simulation/vfl_sim.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Direct Vertical Federated Learning Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_diabetes\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# Load the diabetes dataset\n",
    "diabetes = load_diabetes()\n",
    "X = diabetes.data\n",
    "y = diabetes.target \n",
    "\n",
    "# Split the data into training and testing sets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
    "\n",
    "# Standardize the features\n",
    "scaler = StandardScaler()\n",
    "X_train = scaler.fit_transform(X_train)\n",
    "X_test = scaler.transform(X_test)\n",
    "\n",
    "# Convert to PyTorch tensors\n",
    "X_train = torch.tensor(X_train, dtype=torch.float32)\n",
    "X_test = torch.tensor(X_test, dtype=torch.float32)\n",
    "y_train = torch.tensor(y_train, dtype=torch.float32).unsqueeze(1)\n",
    "y_test = torch.tensor(y_test, dtype=torch.float32).unsqueeze(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class DiabetesClientEmbeddingModel(nn.Module):\n",
    "    \"\"\"\n",
    "    Embedding model for the VFL clients.\n",
    "    \"\"\"\n",
    "    def __init__(self, input_dim, output_dim=8, hidden_dim=24):\n",
    "        super(DiabetesClientEmbeddingModel, self).__init__()\n",
    "        self.fc1 = nn.Linear(input_dim, hidden_dim)\n",
    "        self.fc2 = nn.Linear(hidden_dim, output_dim)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = torch.relu(self.fc1(x))\n",
    "        x = torch.relu(self.fc2(x))\n",
    "        return x\n",
    "    \n",
    "class DiabetesServerModel(nn.Module):\n",
    "    \"\"\"\n",
    "    Model for the VFL server.\n",
    "    \"\"\"\n",
    "    def __init__(self, input_dim, output_dim=1, hidden_dim=12):\n",
    "        super(DiabetesServerModel, self).__init__()\n",
    "        self.fc1 = nn.Linear(input_dim, hidden_dim)\n",
    "        self.fc2 = nn.Linear(hidden_dim, output_dim)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = torch.relu(self.fc1(x))\n",
    "        x = self.fc2(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create client embedding models and server model\n",
    "client1_embedding_model = DiabetesClientEmbeddingModel(input_dim=3, output_dim=8, hidden_dim=24)\n",
    "client2_embedding_model = DiabetesClientEmbeddingModel(input_dim=3, output_dim=8, hidden_dim=24)\n",
    "client3_embedding_model = DiabetesClientEmbeddingModel(input_dim=4, output_dim=8, hidden_dim=24)\n",
    "server_model = DiabetesServerModel(input_dim=24, output_dim=1, hidden_dim=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prepare the training data for each client\n",
    "X_train_client1 = X_train[:, :3]\n",
    "X_train_client2 = X_train[:, 3:6]\n",
    "X_train_client3 = X_train[:, 6:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Prepare the testing data for each client\n",
    "X_test_client1 = X_test[:, :3]\n",
    "X_test_client2 = X_test[:, 3:6]\n",
    "X_test_client3 = X_test[:, 6:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the loss function and optimizer\n",
    "criterion = nn.MSELoss()\n",
    "optimizer_client1 = optim.Adam(client1_embedding_model.parameters(), lr=0.01)\n",
    "optimizer_client2 = optim.Adam(client2_embedding_model.parameters(), lr=0.01)\n",
    "optimizer_client3 = optim.Adam(client3_embedding_model.parameters(), lr=0.01)\n",
    "optimizer_server = optim.Adam(server_model.parameters(), lr=0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch [50/500] train loss: 3498.971923828125 val loss: 3299.949462890625\n",
      "Epoch [100/500] train loss: 2922.73681640625 val loss: 2929.160400390625\n",
      "Epoch [150/500] train loss: 2810.5126953125 val loss: 2786.905517578125\n",
      "Epoch [200/500] train loss: 2751.050537109375 val loss: 2710.25927734375\n",
