",
      "   76    |   2.253e-11   |   2.535e-12   |\n",
      "   77    |   1.588e-11   |   1.787e-12   |\n",
      "   78    |   1.131e-11   |   1.273e-12   |\n",
      "   79    |   1.004e-11   |   1.130e-12   |\n",
      "   80    |   1.075e-11   |   1.210e-12   |\n",
      "   81    |   6.623e-12   |   7.454e-13   |\n",
      "   82    |   4.653e-12   |   5.237e-13   |\n",
      "   83    |   4.232e-12   |   4.763e-13   |\n",
      "   84    |   3.094e-12   |   3.483e-13   |\n",
      "   85    |   2.504e-12   |   2.818e-13   |\n",
      "   86    |   1.927e-12   |   2.169e-13   |\n",
      "   87    |   1.559e-12   |   1.755e-13   |\n",
      "   88    |   1.317e-12   |   1.482e-13   |\n",
      "   89    |   1.543e-12   |   1.736e-13   |\n",
      "   90    |   1.183e-12   |   1.331e-13   |\n",
      "   91    |   8.194e-13   |   9.222e-14   |\n",
      "   92    |   5.638e-13   |   6.346e-14   |\n",
      "   93    |   4.013e-13   |   4.516e-14   |\n",
      "   94    |   3.133e-13   |   3.526e-14   |\n",
      "   95    |   2.853e-13   |   3.211e-14   |\n",
      "   96    |   2.027e-13   |   2.281e-14   |\n",
      "   97    |   1.536e-13   |   1.729e-14   |\n",
      "   98    |   1.123e-13   |   1.264e-14   |\n",
      "   99    |   8.456e-14   |   9.518e-15   |\n",
      "  100    |   8.042e-14   |   9.051e-15   |\n",
      "========================================== \n",
      "\n",
      "Solver status (VR-FRBS): Exceed the maximum number of epochs. Increase it to run further ...\n",
      "Solver: Variance-Reduced Extragradient Method (Alacaoglu & Malitsky 2022) ...\n",
      "========================================== \n",
      "  Epoch  |     Error     | ||G_eta(x)||  \n",
      " ------------------------------------------\n",
      "   1     |   8.898e+00   |   1.001e+00   |\n",
      "   2     |   4.880e-02   |   9.858e-03   |\n",
      "   3     |   4.183e-02   |   8.433e-03   |\n",
      "   4     |   1.608e-02   |   3.470e-03   |\n",
      "   5     |   4.701e-03   |   1.141e-03   |\n",
      "   6     |   2.162e-03   |   4.605e-04   |\n",
      "   7     |   1.012e-03   |   2.130e-04   |\n",
      "   8     |   4.453e-04   |   1.129e-04   |\n",
      "   9     |   3.129e-04   |   7.305e-05   |\n",
      "   10    |   2.283e-04   |   4.609e-05   |\n",
      "   11    |   1.141e-04   |   2.428e-05   |\n",
      "   12    |   7.359e-05   |   1.609e-05   |\n",
      "   13    |   3.522e-05   |   8.513e-06   |\n",
      "   14    |   3.488e-05   |   7.833e-06   |\n",
      "   15    |   2.772e-05   |   6.526e-06   |\n",
      "   16    |   1.631e-05   |   3.670e-06   |\n",
      "   17    |   2.128e-05   |   2.395e-06   |\n",
      "   18    |   5.303e-06   |   1.383e-06   |\n",
      "   19    |   2.317e-06   |   5.903e-07   |\n",
      "   20    |   1.556e-06   |   3.679e-07   |\n",
      "   21    |   1.135e-06   |   2.642e-07   |\n",
      "   22    |   5.493e-07   |   1.383e-07   |\n",
      "   23    |   4.152e-07   |   1.118e-07   |\n",
      "   24    |   3.071e-07   |   6.577e-08   |\n",
      "   25    |   2.292e-07   |   5.581e-08   |\n",
      "   26    |   2.253e-07   |   5.601e-08   |\n",
      "   27    |   8.422e-08   |   1.919e-08   |\n",
      "   28    |   6.260e-08   |   1.404e-08   |\n",
      "   29    |   3.533e-08   |   8.303e-09   |\n",
      "   30    |   3.489e-08   |   8.363e-09   |\n",
