{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## 0. Define MDP environment: Cliff Walk\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "\"\"\" Tile layout (36=start, 47=goal, 37-46=cliff)\n", "0\t1\t2\t3\t4\t5\t6\t7\t8\t9\t10\t11\n", "12\t13\t14\t15\t16\t17\t18\t19\t20\t21\t22\t23\n", "24\t25\t26\t27\t28\t29\t30\t31\t32\t33\t34\t35\n", "36\t37\t38\t39\t40\t41\t42\t43\t44\t45\t46\t47\n", "\"\"\"\n", "\n", "cliff_states = np.arange(37, 47) # States for cliff tiles\n", "goal_state = 47 # Goal state\n", "\n", "# def get_reward(state: int, cliff_pos: np.array, goal_pos: int) -> int:\n", "def get_reward(state): #when arriving at state\n", " \"\"\"\n", " Compute reward for given state\n", " \"\"\"\n", " if state == goal_state: # Reward of +100 for reaching goal\n", " return 100\n", " elif state in cliff_states: # Reward of -100 for falling down cliff\n", " return -100\n", " else: # Otherwise, reward of -1 for each move\n", " return -1\n", "\n", "\n", "\n", "def get_state(agent_pos):\n", " \"\"\"\n", " (x,y)-position -> state integer in [0,47]\n", " \"\"\"\n", " return 12 * agent_pos[0] + agent_pos[1]\n", "\n", "\n", "def get_position(state):\n", " \"\"\"\n", " state integer in [0,47] -> (x,y)-position\n", " \"\"\"\n", " return (int(np.floor(state / 12)), state % 12)\n", "\n", "\n", "\n", "def move_agent(agent_pos, action):\n", " \"\"\"\n", " Move agent to new position based on current position and action\n", " \"\"\"\n", " # Retrieve agent position\n", " (pos_x, pos_y) = agent_pos\n", "\n", " if action == 0: # Up\n", " pos_x = pos_x - 1 if pos_x > 0 else pos_x\n", " elif action == 1: # Down\n", " pos_x = pos_x + 1 if pos_x < 3 else pos_x\n", " elif action == 2: # Left\n", " pos_y = pos_y - 1 if pos_y > 0 else pos_y\n", " elif action == 3: # Right\n", " pos_y = pos_y + 1 if pos_y < 11 else pos_y\n", " else: # Infeasible move\n", " raise Exception(\"Infeasible move\")\n", "\n", " agent_pos = (pos_x, pos_y)\n", "\n", " return agent_pos\n", "\n", "\n", "def get_Q_from_V(V_table, gamma):\n", " \"\"\"\n", " Given V_table, output Q_table of size (4,48)\n", "\n", " \"\"\"\n", " Q_table = np.zeros((4, 48))\n", "\n", " for state in range(37): \n", " for action in range(4):\n", " pos = get_position(state)\n", " pos_next = move_agent(pos, action)\n", " state_next = get_state(pos_next)\n", " r = get_reward(state_next)\n", " Q_table[action, state] = r + gamma * V_table[state_next] # Q (a, s) = r + gamma * V(s')\n", " \n", " return Q_table\n", "\n", "\n", "def visualize_value_function(V, title=\"Value Function\"):\n", " \"\"\"\n", " Visualizes the value function as a heatmap.\n", " V should be a vector of length 48.\n", " \"\"\"\n", " V_grid = V.reshape((4,12))\n", " plt.figure(figsize=(8, 6))\n", " ax = sns.heatmap(V_grid, annot=True, fmt=\".1f\", cmap=\"viridis\",\n", " cbar=True, square=True, xticklabels=False, yticklabels=False)\n", " ax.set_title(title)\n", " plt.show()\n", "\n", "def visualize_policy(policy, title=\"Policy (Greedy)\"):\n", " \"\"\"\n", " Visualizes the policy as arrows on the grid.\n", " The policy is assumed to be of shape (4,37) for nonterminal states.\n", " Terminal states (37-47) are left blank.