diff --git a/M2/Reinforcement Learning/Lab 3 - Solving Maze Game with Dynamic Programming.ipynb b/M2/Reinforcement Learning/Lab 3 - Solving Maze Game with Dynamic Programming.ipynb
index e3b2385..9260220 100644
--- a/M2/Reinforcement Learning/Lab 3 - Solving Maze Game with Dynamic Programming.ipynb	
+++ b/M2/Reinforcement Learning/Lab 3 - Solving Maze Game with Dynamic Programming.ipynb	
@@ -30,7 +30,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 77,
+   "execution_count": 1,
    "id": "100d1e0d",
    "metadata": {},
    "outputs": [],
@@ -96,7 +96,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 78,
+   "execution_count": 2,
    "id": "f91cda05",
    "metadata": {},
    "outputs": [],
@@ -124,7 +124,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 79,
+   "execution_count": 3,
    "id": "24d7b74c-66c7-4615-b5e6-c2973a975fc9",
    "metadata": {},
    "outputs": [
@@ -148,7 +148,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 80,
+   "execution_count": 4,
    "id": "26c821d3-2362-4b60-8c77-3d09296d130d",
    "metadata": {},
    "outputs": [
@@ -198,7 +198,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 81,
+   "execution_count": 5,
    "id": "7116044b-c134-43de-9f30-01ab62325300",
    "metadata": {},
    "outputs": [],
@@ -229,7 +229,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 82,
+   "execution_count": 6,
    "id": "a1258de4",
    "metadata": {},
    "outputs": [
@@ -290,7 +290,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 83,
+   "execution_count": 7,
    "id": "68744dd6-7278-4c20-8b82-34212685352f",
    "metadata": {},
    "outputs": [
@@ -362,7 +362,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 84,
+   "execution_count": 8,
    "id": "fc61ceef-217c-47f4-8eba-0353369210db",
    "metadata": {},
    "outputs": [
@@ -472,7 +472,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 85,
+   "execution_count": 9,
    "id": "f7f0b8e4-1f48-4d03-9e5f-a47e59c3e827",
    "metadata": {},
    "outputs": [],
@@ -484,7 +484,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 86,
+   "execution_count": 10,
    "id": "3773781c-a0cd-48db-967b-d4b432d17046",
    "metadata": {},
    "outputs": [
@@ -516,7 +516,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 87,
+   "execution_count": 11,
    "id": "4b06da5e-bc63-48e5-a336-37bce952443d",
    "metadata": {},
    "outputs": [],
@@ -595,7 +595,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 88,
+   "execution_count": 12,
    "id": "610253e7-f3f7-4a30-be3e-2ec5a1e2ed04",
    "metadata": {},
    "outputs": [],