      "   31    |   3.298e-08   |   7.310e-09   |\n",
      "   32    |   2.323e-08   |   6.162e-09   |\n",
      "   33    |   2.645e-08   |   6.313e-09   |\n",
      "   34    |   2.401e-08   |   2.702e-09   |\n",
      "   35    |   1.173e-08   |   2.533e-09   |\n",
      "   36    |   7.883e-09   |   2.006e-09   |\n",
      "   37    |   6.672e-09   |   1.493e-09   |\n",
      "   38    |   3.012e-09   |   8.296e-10   |\n",
      "   39    |   1.748e-09   |   3.999e-10   |\n",
      "   40    |   5.795e-10   |   1.111e-10   |\n",
      "   41    |   2.905e-10   |   7.810e-11   |\n",
      "   42    |   1.289e-10   |   2.720e-11   |\n",
      "   43    |   8.576e-11   |   2.085e-11   |\n",
      "   44    |   5.178e-11   |   1.225e-11   |\n",
      "   45    |   2.678e-11   |   6.343e-12   |\n",
      "   46    |   2.528e-11   |   5.513e-12   |\n",
      "   47    |   1.254e-11   |   2.923e-12   |\n",
      "   48    |   7.396e-12   |   1.870e-12   |\n",
      "   49    |   1.930e-12   |   4.943e-13   |\n",
      "   50    |   1.771e-12   |   4.705e-13   |\n",
      "   51    |   5.161e-13   |   1.240e-13   |\n",
      "   52    |   5.083e-13   |   1.328e-13   |\n",
      "   53    |   2.440e-13   |   6.080e-14   |\n",
      "   54    |   1.727e-13   |   4.178e-14   |\n",
      "   55    |   1.055e-13   |   2.308e-14   |\n",
      "   56    |   4.089e-14   |   1.006e-14   |\n",
      "   57    |   4.473e-14   |   1.034e-14   |\n",
      "   58    |   4.087e-14   |   1.046e-14   |\n",
      "   59    |   3.373e-14   |   8.488e-15   |\n",
      "   60    |   1.620e-14   |   4.181e-15   |\n",
      "   61    |   1.713e-14   |   3.676e-15   |\n",
      "   62    |   8.299e-15   |   2.225e-15   |\n",
      "   63    |   6.152e-15   |   1.520e-15   |\n",
      "   64    |   3.395e-15   |   9.291e-16   |\n",
      "   65    |   2.343e-15   |   6.014e-16   |\n",
      "   66    |   1.167e-15   |   2.511e-16   |\n",
      "   67    |   8.570e-16   |   1.913e-16   |\n",
      "   68    |   7.980e-16   |   1.497e-16   |\n",
      "   69    |   4.282e-16   |   8.474e-17   |\n",
      "   70    |   3.327e-16   |   7.271e-17   |\n",
      "   71    |   2.100e-16   |   3.858e-17   |\n",
      "   72    |   2.206e-16   |   3.748e-17   |\n",
      "   73    |   1.858e-16   |   2.919e-17   |\n",
      "   74    |   1.565e-16   |   1.777e-17   |\n",
      "   75    |   1.364e-16   |   1.561e-17   |\n",
      "   76    |   1.160e-16   |   1.204e-17   |\n",
      "   77    |   1.417e-16   |   1.382e-17   |\n",
      "   78    |   1.246e-16   |   1.429e-17   |\n",
      "   79    |   1.296e-16   |   1.386e-17   |\n",
      "   80    |   9.883e-17   |   1.292e-17   |\n",
      "   81    |   1.218e-16   |   1.535e-17   |\n",
      "   82    |   9.624e-17   |   1.229e-17   |\n",
      "   83    |   1.132e-16   |   9.401e-18   |\n",
      "   84    |   1.107e-16   |   9.681e-18   |\n",
      "   85    |   9.460e-17   |   9.601e-18   |\n",
      "   86    |   9.118e-17   |   1.058e-17   |\n",
      "   87    |   1.582e-16   |   1.833e-17   |\n",
      "   88    |   1.162e-16   |   1.130e-17   |\n",
      "   89    |   7.826e-17   |   8.808e-18   |\n",
      "   90    |   1.542e-16   |   1.434e-17   |\n",
      "   91    |   9.081e-17   |   8.776e-18   |\n",
      "   92    |   9.399e-17   |   1.098e-17   |\n",