\n", " \"\"\"\n", " fig, ax = plt.subplots(figsize=(8, 6))\n", " ax.imshow(np.zeros((4,12)), cmap=\"Greys\", vmin=0, vmax=1)\n", " action_arrows = {0: '↑', 1: '↓', 2: '←', 3: '→'}\n", " for state in range(37):\n", " pos = get_position(state)\n", " best_action = np.argmax(policy[:,state])\n", " arrow = action_arrows[best_action]\n", " ax.text(pos[1], pos[0], arrow, ha=\"center\", va=\"center\", color=\"red\", fontsize=16)\n", " ax.set_title(title)\n", " ax.set_xticks([])\n", " ax.set_yticks([])\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. MC Policy evaluation of $V^\\pi$ for a given policy $ \\pi$\n", "\n", "We start with the tabular Monte Carlo (MC) policy evaluation. (No neural network. $V^\\pi(s)$ value estimated saparately for eah $s\\in \\mathcal{S}$.) The following code considers the uniform random action policy for the policy $\\pi$.\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "V_table = np.zeros(48)\n", "gamma = 1.0\n", "N = 1024\n", "\n", "\n", "#Perform MC Policy Evaluation\n", "for starting_state in range(37):\n", "# range(37) contains non-terminal states\n", " for _ in range(N):\n", " reward_cache = []\n", " agent_pos = get_position(starting_state)\n", " game_over = False # game_over flag\n", " while True: #Simulate episode\n", " action = np.random.randint(4) #random action policy\n", " agent_pos = move_agent(agent_pos, action)\n", " state = get_state(agent_pos)\n", " reward_cache.append(get_reward(state))\n", " #End episode if game over\n", " if (state == goal_state or state in cliff_states):\n", " break\n", " # update value function\n", " V_table[starting_state] += sum(gamma**k * r for k, r in enumerate(reward_cache))\n", " V_table[starting_state] /= N\n", "\n", " \n", "# print(V_table.reshape(4,-1))\n", "visualize_value_function(V_table, 'Value Function V^\\pi')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Estimate $V^\\star$ and $\\pi^\\star$ via Value Iteration\n", "\n", "Next, we implement Value Iteration:\n", "\\begin{align*}\n", "V^{k+1} = \\max_{a \\in \\mathcal{A}} \\mathbb{E}_{(r,s')\\sim p(\\cdot,\\cdot|s,a)} [r + \\gamma V^k (s') | s, a]\n", "\\end{align*}\n", "\n", "and obtain the greedy policy:\n", "\\begin{align*}\n", "\\pi^{k+1}(s) = \\text{argmax}_{a \\in \\mathcal{A}} \\mathbb{E}_{(r,s')\\sim p(\\cdot,\\cdot|s,a)} [r + \\gamma V^k (s') | s, a].\n", "\\end{align*}\n" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "num_iterations = 20\n", "gamma = 1.0\n", "\n", "\n", "V_table = np.zeros(48) # inititalize v table.\n", "\n", "#Perform Value Iteration\n", "for itr in range(num_iterations):\n", "\n", " V_table_prev = V_table.copy()\n", "\n", " # Update value function for all states\n", " for state in range(37): #range(37) are non-terminal states\n", " candidates = []\n", " for action in range(4):\n", " pos = get_position(state)\n", " pos_next = move_agent(pos, action)\n", " state_next = get_state(pos_next)\n", " r = get_reward(state_next)\n", " new_value = r + gamma * V_table_prev[state_next]\n", " candidates.append(new_value)\n", " V_table[state] = max(candidates)\n", " \n", "visualize_value_function(V_table, 'Estimate of Optimal Value function V*')\n", "\n", "\n", "#Compute greedy policy from V\n", "Q_table = get_Q_from_V(V_table, gamma)\n", "# get policy based off the value