@@ -626,7 +626,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 89,
+   "execution_count": 13,
    "id": "7a51f242-fe4e-4e74-8a1f-a8df32b194b8",
    "metadata": {},
    "outputs": [],
@@ -654,7 +654,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 90,
+   "execution_count": 14,
    "id": "49d54d1f-dc29-45b6-ad31-ad0e848f920d",
    "metadata": {},
    "outputs": [],
@@ -697,7 +697,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 91,
+   "execution_count": 15,
    "id": "c70885b4-a301-42f2-ab70-2901d941cde7",
    "metadata": {},
    "outputs": [],
@@ -723,7 +723,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 92,
+   "execution_count": 16,
    "id": "eca4c571-39c7-468b-af86-0bab9489415e",
    "metadata": {},
    "outputs": [],
@@ -754,7 +754,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 93,
+   "execution_count": 17,
    "id": "2d03276b-e206-4d1f-9024-f6948ca61523",
    "metadata": {},
    "outputs": [],
@@ -817,7 +817,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 94,
+   "execution_count": 18,
    "id": "341fe630-8f87-4773-84ad-92d3516e53e2",
    "metadata": {},
    "outputs": [
@@ -966,7 +966,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 95,
+   "execution_count": 19,
    "id": "3a05f8bc-2b8f-4a4c-9931-6d28c3b0db35",
    "metadata": {},
    "outputs": [],
@@ -1035,7 +1035,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 96,
+   "execution_count": 20,
    "id": "b4a44e38",
    "metadata": {},
    "outputs": [
@@ -1064,7 +1064,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 97,
+   "execution_count": 21,
    "id": "c5f559b2-452a-477c-a1fa-258b40805670",
    "metadata": {},
    "outputs": [
@@ -1108,7 +1108,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 98,
+   "execution_count": 22,
    "id": "4c428327",
    "metadata": {},
    "outputs": [
@@ -1182,7 +1182,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 99,
+   "execution_count": 23,
    "id": "c1ab67f0-bd5e-4ffe-b655-aec030401b78",
    "metadata": {},
    "outputs": [],
@@ -1267,7 +1267,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 100,
+   "execution_count": 24,
    "id": "d452681c-c89c-41cc-95dc-df75993b0391",
    "metadata": {},
    "outputs": [
@@ -1296,7 +1296,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 101,
+   "execution_count": 25,
    "id": "929707e6-3022-4d86-96cc-12f251f890a9",
    "metadata": {},
    "outputs": [
@@ -1447,15 +1447,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 102,
+   "execution_count": 26,
    "id": "998e3005-9a8b-4759-a008-aeccedd25924",
    "metadata": {},
    "outputs": [],