      "   93    |   1.064e-16   |   1.003e-17   |\n",
      "   94    |   9.915e-17   |   8.961e-18   |\n",
      "   95    |   1.049e-16   |   9.748e-18   |\n",
      "   96    |   1.102e-16   |   1.219e-17   |\n",
      "   97    |   1.340e-16   |   1.152e-17   |\n",
      "   98    |   1.240e-16   |   1.279e-17   |\n",
      "   99    |   1.460e-16   |   1.360e-17   |\n",
      "  100    |   1.032e-16   |   9.699e-18   |\n",
      "========================================== \n",
      "\n",
      "Solver status (VR-EG):   Exceed the maximum number of epochs. Increase it to run further ...\n",
      "Solver: Accelerated Loopless-SVRG-Forward-Reflected Method for Monotone Inclusions ...\n",
      "========================================== \n",
      "  Epoch  |     Error     |   ||G(x)||    \n",
      " ------------------------------------------\n",
      "   1     |   2.390e+00   |   9.524e-01   |\n",
      "   2     |   2.006e-02   |   3.562e-03   |\n",
      "   3     |   1.415e-03   |   4.435e-04   |\n",
      "   4     |   2.444e-04   |   7.429e-05   |\n",
      "   5     |   1.851e-05   |   4.317e-06   |\n",
      "   6     |   4.359e-06   |   1.367e-06   |\n",
      "   7     |   1.278e-06   |   3.121e-07   |\n",
      "   8     |   2.250e-07   |   3.557e-08   |\n",
      "   9     |   3.982e-08   |   7.069e-09   |\n",
      "   10    |   8.458e-09   |   1.668e-09   |\n",
      "   11    |   2.200e-09   |   4.157e-10   |\n",
      "   12    |   1.461e-09   |   3.874e-10   |\n",
      "   13    |   3.000e-10   |   5.712e-11   |\n",
      "   14    |   9.118e-11   |   1.684e-11   |\n",
      "   15    |   2.111e-11   |   3.062e-12   |\n",
      "   16    |   7.032e-12   |   1.351e-12   |\n",
      "   17    |   1.922e-12   |   2.431e-13   |\n",
      "   18    |   5.183e-13   |   6.155e-14   |\n",
      "   19    |   1.847e-13   |   1.973e-14   |\n",
      "   20    |   8.077e-14   |   1.248e-14   |\n",
      "   21    |   2.680e-14   |   4.809e-15   |\n",
      "   22    |   1.052e-14   |   1.065e-15   |\n",
      "   23    |   4.995e-15   |   9.675e-16   |\n",
      "   24    |   2.517e-15   |   3.343e-16   |\n",
      "   25    |   1.086e-15   |   1.659e-16   |\n",
      "   26    |   5.121e-16   |   1.206e-16   |\n",
      "   27    |   2.962e-16   |   8.102e-17   |\n",
      "   28    |   3.470e-16   |   8.568e-17   |\n",
      "   29    |   2.848e-16   |   8.236e-17   |\n",
      "   30    |   3.059e-16   |   6.222e-17   |\n",
      "   31    |   3.531e-16   |   9.068e-17   |\n",
      "   32    |   3.351e-16   |   9.253e-17   |\n",
      "   33    |   2.674e-16   |   8.150e-17   |\n",
      "   34    |   3.073e-16   |   6.763e-17   |\n",
      "   35    |   3.496e-16   |   7.729e-17   |\n",
      "   36    |   3.056e-16   |   5.875e-17   |\n",
      "   37    |   3.073e-16   |   8.741e-17   |\n",
      "   38    |   2.686e-16   |   7.017e-17   |\n",
      "   39    |   3.402e-16   |   7.081e-17   |\n",
      "   40    |   3.294e-16   |   8.289e-17   |\n",
      "   41    |   2.703e-16   |   8.370e-17   |\n",
      "   42    |   2.758e-16   |   7.122e-17   |\n",
      "   43    |   3.564e-16   |   9.250e-17   |\n",
      "   44    |   3.426e-16   |   7.271e-17   |\n",
      "   45    |   2.763e-16   |   7.797e-17   |\n",
      "   46    |   2.722e-16   |   7.827e-17   |\n",