function\n", "pi = np.zeros((4,37))\n", "for state in range(37):\n", " pi[np.argmax(Q_table[:,state]), state] = 1\n", "visualize_policy(pi, \"Greedy policy\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Policy Evaluation using Linear Algebra\n", "\n", "Next, we use linear algebra (matrix inverse) to carry out policy evaluation exactly. This approach works in the tabular setting when the size of the state space is small. Consider the tabular setting where $|\\mathcal{S}|, |\\mathcal{A}| < \\infty$, and a policy $\\pi$ is given.\n", "\n", "The key idea is to directly solve the Bellman equation:\n", "\\begin{align*}\n", "V_{\\pi}(s) &= \\underset{\\substack{a \\sim \\pi(a|s) \\\\ (r,s')\\sim p(\\cdot,\\cdot|s,a)}}{\\mathbb{E}} [r + \\gamma V_{\\pi} (s') | s]\\\\\n", "&= \\sum_a \\pi(a|s) \\sum_{s', r} p(s', r \\mid s, a)[r + \\gamma V_\\pi(s')] \\\\\n", "&= \\sum_a \\pi(a|s) \\sum_{s', r} r \\cdot p(s', r \\mid s, a) + \\sum_a \\pi(a|s) \\sum_{s', r} p(s', r \\mid s, a) \\gamma V_\\pi(s') \\\\\n", "&= \\sum_a \\pi(a|s) r(s, a) + \\gamma \\sum_{s'} \\left\\{ \\sum_a \\pi(a|s) \\cdot p(s' \\mid s, a) \\right\\} V_\\pi(s') \\\\\n", "&= r_\\pi(s) + \\gamma \\sum_{s'} P_\\pi(s' \\mid s) V_\\pi(s'),\n", "\\end{align*}\n", "where $r(s,a)$ is the deterministic reward (for the Cliff Walk environment) given state $s$ and action $a$ and $V_\\pi \\in \\mathbb{R}^{|\\mathcal{S}|}, r_\\pi \\in \\mathbb{R}^{|\\mathcal{S}|}, P_\\pi \\in \\mathbb{R}^{|\\mathcal{S}| \\times |\\mathcal{S}|}$ are defined as:\n", "\n", "\n", "\\begin{align*}\n", "V_\\pi &= \n", "\\begin{bmatrix}\n", "V_\\pi(s_1) \\\\\n", "V_\\pi(s_2) \\\\\n", "\\vdots \\\\\n", "V_\\pi(s_n)\n", "\\end{bmatrix} \\\\\n", "r_\\pi &= \n", "\\begin{bmatrix}\n", "r_\\pi(s_1) \\\\\n", "r_\\pi(s_2) \\\\\n", "\\vdots \\\\\n", "r_\\pi(s_n)\n", "\\end{bmatrix}\n", "=\n", "\\begin{bmatrix}\n", "\\sum_a \\pi(a|s_1) r(s_1, a) \\\\\n", "\\sum_a \\pi(a|s_2) r(s_2, a) \\\\\n", "\\vdots \\\\\n", "\\sum_a \\pi(a|s_n) r(s_n, a)\n", "\\end{bmatrix} \\\\\n", "P_\\pi &=\n", "\\begin{bmatrix}\n", "P_\\pi(s_1|s_1) & P_\\pi(s_2|s_1) & \\cdots & P_\\pi(s_n|s_1) \\\\\n", "P_\\pi(s_1|s_2) & P_\\pi(s_2|s_2) & \\cdots & P_\\pi(s_n|s_2) \\\\\n", "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n", "P_\\pi(s_1|s_n) & P_\\pi(s_2|s_n) & \\cdots & P_\\pi(s_n|s_n)\n", "\\end{bmatrix}\n", "\\end{align*}\n", "\n", "Then, we can express the Bellman equation linear algebraically\n", "$$\n", "V_\\pi = r_\\pi + \\gamma P_\\pi V_\\pi\n", "$$\n", "(excludes terminal states)\n", "and we can solve it with\n", "$$\n", "V_\\pi = (I - \\gamma P_\\pi)^{-1}r_\\pi.\n", "$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gamma = 1.0\n", "\n", "# Choose any policy (a uniform random one)\n", "pi = np.ones((37,4)) # excluding terminal states\n", "pi = pi / 4\n", "\n", "# Construct r_\\pi\n", "R = np.zeros(37)\n", "for state in range(37):\n", " agent_pos = get_position(state)\n", " R[state] = sum(\n", " pi[state, action] * get_reward(get_state(move_agent(agent_pos, action)))\n", " for action in range(4)\n", " )\n", " \n", "# print(f\"Reward vector R is:\\n{R[0:36].reshape(4,-1)}\")\n", "# print(R[36])\n", "\n", "# Construct P_pi\n", "P = np.zeros((37,37))\n", "\n", "for state in