    "source": [
     "def policy_improvement(\n",
-    "    V: np.ndarray, P: np.ndarray, R: np.ndarray, gamma: float,\n",
+    "    V: np.ndarray,\n",
+    "    P: np.ndarray,\n",
+    "    R: np.ndarray,\n",
+    "    gamma: float,\n",
     ") -> np.ndarray:\n",
-    "    \"\"\"Given a value function V, compute the improved policy.\n",
+    "    \"\"\"Given a value function V, output a greedy policy.\n",
     "\n",
     "    Args:\n",
     "        V: array of shape (n_states,)\n",
@@ -1465,21 +1468,30 @@
     "\n",
     "    Returns:\n",
     "        policy: array of shape (n_states,), with values in {0,1,2,3}\n",
+    "        n_states = len(R)\n",
     "\n",
     "    \"\"\"\n",
     "    n_actions = P.shape[0]\n",
-    "    policy = np.zeros(n_states, dtype=int)\n",
-    "    for s in range(n_states):  # We decide the best action separately for each state.\n",
-    "        # For terminal states, action choice is irrelevant; keep 0\n",
+    "    policy = np.zeros(\n",
+    "        n_states,\n",
+    "        dtype=int,\n",
+    "    )\n",
+    "\n",
+    "    for s in range(n_states):\n",
     "        if is_terminal(s):\n",
+    "            policy[s] = 0\n",
     "            continue\n",
     "\n",
     "        Q_values = np.zeros(n_actions)\n",
     "        for a in range(n_actions):\n",
-    "            Q_values[a] = R[s] + gamma * np.dot(P[a, s, :], V)\n",
-    "        policy[s] = np.argmax(Q_values)\n",
-    "\n",
-    "    return policy"
+    "            Q_values[a] = R[s] + gamma * np.dot(\n",
+    "                P[a, s, :],\n",
+    "                V,\n",
+    "            )\n",
+    "        policy[s] = int(\n",
+    "            np.argmax(Q_values),\n",
+    "        )\n",
+    "    return policy\n"
    ]
   },
   {
@@ -1513,7 +1525,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 103,
+   "execution_count": 27,
    "id": "8b6c2216",
    "metadata": {},
    "outputs": [],
@@ -1550,13 +1562,8 @@
     "    policy = initial_policy\n",
     "\n",
     "    for _it in range(max_iter):\n",
-    "        # Compute the value function V^pi for the current policy.\n",
     "        V = policy_evaluation(policy, P, R, gamma, theta)\n",
-    "\n",
-    "        # Improve the policy by acting greedily with respect to V.\n",
     "        new_policy = policy_improvement(V, P, R, gamma)\n",
-    "\n",
-    "        # Check whether the policy has stopped changing.\n",
     "        if np.array_equal(new_policy, policy):\n",
     "            break\n",
     "        policy = new_policy\n",