      "   47    |   3.454e-16   |   8.166e-17   |\n",
      "   48    |   3.119e-16   |   7.882e-17   |\n",
      "   49    |   2.993e-16   |   7.876e-17   |\n",
      "   50    |   3.057e-16   |   7.889e-17   |\n",
      "   51    |   2.621e-16   |   7.399e-17   |\n",
      "   52    |   3.400e-16   |   8.491e-17   |\n",
      "   53    |   3.701e-16   |   1.015e-16   |\n",
      "   54    |   2.919e-16   |   7.675e-17   |\n",
      "   55    |   3.485e-16   |   7.923e-17   |\n",
      "   56    |   2.666e-16   |   6.275e-17   |\n",
      "   57    |   2.412e-16   |   5.780e-17   |\n",
      "   58    |   3.218e-16   |   7.211e-17   |\n",
      "   59    |   3.394e-16   |   7.929e-17   |\n",
      "   60    |   3.240e-16   |   9.090e-17   |\n",
      "   61    |   3.033e-16   |   6.898e-17   |\n",
      "   62    |   3.110e-16   |   8.366e-17   |\n",
      "   63    |   2.909e-16   |   7.836e-17   |\n",
      "   64    |   3.049e-16   |   7.165e-17   |\n",
      "   65    |   2.958e-16   |   7.965e-17   |\n",
      "   66    |   3.407e-16   |   6.717e-17   |\n",
      "   67    |   3.542e-16   |   7.877e-17   |\n",
      "   68    |   3.749e-16   |   9.811e-17   |\n",
      "   69    |   3.077e-16   |   8.523e-17   |\n",
      "   70    |   3.065e-16   |   6.677e-17   |\n",
      "   71    |   3.813e-16   |   9.645e-17   |\n",
      "   72    |   3.615e-16   |   9.386e-17   |\n",
      "   73    |   3.438e-16   |   8.884e-17   |\n",
      "   74    |   3.197e-16   |   9.550e-17   |\n",
      "   75    |   3.338e-16   |   9.154e-17   |\n",
      "   76    |   3.391e-16   |   8.503e-17   |\n",
      "   77    |   3.463e-16   |   6.896e-17   |\n",
      "   78    |   3.061e-16   |   7.559e-17   |\n",
      "   79    |   3.310e-16   |   7.679e-17   |\n",
      "   80    |   3.630e-16   |   8.830e-17   |\n",
      "   81    |   2.925e-16   |   8.307e-17   |\n",
      "   82    |   3.313e-16   |   8.467e-17   |\n",
      "   83    |   3.276e-16   |   7.940e-17   |\n",
      "   84    |   3.278e-16   |   6.630e-17   |\n",
      "   85    |   3.006e-16   |   7.245e-17   |\n",
      "   86    |   3.334e-16   |   7.637e-17   |\n",
      "   87    |   3.047e-16   |   7.863e-17   |\n",
      "   88    |   3.288e-16   |   1.015e-16   |\n",
      "   89    |   2.564e-16   |   7.628e-17   |\n",
      "   90    |   3.161e-16   |   7.707e-17   |\n",
      "   91    |   3.493e-16   |   7.487e-17   |\n",
      "   92    |   3.022e-16   |   9.025e-17   |\n",
      "   93    |   3.174e-16   |   7.897e-17   |\n",
      "   94    |   2.758e-16   |   6.808e-17   |\n",
      "   95    |   3.267e-16   |   8.588e-17   |\n",
      "   96    |   2.800e-16   |   7.402e-17   |\n",
      "   97    |   2.955e-16   |   7.413e-17   |\n",
      "   98    |   2.934e-16   |   7.807e-17   |\n",
      "   99    |   2.756e-16   |   8.777e-17   |\n",
      "  100    |   2.695e-16   |   7.035e-17   |\n",
      "========================================== \n",
      "\n",
      "Solver status (SvrgAcFR): Exceed the maximum number of epochs. Increase it to run further ...\n",
      "Solver: Accelerated SAGA-Forward-Reflected Method for Monotone Inclusions ...\n",
      "========================================== \n",
      "  Iters  |     Error     |   ||G(x)||    \n",
      " ------------------------------------------\n",
      "   1     |   2.557e+00   |   9.756e-01   |\n",