range(37):\n", " agent_pos = get_position(state)\n", " for action in range(4):\n", " state_next = get_state(move_agent(agent_pos,action))\n", " if state_next > 36:\n", " continue # Do not record transition to terminal states\n", " P[state, state_next] += pi[state, action]\n", "\n", "\n", " \n", "# print(f\"Transition matrix P_pi is:\\n {P}\")\n", "\n", "# Compute V_pi by solving the linear equation. \n", "V = np.linalg.inv(np.identity(37) - gamma * P) @ R\n", "V = np.concatenate((V, np.zeros(11))) # V=0 at terminal states\n", "visualize_value_function(V, 'Value Function V^\\pi')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Fitted Monte Carlo policy evaluation for $V^\\pi$ for a given $\\pi$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import torch\n", "import torch.nn as nn\n", "import torch.optim as optim\n", "from tqdm import trange\n", "\n", "class ValueNetwork(nn.Module):\n", " def __init__(self, input_dim=2, fourier_dim=32, hidden_dim=128):\n", " super().__init__()\n", " B = torch.randn(fourier_dim, input_dim) * 10 # Frequency matrix\n", " self.register_buffer('B', B) # B is not trained\n", "\n", " self.net = nn.Sequential(\n", " nn.Linear(2 * fourier_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, 1)\n", " )\n", "\n", " def fourier_features(self, x):\n", " # x: (batch_size, 2)\n", " proj = 2 * np.pi * x @ self.B.T\n", " return torch.cat([torch.sin(proj), torch.cos(proj)], dim=-1)\n", "\n", " def forward(self, x): # x in R^2\n", " phi = self.fourier_features(x)\n", " return self.net(phi).squeeze(-1)\n", "\n", "\n", "gamma = 1.0\n", "N = 1024\n", "batchsize = 64\n", "learning_rate = 1e-3\n", "\n", "Vnet = ValueNetwork() #V_\\phi \\approx V^\\pi\n", "optimizer = optim.Adam(Vnet.parameters(), lr=learning_rate)\n", "loss_fn = nn.MSELoss()\n", "\n", "\n", "for _ in range(N):\n", " batch = []\n", " for _ in range(batchsize):\n", " s0 = np.random.randint(37) # random starting state\n", " rewards = []\n", " agent_pos = get_position(s0)\n", " while True: #simulate full trajectory\n", " action = np.random.randint(4)\n", " agent_pos = move_agent(agent_pos, action)\n", " s = get_state(agent_pos)\n", " rewards.append(get_reward(s))\n", " if s == goal_state or s in cliff_states:\n", " break\n", " G = sum(gamma ** k * r for k, r in enumerate(rewards))\n", " x, y = get_position(s0)\n", " batch.append(((x / 3.0, y / 11.0), G)) # normalize (x,y) such that x/3\\in [0,1] and y/11\\in[0,1]\n", " xy = torch.tensor([pos for pos, _ in batch], dtype=torch.float32)\n", " G_vals = torch.tensor([G for _, G in batch], dtype=torch.float32)\n", " loss = loss_fn(Vnet(xy), G_vals)\n", " optimizer.zero_grad()\n", " loss.backward()\n", " optimizer.step()\n", "\n", "# Predict value for all 48 states\n", "grid_input = torch.tensor([\n", " (x / 3.0, y / 11.0) for x in range(4) for y in range(12)\n", "], dtype=torch.float32)\n", "\n", "with torch.no_grad():\n", " predicted_V = Vnet(grid_input).numpy()\n", "predicted_V[-11:] = 0 # Set terminal state values to 0\n", "\n", "visualize_value_function(predicted_V, title=\"Value Function V^\\pi (NN Approx)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Fitted k-step TD policy evaluation for V" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import torch\n", "import torch.nn as nn\n", "import torch.optim as optim\n", "from tqdm import trange\n", "\n", "class ValueNetwork(nn.Module):\n", " def __init__(self, input_dim=2, fourier_dim=32, hidden_dim=128):\n", " super().