@@ -1576,7 +1583,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 104,
+   "execution_count": 28,
    "id": "e12d62ee-3324-4e1b-b5e2-6be96404ac2c",
    "metadata": {},
    "outputs": [
@@ -1584,15 +1591,19 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Optimal policy found by Policy Iteration:\n",
-      "[1 1 1 2 2 0 2 2 3 0 1 2 0 3 1 1 0 0 0 0 1 0]\n"
+      "[0 3 3 2 1 3 2 1 1 0 0 2 3 0 3 3 1 2 0 3 2 1]\n",
+      "[1 1 1 2 2 0 2 2 3 0 1 2 0 3 1 1 0 0 0 0 1 0]\n",
+      "Optimal value function:\n",
+      "[ 11.62   12.311  13.095  13.901  13.875  11.596  14.756  15.6    14.699\n",
+      "  10.921  15.631  16.589  10.263   9.633  17.643  18.804  20.      9.633\n",
+      "   8.156 -20.     15.522  17.679]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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ZupJq23fgxUiXXnS9+uqrTdPORx99ZE53tTlE+y+7dAPVo+3p06ebNmR9b/dCdG3SZjG9y1nv99CjL20q0w0zsG97TWjbtfb51yMgLbceuesduHp67/Y3v+qqq0xf7/Hjx5v5pvXXz37nnXfM6XVl864qejT03HPPmffUHc5tt91mdj56ZKRfpxK849SzCm0KUEfa7KTNMbrD1OYAXQ+0LVk3NG0aCOxHrzug+++/39xophcLta1fy6xnXTW9GKlngjqf9aKi9rF3N3K95+JwTaMuXb8effRRswy0LLrT0AvL2l8++Ghc19Pf/e53Jtzuvvtu69H60ZqPodDl+8orr5iL5f/+97/N/NGzJt2mdD4F3j+hZxQaenp9Qj9fd+w1oQeO2qlE55/ORz1b0bMwHfTgUFsedF+hF6r1LGPnzp1m+9d7UT799NOQWjH0a2N0fujn6Gu1Plr2QLr+a6joMtUDE72eoZ1aKqvXb37zGxNg2olAOy7oGaSeubhnVjW5bhcxThTTfuza5VL7u2tf5NatW5vHa9eurbIbpHZf1C6gTZo0Mf2gtf/6vn37yk27YcMG089au7fqa9yuoVV1jw3spmfru+52c3vsscfKxm3bts30/W7WrJnp6z148GDnm2++qdDVrzrdY7V7r/bpvvzyy03ff+2Dr+8V2C1V7d271/Tf1i6rOv+0q6CWLbhrYij3UagPP/zQSU5ONvNWy6DdNwO7k7p27NhhupBqn/1QVdU9Vi1evNjp0aOHWV4JCQnmfhBdzsH03oukpCTT9VXvfdFuiVV1jw1edpXNB7VixQqnS5cu5j31XotZs2ZV+p6V0a6SHTt2dD7++GPTJVK72upnaD//qgwYMKBCd+zDqao+NZmPoXSPdbuT6r0S2m3a3TZ1u9P1MpjbRT0zMzPkOlW23ek8cZdF8Pajn6vdfLUcWh6910nvL3rrrbcq1G316tUVPk+7fd92223m3gXtutqvXz+zn6hsnXjxxRfNuuB2k3a3k8rm086dO8veV8ut3XiDu4pXtt9wVdUlONyiOiiqw9143fsI/MoNimimy0Bv7tKbDFE9eu/G6aef7viJ3uCpBxfujWvwnqi8RgFv06860Lbd2uwGWRdoG7s2IfppvukFYW3+1esa7nUGeE9UXqOAN+mNT3rh8uGHHzY3qlX23UuoSK9Zabu1dgDQ6xLV+R6kaKX3Lmgbv7bJa4eUyr7LCt5BUKDW6BcT6j0jPXr0qLWunXWB3qGrHQT0hivtxKF383qdHjBoZxS9yPv000+bi8Dwrhhtf4p0IQAA0YtrFAAAK4ICAFA71yiKiorM4NLb0vUuab0hJVxfiQEAqB161UG/4kdvCg3+4sIaB4X+ypb7m7UAAH/4+uuvy37p74gvZgefUejt69pLQ7/DpTa/aiCSNFX19n3tseGHb3b1W30UdfIG6hT99GuF9Ktd9HurDvctxSGfUeh3mugQTEPCLz8qriuC3hSk9fHDiuC3+ijq5A3UyTtCuXTAxWwAgBVBAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAABWBAUAwIqgAABYERQAACuCAgBgRVAAAKwICgCAFUEBALAiKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACsCAoAgBVBAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAABWBAUAwIqgAABYERQAACuCAgBgRVAAAKwICgCAFUEBALAiKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACs6oU6YVFRkRlc+fn55m9sbKwZ/MCtB/WJXtTJG6hT9KtOPWIcx3FCmTA9PV0yMjIqjM/MzJT4+PjqlRAAEFGFhYWSkpIieXl5kpCQUDtBUdkZRWJiouzYsUNatGghflBSUiJZWVmSnJws9evXF6/zW338Xqfs7GwpLS0VvxytJiUlsZyiWHFxsUyePDmkoAi56SkuLs4MwXQl8MuK4Nc6+a0+fq2T7nz8sAMKxHKKXtWpgz8a2wAARw1BAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAABWBAUAwIqgAABYERQAACuCAgBgRVAAALwZFH/O/rP0e62fnPD4CVL/ofrSdGpTOXXGqdJ7bm8Z/e5oeW/ze5EuInxs9OjR0rp160gXA4fBcgqPkH/hLpyG/W2YvPrZq+XG5Rflm+HLPV/Kiq0rZGveVul3Rr+IlRH+pj8PuXPnzkgXA4fBcqqjQbFw88JyIdGlTRfpd3o/adygseQW5sqaHWvko20fRbSMAFCXRF1QLNqyqOz/ZzQ/Q1bduUqOiT2m3DR6ZrF251rxA/2B83Hjxsl9990n7dq1Ez/wY52AuizqrlHsL91f9v89P+0xTU3BEuISpMfJPcQP1qxZI7Nnz5aePXvKli1bxA/8WCegLou6oLigzQVl//++8Hs589kzpcsLXeSuf9wlL/7nRdn8w2bxk+7du8v8+fMlNzfX7Fg3btwoXufHOgF1WdQ1Pd103k0yc/VM+fibj83jUqfUXJfQwXXJyZfIs798Vjq17iTRbMKECbJ79+6Qpk1KSpLVq1dLr169ZMWKFdKhQweJRn6sEwCPBUW92HqydNhSeeTDR+SP//2j7PyxYo+GD7/6UJJfTZZ1I9ZJq0atJFrNmTNHtm/fXq3XaA+OnJycqN2p+rFOADzW9KSaxDWRKZdOkR2pOyT77mx56eqX5JZOt0iTBk3KptEeUMFdaKPNtm3bxHGcww4FBQXSu3dv85qMjAwZOHCgRCs/1gmAB4PCFRMTIx2P7yi3d75d5l47Vz67+zOJjTlU5M93fS5et3fvXunfv78sX75cpk6dKhMnThSv82qd9CL8rFmzKoxfv369zJgxIyJlQkUsp/CLuqanlz95WX7a/5PceO6NpndToEb1G5mg0OsWqtmxzcTrNm/eLGvXrpXp06fL2LFjxQ+8Wqfx48fLwoULpbCwsGzcunXrpG/fvrJv3z4ZNGiQJCYmRrSMYDlFQtQFxRd7vpCMFRky5r0x5qL1+SecL80bNpdd+3bJWzlvles+2/+M/uJ1nTt3NjvWli1bil94tU5vvPGGDBgwQFJTU6VVq4PXvvr06WPuC1m0aBE7nyjBcgq/qAsKl55VLP7fYjNU5tcX/Fp6ndJL/MBrO1S/1qlJkybmSPWqq66SZcuWmXH79++XxYsXS9euXSNdPPyM5RR+URcUY7qPkXOPP1eWfrFUPt7xsXxb8K3k/pgrB5wD0iq+lXQ5sYu5sD3o7EGRLip8qFGjRrJgwQK55pprTFt4VlaWOUNCdGE51fGg0OsO151znRmASGjYsKFpwkB0YzmFT1T3egIARB5BAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAABWBAUAwIqgAABYERQAACuCAgBgRVAAAKwICgCAFUEBAKidn0ItKioygys/P9/8LSkpMYMfuPWgPtHLz3WKjfXPcZtbF5ZT9KpOPWIcx3FCmTA9PV0yMjIqjM/MzJT4+PjqlRAAEFGFhYWSkpIieXl5kpCQUDtnFGlpaTJu3LhyZxSJiYmSk5MjDRo0EL8kbFJSkiQnJ0v9+vXFD0dAWVlZkp2dLaWlpeIHfltGgcuJOkW3Ep9tT8XFxSFPG3JQxMXFmSGYzjA/zLRAumL7ZeVWLCNvoE7eUOqT7ak6dfBHYxsA4KghKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACsCAoAgBVBAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQRFm+/fvl6FDh8pZZ50lmzZtinRxUIXRo0dL69atxU/8WCeEB0ER5p8eHDx4sPmd8Y0bN0rv3r1lw4YNkS4WKqG/I7xz507xEz/WCeFBUIRJUVGRDBo0SObNm1f2Q+YFBQUmLNatWxfp4gFAlQiKMBkyZIgsWLBA0tLSZODAgWbcokWLZN++fdKnTx/Ztm1bpIsIeOa3nlNTUyUnJyfSRakz6kW6AHXFmDFj5MILL5Tx48fLrbfeasZ1795dsrKyZP78+dK2bdtIFxGIegcOHJBhw4aZ5tvY2Fh57LHHIl2kOoGgCBNtYtIhWLdu3cwA4PAdQVJSUuTNN9+UESNGyLRp0yJdpDqDoADgCdoRRK/xNW3aVGJiYmTUqFEh9/Zq3779US