      "   2     |   1.097e-01   |   4.330e-02   |\n",
      "   3     |   5.553e-02   |   1.728e-02   |\n",
      "   4     |   2.417e-02   |   7.517e-03   |\n",
      "   5     |   1.365e-02   |   3.631e-03   |\n",
      "   6     |   7.437e-03   |   2.186e-03   |\n",
      "   7     |   4.240e-03   |   1.224e-03   |\n",
      "   8     |   2.449e-03   |   7.959e-04   |\n",
      "   9     |   1.114e-03   |   2.679e-04   |\n",
      "   10    |   5.340e-04   |   1.459e-04   |\n",
      "   11    |   3.749e-04   |   8.913e-05   |\n",
      "   12    |   2.108e-04   |   5.690e-05   |\n",
      "   13    |   1.128e-04   |   2.656e-05   |\n",
      "   14    |   7.100e-05   |   2.023e-05   |\n",
      "   15    |   3.768e-05   |   1.054e-05   |\n",
      "   16    |   2.228e-05   |   5.634e-06   |\n",
      "   17    |   1.220e-05   |   2.579e-06   |\n",
      "   18    |   5.034e-06   |   1.368e-06   |\n",
      "   19    |   2.269e-06   |   7.417e-07   |\n",
      "   20    |   1.574e-06   |   3.594e-07   |\n",
      "   21    |   9.318e-07   |   1.900e-07   |\n",
      "   22    |   5.693e-07   |   1.038e-07   |\n",
      "   23    |   3.473e-07   |   1.126e-07   |\n",
      "   24    |   1.100e-07   |   2.625e-08   |\n",
      "   25    |   6.922e-08   |   1.455e-08   |\n",
      "   26    |   2.953e-08   |   8.528e-09   |\n",
      "   27    |   1.892e-08   |   4.490e-09   |\n",
      "   28    |   9.133e-09   |   1.979e-09   |\n",
      "   29    |   6.962e-09   |   1.457e-09   |\n",
      "   30    |   3.655e-09   |   8.573e-10   |\n",
      "   31    |   1.239e-09   |   2.913e-10   |\n",
      "   32    |   1.370e-09   |   2.967e-10   |\n",
      "   33    |   6.428e-10   |   1.694e-10   |\n",
      "   34    |   3.181e-10   |   8.964e-11   |\n",
      "   35    |   4.490e-10   |   1.498e-10   |\n",
      "   36    |   1.166e-10   |   2.427e-11   |\n",
      "   37    |   7.784e-11   |   1.795e-11   |\n",
      "   38    |   6.861e-11   |   1.359e-11   |\n",
      "   39    |   2.578e-11   |   4.957e-12   |\n",
      "   40    |   1.319e-11   |   2.604e-12   |\n",
      "   41    |   5.402e-12   |   1.071e-12   |\n",
      "   42    |   3.691e-12   |   7.697e-13   |\n",
      "   43    |   1.785e-12   |   4.666e-13   |\n",
      "   44    |   1.200e-12   |   2.512e-13   |\n",
      "   45    |   1.223e-12   |   2.480e-13   |\n",
      "   46    |   3.218e-13   |   8.804e-14   |\n",
      "   47    |   3.519e-13   |   1.214e-13   |\n",
      "   48    |   1.292e-13   |   2.902e-14   |\n",
      "   49    |   8.798e-14   |   1.633e-14   |\n",
      "   50    |   3.606e-14   |   8.979e-15   |\n",
      "   51    |   3.856e-14   |   1.148e-14   |\n",
      "   52    |   1.177e-14   |   2.168e-15   |\n",
      "   53    |   1.096e-14   |   2.394e-15   |\n",
      "   54    |   4.018e-15   |   8.372e-16   |\n",
      "   55    |   2.549e-15   |   5.046e-16   |\n",
      "   56    |   1.285e-15   |   2.947e-16   |\n",
      "   57    |   9.067e-16   |   1.974e-16   |\n",
      "   58    |   6.883e-16   |   1.742e-16   |\n",
      "   59    |   4.127e-16   |   1.033e-16   |\n",
      "   60    |   3.148e-16   |   7.625e-17   |\n",
      "   61    |   3.685e-16   |   7.967e-17   |\n",
      "   62    |   2.740e-16   |   7.231e-17   |\n",
      "   63    |   3.106e-16   |   7.753e-17   |\n",