__init__()\n", " B = torch.randn(fourier_dim, input_dim) * 10 # Frequency matrix\n", " self.register_buffer('B', B) # B is not trained\n", "\n", " self.net = nn.Sequential(\n", " nn.Linear(2 * fourier_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, 1)\n", " )\n", "\n", " def fourier_features(self, x):\n", " # x: (batch_size, 2)\n", " proj = 2 * np.pi * x @ self.B.T\n", " return torch.cat([torch.sin(proj), torch.cos(proj)], dim=-1)\n", "\n", " def forward(self, x): # x in R^2\n", " phi = self.fourier_features(x)\n", " return self.net(phi).squeeze(-1)\n", "\n", "\n", "gamma = 1.0\n", "k = 5\n", "N = 1024\n", "batchsize = 64\n", "learning_rate = 1e-4\n", "\n", "Vnet = ValueNetwork()\n", "optimizer = optim.Adam(Vnet.parameters(), lr=learning_rate)\n", "loss_fn = nn.MSELoss()\n", "\n", "\n", "for kkk in range(N):\n", " batch = []\n", " for _ in range(batchsize):\n", " s0 = np.random.randint(37) # random starting state\n", " agent_pos = get_position(s0)\n", " G = 0\n", " hit_terminal = False\n", " for t in range(k):\n", " action = np.random.randint(4)\n", " agent_pos = move_agent(agent_pos, action)\n", " s = get_state(agent_pos)\n", " G += gamma**t * get_reward(s)\n", " if s == goal_state or s in cliff_states:\n", " hit_terminal = True\n", " break\n", " if not hit_terminal:\n", " x, y = get_position(s)\n", " last_pos = (x / 3.0, y / 11.0) # normalize (x,y)\n", " G += gamma**k * Vnet(torch.tensor(last_pos)).detach() #stop gradient operator\n", " x, y = get_position(s0)\n", " init_pos = (x / 3.0, y / 11.0) # normalize (x,y)\n", " batch.append((init_pos, G))\n", " xy = torch.tensor([pos for pos, _ in batch], dtype=torch.float32)\n", " G_vals = torch.tensor([G for _, G in batch], dtype=torch.float32)\n", " loss = loss_fn(Vnet(xy), G_vals)\n", " optimizer.zero_grad()\n", " loss.backward()\n", " optimizer.step()\n", "\n", "# Predict value for all 48 states\n", "grid_input = torch.tensor([\n", " (x / 3.0, y / 11.0) for x in range(4) for y in range(12)\n", "], dtype=torch.float32)\n", "\n", "with torch.no_grad():\n", " predicted_V = Vnet(grid_input).numpy()\n", "predicted_V[-11:] = 0 # Set terminal state values to 0\n", "\n", "visualize_value_function(predicted_V, title=\"Value Function V^\\pi (NN Approx)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6. Policy gradient method (A2C)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|████████████████████████████████████| 10240/10240 [00:43<00:00, 237.10it/s]\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import torch\n", "import torch.nn as nn\n", "import torch.optim as optim\n", "import numpy as np\n", "from tqdm import trange\n", "\n", "\n", "\n", "class ValueNetwork(nn.Module):\n", " def __init__(self, input_dim=2, fourier_dim=32, hidden_dim=128):\n", " super().