      "Epoch [250/500] train loss: 2712.77490234375 val loss: 2674.999755859375\n",
      "Epoch [300/500] train loss: 2682.02001953125 val loss: 2665.3828125\n",
      "Epoch [350/500] train loss: 2661.5048828125 val loss: 2662.342041015625\n",
      "Epoch [400/500] train loss: 2644.515625 val loss: 2660.0244140625\n",
      "Epoch [450/500] train loss: 2629.01123046875 val loss: 2654.90771484375\n",
      "Epoch [500/500] train loss: 2613.109130859375 val loss: 2654.285888671875\n"
     ]
    }
   ],
   "source": [
    "num_epochs = 500\n",
    "train_losses = []\n",
    "val_losses = []\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    # Train the client models\n",
    "    client1_embedding_model.train()\n",
    "    client2_embedding_model.train()\n",
    "    client3_embedding_model.train()\n",
    "    optimizer_client1.zero_grad()\n",
    "    optimizer_client2.zero_grad()\n",
    "    optimizer_client3.zero_grad()\n",
    "    \n",
    "    client1_embedding = client1_embedding_model(X_train_client1)\n",
    "    client2_embedding = client2_embedding_model(X_train_client2)\n",
    "    client3_embedding = client3_embedding_model(X_train_client3)\n",
    "    \n",
    "    client1_embedding_clone = client1_embedding.detach().clone()\n",
    "    client2_embedding_clone = client2_embedding.detach().clone()\n",
    "    client3_embedding_clone = client3_embedding.detach().clone()\n",
    "    \n",
    "    # Train the server model\n",
    "    server_model.train()\n",
    "    optimizer_server.zero_grad()\n",
    "    embedding_server = torch.cat([client1_embedding_clone, client2_embedding_clone, client3_embedding_clone], dim=1)\n",
    "    embedding_server = embedding_server.detach().requires_grad_()\n",
    "    y_pred = server_model(embedding_server)\n",
    "    loss = criterion(y_pred, y_train)\n",
    "    train_losses.append(loss.item())\n",
    "    loss.backward()\n",
    "    optimizer_server.step()\n",
    "        \n",
    "    # Update the client models\n",
    "    grads = embedding_server.grad.split([8, 8, 8], dim=1)\n",
    "    client1_embedding.backward(grads[0])\n",
    "    client2_embedding.backward(grads[1])\n",
    "    client3_embedding.backward(grads[2])\n",
    "    optimizer_client1.step()\n",
    "    optimizer_client2.step()\n",
    "    optimizer_client3.step()\n",
    "    \n",
    "    # Evaluate the overall model\n",
    "    with torch.no_grad():\n",
    "        client1_embedding_model.eval()\n",
    "        client2_embedding_model.eval()\n",
    "        client3_embedding_model.eval()\n",
    "        server_model.eval()\n",
    "        client1_embedding_val = client1_embedding_model(X_test_client1)\n",
    "        client2_embedding_val = client2_embedding_model(X_test_client2)\n",
    "        client3_embedding_val = client3_embedding_model(X_test_client3)\n",
    "        embedding_aggregated_val = torch.cat([client1_embedding_val, client2_embedding_val, client3_embedding_val], dim=1)\n",
    "        y_pred_val = server_model(embedding_aggregated_val)\n",
    "        val_loss = criterion(y_pred_val, y_test)\n",
    "        val_losses.append(val_loss.item())\n",
    "        \n",
    "    if (epoch+1) % 50 == 0:\n",
    "        print(f\"Epoch [{epoch+1}/{num_epochs}] train loss: {loss.item()} val loss: {val_loss.item()}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 5))\n",
    "plt.plot(train_losses, label='Training MSE')\n",
    "plt.plot(val_losses, label='Validation MSE')\n",
    "plt.xlabel('Epochs')\n",
    "plt.ylabel('Mean Squared Error')\n",
    "plt.legend()\n",
    "plt.title('Training and Validation MSE')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "appfl",
   "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": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}