      "   64    |   3.189e-16   |   7.472e-17   |\n",
      "   65    |   3.408e-16   |   8.147e-17   |\n",
      "   66    |   3.271e-16   |   8.667e-17   |\n",
      "   67    |   2.903e-16   |   7.813e-17   |\n",
      "   68    |   3.472e-16   |   9.789e-17   |\n",
      "   69    |   3.381e-16   |   8.679e-17   |\n",
      "   70    |   3.483e-16   |   9.110e-17   |\n",
      "   71    |   3.231e-16   |   7.893e-17   |\n",
      "   72    |   2.829e-16   |   8.487e-17   |\n",
      "   73    |   3.176e-16   |   8.062e-17   |\n",
      "   74    |   3.126e-16   |   7.802e-17   |\n",
      "   75    |   2.955e-16   |   7.954e-17   |\n",
      "   76    |   2.655e-16   |   7.587e-17   |\n",
      "   77    |   3.332e-16   |   9.478e-17   |\n",
      "   78    |   2.977e-16   |   8.450e-17   |\n",
      "   79    |   3.213e-16   |   8.851e-17   |\n",
      "   80    |   2.963e-16   |   8.759e-17   |\n",
      "   81    |   3.182e-16   |   8.261e-17   |\n",
      "   82    |   3.733e-16   |   1.100e-16   |\n",
      "   83    |   2.946e-16   |   8.154e-17   |\n",
      "   84    |   3.314e-16   |   8.761e-17   |\n",
      "   85    |   3.626e-16   |   7.965e-17   |\n",
      "   86    |   2.744e-16   |   7.395e-17   |\n",
      "   87    |   3.311e-16   |   8.845e-17   |\n",
      "   88    |   3.421e-16   |   8.562e-17   |\n",
      "   89    |   2.869e-16   |   7.514e-17   |\n",
      "   90    |   3.593e-16   |   8.112e-17   |\n",
      "   91    |   2.896e-16   |   7.622e-17   |\n",
      "   92    |   3.601e-16   |   8.484e-17   |\n",
      "   93    |   2.561e-16   |   7.404e-17   |\n",
      "   94    |   3.303e-16   |   8.299e-17   |\n",
      "   95    |   3.038e-16   |   7.880e-17   |\n",
      "   96    |   3.100e-16   |   7.963e-17   |\n",
      "   97    |   3.361e-16   |   8.799e-17   |\n",
      "   98    |   3.315e-16   |   8.143e-17   |\n",
      "   99    |   3.150e-16   |   8.303e-17   |\n",
      "  100    |   3.193e-16   |   8.645e-17   |\n",
      "========================================== \n",
      "\n",
      "Solver status (SagaAcFR): Exceed the maximum number of epochs. Increase it to run further ...\n"
     ]
    }
   ],
   "source": [
    "## Optimistic gradient method\n",
    "my_max_iters1 = def_n_max_epochs\n",
    "my_lr1        = 1.0/(2.0*Lips)\n",
    "output1       = solver.OG(my_data, G_op_eval, J_op_eval, x0, gamma=0.5, eta=my_lr1, verbose=my_verbose, \\\n",
    "                          n_max_iters=my_max_iters1, tol=def_tol, is_term = my_is_term)\n",
    "print(\"Solver status (OG):     \", output1[\"message\"])\n",
    "output_all.append(output1)\n",
    "\n",
    "## Accelerated optimistic gradient \n",
    "my_max_iters2 = def_n_max_epochs\n",
    "my_mb_size2   = int(0.5*n**0.67)   # default\n",
    "my_rho2       = 1.0/my_data.get(\"L\")\n",
    "my_lr2        = 0.5/my_data.get(\"L\")\n",
    "my_shift2     = 10.0\n",
    "output2       = acc_solver.AOG(my_data, G_op_eval, J_op_eval, x0, beta=my_lr2, rho=my_rho2, \\\n",
    "                               r_shift=my_shift2, verbose=my_verbose, n_max_iters=my_max_iters2, \\\n",
    "                               tol=def_tol, is_term = my_is_term)\n",
    "print(\"Solver status (AOG):    \", output2[\"message\"])\n",
    "output_all.append(output2)\n",
    "\n",
    "## Saga Root-finding Method from Davis' paper.\n",