__init__()\n", " B = torch.randn(fourier_dim, input_dim) * 10 # Frequency matrix\n", " self.register_buffer('B', B) # B is not trained\n", "\n", " self.net = nn.Sequential(\n", " nn.Linear(2 * fourier_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, 1)\n", " )\n", "\n", " def fourier_features(self, x):\n", " # x: (batch_size, 2)\n", " proj = 2 * np.pi * x @ self.B.T\n", " return torch.cat([torch.sin(proj), torch.cos(proj)], dim=-1)\n", "\n", " def forward(self, x): # x in R^2\n", " phi = self.fourier_features(x)\n", " return self.net(phi).squeeze(-1)\n", "\n", " \n", "class PolicyNetwork(nn.Module):\n", " def __init__(self, input_dim=2, fourier_dim=32, hidden_dim=128, n_actions=4):\n", " super().__init__()\n", " B = torch.randn(fourier_dim, input_dim) * 10\n", " self.register_buffer('B', B)\n", "\n", " self.net = nn.Sequential(\n", " nn.Linear(2 * fourier_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, n_actions)\n", " )\n", "\n", " def fourier_features(self, x):\n", " proj = 2 * np.pi * x @ self.B.T\n", " return torch.cat([torch.sin(proj), torch.cos(proj)], dim=-1)\n", "\n", " def forward(self, x):\n", " phi = self.fourier_features(x)\n", " logits = self.net(phi)\n", " return torch.softmax(logits, dim=-1)\n", "\n", "# Initialize networks\n", "Vnet = ValueNetwork()\n", "Pnet = PolicyNetwork()\n", "\n", "value_optimizer = optim.Adam(Vnet.parameters(), lr=3e-4)\n", "policy_optimizer = optim.Adam(Pnet.parameters(), lr=3e-4)\n", "\n", "\n", "gamma = 1.0\n", "k = 5\n", "N = 10240\n", "\n", "s = goal_state\n", "for _ in trange(N):\n", " if s == goal_state or s in cliff_states: # if at terminal\n", " s0 = 36 # initial state\n", " else:\n", " s0 = s\n", " agent_pos = get_position(s0)\n", "\n", " hit_terminal = False\n", " dynamics = []\n", " for t in range(k):\n", " x0, y0 = agent_pos\n", " input_pos = torch.tensor([(x0 / 3.0, y0 / 11.0)], dtype=torch.float32)\n", "\n", " probs = Pnet(input_pos).squeeze(0)\n", " action = torch.multinomial(probs, 1).item()\n", "\n", " agent_pos = move_agent(agent_pos, action)\n", " s = get_state(agent_pos)\n", " \n", " reward = get_reward(s)\n", "\n", " dynamics.append( (input_pos,action,reward) )\n", "\n", " if s == goal_state or s in cliff_states:\n", " hit_terminal = True\n", " break\n", "\n", " loss_P, loss_V = torch.tensor(0.0), torch.tensor(0.0)\n", " Qhat = 0.0\n", " if not hit_terminal:\n", " x, y = get_position(s)\n", " last_pos = torch.tensor([(x / 3.0, y / 11.0)], dtype=torch.float32)\n", " Qhat = Vnet(last_pos).detach().item() \n", " for (state,action,r) in reversed(dynamics):\n", " Qhat = r + gamma*Qhat\n", " loss_P += - torch.log(Pnet(state)[0,action]) * (Qhat-Vnet(state).detach().item())\n", "# loss_P += - torch.log(Pnet(state)[0,action]) * (Qhat) #Try removing the baseline function\n", " loss_V += 0.5 * (Qhat - Vnet(state).squeeze(0))**2\n", " \n", " # Update policy network\n", " policy_optimizer.zero_grad()\n", " loss_P.backward()\n", " policy_optimizer.step()\n", " \n", " # Update value network\n", " value_optimizer.zero_grad()\n", " loss_V.backward()\n", " value_optimizer.step()\n", "\n", "\n", "# Visualize optimal value function\n", "\n", "# Predict value for all 48 states\n", "grid_input = torch.tensor([\n", " (x / 3.0, y / 11.0) for x in range(4) for y in range(12)\n", "], dtype=torch.float32)\n", "\n", "with torch.no_grad():\n", " predicted_V = Vnet(grid_input).numpy()\n", "predicted_V[-11:] = 0 # Set terminal state values to 