    "my_mb_size3 = int(0.5*n**0.67) # default value.\n",
    "my_rho3     = 1.0/my_data.get(\"L\")\n",
    "my_lr3      = 0.5/my_data.get(\"L\")\n",
    "output3     = solver.SagaRF(my_data, G_op_eval, Gb_op_eval, J_op_eval, x0, mb_size=my_mb_size3, \\\n",
    "                            eta=my_lr3, rho = my_rho3, verbose=my_verbose, n_epochs=def_n_max_epochs, \\\n",
    "                            tol=def_tol, is_term = my_is_term)\n",
    "print(\"Solver status (SagaVrRF):\", output3.get(\"message\"))\n",
    "output_all.append(output3)\n",
    "\n",
    "## SVRG Forward-Reflected-Backward Splitting Method\n",
    "my_prob4    = 1.0/(n**0.33)    # default value\n",
    "my_mb_size4 = int(0.5*n**0.67) # default\n",
    "# Theoretical learning rate\n",
    "my_lr4      = 0.95*(1 - np.sqrt(1-my_prob4))/(2.0*my_data.get(\"L\"))\n",
    "output4     = solver.VrFRBS(my_data, G_op_eval, J_op_eval, x0, mb_size=my_mb_size4, prob=my_prob4, eta=my_lr4, \\\n",
    "                            verbose=my_verbose, n_epochs=def_n_max_epochs, tol=def_tol, is_term = my_is_term)\n",
    "print(\"Solver status (VR-FRBS):\", output4[\"message\"])\n",
    "output_all.append(output4)\n",
    "\n",
    "## SVRG Extragradient method\n",
    "my_prob5    = 1.0/(n**0.33)    # detault value\n",
    "my_mb_size5 = int(0.5*n**0.67) # default value\n",
    "my_alpha5   = 1 - my_prob5 \n",
    "my_lr5      = 0.95*np.sqrt(1-my_alpha5)/my_data.get(\"L\")\n",
    "output5     = solver.VrEG(my_data, G_op_eval, J_op_eval, x0, mb_size=my_mb_size5, prob=my_prob5, eta=my_lr5, \\\n",
    "                          alpha=my_alpha5, verbose=my_verbose, n_epochs=def_n_max_epochs, \\\n",
    "                          tol=def_tol, is_term = my_is_term)\n",
    "print(\"Solver status (VR-EG):  \", output5[\"message\"])\n",
    "output_all.append(output5)\n",
    "\n",
    "## Accelerated Loopless SVRG-Forward Reflected method\n",
    "my_mb_size6 = int(0.5*n**0.67)  # default\n",
    "my_prob6    = 1.0/(n**0.33)     # default\n",
    "my_rho6     = 1.0/my_data.get(\"L\")\n",
    "my_lr6      = 0.15/my_data.get(\"L\")\n",
    "my_shift6   = 20.0\n",
    "output6     = acc_solver.SvrgAcFR(my_data, G_op_eval, J_op_eval, x0, mb_size=my_mb_size6, prob=my_prob6, \\\n",
    "                             rho=my_rho6, beta=my_lr6, r_shift=my_shift6, verbose=my_verbose, \\\n",
    "                             n_epochs=def_n_max_epochs, tol=def_tol, is_term = my_is_term)\n",
    "print(\"Solver status (SvrgAcFR):\", output6[\"message\"])\n",
    "output_all.append(output6)\n",
    "\n",
    "## Accelerated Saga FR method.\n",
    "my_mb_size7 = int(0.5*n**0.67) # default value.\n",
    "my_rho7     = 1.0/my_data.get(\"L\")\n",
    "my_lr7      = 0.15/my_data.get(\"L\")\n",
    "my_shift7   = 40.0\n",
    "output7     = acc_solver.SagaAcFR(my_data, G_op_eval, Gb_op_eval, J_op_eval, x0, mb_size=my_mb_size7, beta=my_lr7, \\\n",
    "                              rho=my_rho7, r_shift=my_shift7, verbose=my_verbose, n_epochs=def_n_max_epochs, \\\n",
    "                              tol=def_tol, is_term = my_is_term)\n",
    "print(\"Solver status (SagaAcFR):\", output7.get(\"message\"))\n",
    "output_all.append(output7)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c06f764a-a50c-4388-84e3-27586bd2c2be",
   "metadata": {},
   "source": [
    "## Plot the results of experiments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "2df1ce40-0e54-40d9-afec-bf9c5a5e463d",
   "metadata": {},
   "outputs": [
    {
     "ename": "IndexError",
     "evalue": "list index out of range",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[48], line 20\u001b[0m\n\u001b[1;32m     17\u001b[0m fig, axs \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39msubplots(\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m2\u001b[39m)\u001b[38;5;66;03m# , figsize=(10, 8))\u001b[39;00m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(\u001b[38;5;28mlen\u001b[39m(output_all)):\n\u001b[1;32m     19\u001b[0m     axs[\u001b[38;5;241m0\u001b[39m]\u001b[38;5;241m.\u001b[39msemilogy(it_plt[i], error[i], color\u001b[38;5;241m=\u001b[39mcolors[i], linestyle\u001b[38;5;241m=\u001b[39mline_styles[i],\\\n\u001b[0;32m---> 20\u001b[0m                     marker \u001b[38;5;241m=\u001b[39m my_markers[i], markersize\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m4\u001b[39m, markevery\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m5\u001b[39m, label\u001b[38;5;241m=\u001b[39m\u001b[43malg_name\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m)\n\u001b[1;32m     21\u001b[0m     axs[\u001b[38;5;241m1\u001b[39m]\u001b[38;5;241m.\u001b[39msemilogy(it_plt[i], op_norm[i], color\u001b[38;5;241m=\u001b[39mcolors[i], linestyle\u001b[38;5;241m=\u001b[39mline_styles[i],\\\n\u001b[1;32m     22\u001b[0m                     marker \u001b[38;5;241m=\u001b[39m my_markers[i], markersize\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m4\u001b[39m, markevery\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m5\u001b[39m, label\u001b[38;5;241m=\u001b[39malg_name[i])\n\u001b[1;32m     23\u001b[0m axs[\u001b[38;5;241m0\u001b[39m]\u001b[38;5;241m.\u001b[39mlegend()\n",
      "\u001b[0;31mIndexError\u001b[0m: list index out of range"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Number of methods\n",
    "hist, it_plt, error, op_norm = [], [], [], []\n",
    "for i in range(len(output_all)):\n",
    "    hist   = output_all[i].get(\"epoch_hist\")\n",
    "    it_plt.append( [h.get(\"epoch\") for h in hist] )\n",
    "    error.append( [h.get(\"error\") for h in hist] )\n",
    "    op_norm.append( [h.get(\"op_norm\") for h in hist] )\n",
    "\n",
    "## This is for plottings\n",
    "alg_name = ['OG', 'AOG', 'SagaRF', 'VrFRBS', 'VrEG', 'AVFR-Svrg', 'AVFR-Saga']\n",
    "colors   = ['C0', 'g', 'm', 'y', 'k', 'r', 'b', 'C1', 'C2']\n",
    "line_styles = ['--', '-', '-.', ':', '-', '--', '-.', '-', '--']\n",
    "my_markers = ['o', '*', 'd', 'v', '^', '>', '<', 's', 'o']\n",
    "\n",
    "\n",
    "## Now we plot the results.\n",
    "fig, axs = plt.subplots(1, 2)# , figsize=(10, 8))\n",
    "for i in range(len(output_all)):\n",
    "    axs[0].semilogy(it_plt[i], error[i], color=colors[i], linestyle=line_styles[i],\\\n",
    "                    marker = my_markers[i], markersize=4, markevery=5, label=alg_name[i])\n",
    "    axs[1].semilogy(it_plt[i], op_norm[i], color=colors[i], linestyle=line_styles[i],\\\n",
    "                    marker = my_markers[i], markersize=4, markevery=5, label=alg_name[i])\n",
    "axs[0].legend()\n",
    "axs[1].legend()\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e29dfeb-f552-44bf-b8b9-a7cdfe27919a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}