0\n", "\n", "visualize_value_function(predicted_V, title=\"Optimal Value Function (A2C)\")\n", "\n", "\n", "# Visualize optimal policy\n", "with torch.no_grad():\n", " pi = torch.zeros((4, 48))\n", " for state in range(48):\n", " x, y = get_position(state)\n", " input_pos = torch.tensor([(x / 3.0, y / 11.0)], dtype=torch.float32)\n", " probs = Pnet(input_pos).squeeze(0)\n", " pi[:, state] = probs\n", "visualize_policy(pi.numpy(), \"Optimal policy (A2C)\")\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7. Proximal policy optimization (PPO)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████| 128/128 [00:16<00:00, 7.91it/s]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Agent has seen +100 reward\n" ] }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import torch\n", "import torch.nn as nn\n", "import torch.optim as optim\n", "import numpy as np\n", "from tqdm import trange\n", "\n", "\n", "\n", "class ValueNetwork(nn.Module):\n", " def __init__(self, input_dim=2, fourier_dim=32, hidden_dim=128):\n", " super().__init__()\n", " B = torch.randn(fourier_dim, input_dim) * 10 # Frequency matrix\n", " self.register_buffer('B', B) # B is not trained\n", "\n", " self.net = nn.Sequential(\n", " nn.Linear(2 * fourier_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, 1)\n", " )\n", "\n", " def fourier_features(self, x):\n", " # x: (batch_size, 2)\n", " proj = 2 * np.pi * x @ self.B.T\n", " return torch.cat([torch.sin(proj), torch.cos(proj)], dim=-1)\n", "\n", " def forward(self, x): # x in R^2\n", " phi = self.fourier_features(x)\n", " return self.net(phi).squeeze(-1)\n", "\n", " \n", "class PolicyNetwork(nn.Module):\n", " def __init__(self, input_dim=2, fourier_dim=32, hidden_dim=128, n_actions=4):\n", " super().__init__()\n", " B = torch.randn(fourier_dim, input_dim) * 10\n", " self.register_buffer('B', B)\n", "\n", " self.net = nn.Sequential(\n", " nn.Linear(2 * fourier_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, hidden_dim),\n", " nn.ReLU(),\n", " nn.Linear(hidden_dim, n_actions)\n", " )\n", "\n", " def fourier_features(self, x):\n", " proj = 2 * np.pi * x @ self.B.T\n", " return torch.cat([torch.sin(proj), torch.cos(proj)], dim=-1)\n", "\n", " def forward(self, x):\n", " phi = self.fourier_features(x)\n", " logits = self.net(phi)\n", " return torch.softmax(logits, dim=-1)\n", "\n", "# Initialize networks\n", "Vnet = ValueNetwork()\n", "Pnet = PolicyNetwork()\n", "\n", "value_optimizer = optim.Adam(Vnet.parameters(), lr=1e-3)\n", "policy_optimizer = optim.Adam(Pnet.parameters(), lr=1e-3)\n", "\n", "\n", "gamma = 1.0\n", "N = 128\n", "clip_epsilon = 0.2\n", "ppo_epochs = 4\n", "trajectory_batch_size = 32\n", "PPO_batch_size = 32\n", "\n", "reward_flag = False\n", "\n", "for _ in trange(N):\n", " trajectory_batch = []\n", " for _ in range(trajectory_batch_size):\n", " trajectory = []\n", " s0 = np.random.randint(37) # random starting state\n", "# s0 = 36 # initial state\n", "\n", " agent_pos = get_position(s0)\n", "\n", " \n", " while True:\n", " x0, y0 = agent_pos\n", " input_pos = torch.tensor([(x0 / 3.0, y0 / 11.0)], dtype=torch.float32)\n", "\n", " probs = Pnet(input_pos).squeeze(0)\n", " action = torch.multinomial(probs, 1).item()\n", "\n", " agent_pos = move_agent(agent_pos, action)\n", " s = get_state(agent_pos)\n", "\n", " reward = get_reward(s)\n", " if reward==100:\n", " reward_flag = True\n", "\n", " #old probabilities\n", " prob_old = probs[action].detach()\n", "\n", " trajectory.append( (input_pos,action,prob_old,reward) )\n", "\n", " if s == goal_state or s in cliff_states:\n", " hit_terminal = True\n", " break\n", "\n", "\n", " # compute advantage for dynamics into (s,a,prob_old,Q,A)\n", " Qhat = 0.0\n", " dynamics_QA = []\n", " for ind,(state, action, prob_old, r) in enumerate(reversed(trajectory)):\n", " Qhat = r + gamma*Qhat\n", " dynamics_QA.append( (state, action, prob_old, Qhat, Qhat - Vnet(state).detach().item()) )\n", " trajectory_batch += dynamics_QA\n", " \n", " states = torch.cat([state for state,_,_,_,_ in trajectory_batch])\n", " actions = torch.tensor([action for _,action,_,_,_ in trajectory_batch])\n", " old_probs = torch.stack([pb for _,_,pb,_,_ in trajectory_batch])\n", " returns = torch.tensor([Q for _,_,_,Q,_ in trajectory_batch])\n", " advantages = torch.tensor([A for _,_,_,_,A in trajectory_batch])\n", "\n", " \n", " for _ in range(ppo_epochs):\n", " idx = torch.randperm(len(states))\n", " for i in range(0, len(states), PPO_batch_size):\n", " b_idx = idx[i:i+PPO_batch_size]\n", " b_states = states[b_idx]\n", " b_actions = actions[b_idx]\n", " b_old_probs = old_probs[b_idx]\n", " b_advantages = advantages[b_idx]\n", " b_returns = returns[b_idx]\n", "\n", " # Ratio\n", " ratio = Pnet(b_states)[range(len(b_states)), b_actions] / b_old_probs\n", "\n", " # Clipped surrogate objective\n", " surr1 = ratio * b_advantages\n", " surr2 = torch.clamp(ratio, 1 - clip_epsilon, 1 + clip_epsilon) * b_advantages\n", " policy_loss = -torch.min(surr1, surr2).mean()\n", "\n", " # Value function loss\n", " value_preds = Vnet(b_states).squeeze()\n", " value_loss = 0.5 * (b_returns - value_preds).pow(2).mean()\n", "\n", " # Optimize policy\n", " policy_optimizer.zero_grad()\n", " policy_loss.backward()\n", " policy_optimizer.step()\n", "\n", " # Optimize value function\n", " value_optimizer.zero_grad()\n", " value_loss.backward()\n", " value_optimizer.step()\n", "\n", "\n", " \n", "if not reward_flag:\n", " print(\"Agent has never seen +100 reward\")\n", "else:\n", " print(\"Agent has seen +100 reward\")\n", " \n", "# Visualize optimal value function\n", "\n", "# Predict value for all 48 states\n", "grid_input = torch.tensor([\n", " (x / 3.0, y / 11.0) for x in range(4) for y in range(12)\n", "], dtype=torch.float32)\n", "\n", "with torch.no_grad():\n", " predicted_V = Vnet(grid_input).numpy()\n", "predicted_V[-11:] = 0 # Set terminal state values to 0\n", "\n", "visualize_value_function(predicted_V, title=\"Optimal Value Function (PPO)\")\n", "\n", "\n", "# Visualize optimal policy\n", "with torch.no_grad():\n", " pi = torch.zeros((4, 48))\n", " for state in range(48):\n", " x, y = get_position(state)\n", " input_pos = torch.tensor([(x / 3.0, y / 11.0)], dtype=torch.float32)\n", " probs = Pnet(input_pos).squeeze(0)\n", " pi[:, state] = probs\n", "visualize_policy(pi.numpy(), \"Optimal policy (PPO)\")\n" ] } ], "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": "3.9.2" } }, "nbformat": 4, "nbformat_minor": 2 }