+fnxEUADxxXWL58uVlvbdmzpwZ8muvv/56guIIcTEbQNTT6xFLliyR5s2bS7NmzWTVqlXiOE5IQ2VNvqgeggL42Zo1a2TWrFkVxq9fv15mzJghXuSnOl1wwQWydOlSqVevniQnJ8vKlSsjXaQ6g6Yn4GfaI23hwoVSWFhYNk7vcenbt6/pxqz3wSQmJoqX+K1OnTp1kmXLlsmll15qzjAuvvjiSBepTiAogJ+98cYbMmDAANNHv1WrVmac3uOid9TrPS9e2qH6uU5JSUkm7Fq2bBnpotQZND0BP2vSpIk5+tYdaW5ublmXzMWLF5t7XrzIj3VShER4ERRAgEaNGpk76LUNvEWLFqZ5o2vXruJlfqwTwoumpwiYO3euGRCdGjZsaJpl/MSPdUL4cEYBALAiKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACsCAoAgBVBAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAAC181OoRUVFZnDl5+ebv7GxsWbwA7ceJSUl4gduPfyyfPy4jALr4sc6TZs2TUpLS8Uv615SUpJvtqfq1CPGcRwnlAnT09MlIyOjwvjMzEyJj4+vXgkBABFVWFgoKSkpkpeXJwkJCbVzRpGWlibjxo0rd0aRmJgoOTk50qBBA/HTEUNycrLUr19f/HBUl5WVJdnZ2b47qvPLMgpcTn6skx/XvWyf1Km4uDjkaUMOiri4ODME0xnmh5kWSDdWv2ywimXkDX6skx/XvVKf1Kk6dfBHYxsA4KghKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACsCAoAgBVBAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQRFm+/fvl6FDh8pZZ50lmzZtinRxUIeMHj1aWrduHeliwIMIijD/9ODgwYPN74xv3LhRevfuLRs2bIh0sVBH6G8j79y5M9LFgAcRFGFSVFQkgwYNknnz5pX9kHlBQYEJi3Xr1kW6eABQJYIiTIYMGSILFiyQtLQ0GThwoBm3aNEi2bdvn/Tp00e2bdsW6SLiMGeDI0eOlK1bt0a6KEDYERRhMmbMGJk8ebJMmTKlbFz37t0lKytLhg8fLm3bto1o+WC3Zs0amT17tvTs2VO2bNkS6eIAYVUvvB9Xd2kTkw7BunXrZgZENw31+fPnyzXXXGPCYunSpdKhQ4dIFwsIC4ICdd6ECRNk9+7dIU2blJQkq1evll69esmKFSsIC9QJBAXqvDlz5sj27dur9RrtPZSTk0NQoE7gGgXqPO1I4DjOYQe3l5rKyMgo65QA+B1BAYRg79690r9/f1m+fLlMnTpVJk6cKF65CD9r1qwK49evXy8zZsyISJngPTQ9ASHYvHmzrF27VqZPny5jx44Vrxg/frwsXLhQCgsLy8bpfTt9+/Y1XbP13p7ExMSIlhHRj6AAQtC5c2cTFi1bthQveeONN2TAgAGSmpoqrVq1MuP0vh29L0Tv4yEkEAqanoAQeS0kVJMmTcwZhYZDbm5u2feNLV682HT5BUJBUAA+16hRI/OtAMnJydKiRQtZsmSJdO3aNdLFgocQFBEwd+5c04sGCJeGDRuapqbvv//eNKMB1UFQAACsCAoAgBVBAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAABWBAUAwIqgAABYERQAACuCAgBgRVAAAKwICgCAVT0JUVFRkRlc+fn55m9sbKwZ/MCtR0lJifiBW4/U1FSpX7+++KVOWVlZMm3aNCktLRW/rHdJSUm+We/8vu6l+qROu3btkilTpoQ0bYwT4o83p6enS0ZGRoXxmZmZEh8fX/1SAgAiprCwUFJSUiQvL08SEhJqJygqO6NITEyU3//+99KgQQPx05FdcnKyL44Y3CMgv9QnsE7Z2dm+O6Pw43KiTtF9RtGmTZuQgiLkpqe4uDgzBNON1S8brEtXAj+sCH6tj2K98wbqFL2qUwd/XFwAABw1BAUAwIqgAABYERQAACuCAgBgRVAAAKwICgCAFUEBALAiKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACsCAoAgBVBEWb79++XoUOHyllnnSWbNm2KdHEARIFdu0SmTRO5/HKRE08UOfZY/Q0gkTZtRHr2FLnvPpEPPhAJ7Wfmal/IP1yEI1dcXCxDhgyRefPmmce9e/eWpUuXmtAAUDe98ILIuHEiP/5Y8blvvz04aEg8/rjIjh0irVuHv4wERZjoz8hed911smDBAvOzg/pTsgUFBSYslixZIh07dox0EQGE2WOPifzud4cex8SI9Okj0r27SOPGIj/8IPLJJyIffijy00+RKydBESZ6JqEhkZaWJt988428/PLLsmjRIunXr5/06dNH1qxZI23bto10MQGEyfr1Imlphx63aCHy97+LXHxxxWkLCkRefVWkYUOJCK5RhMmYMWNk8uTJMmXKlLJx3bt3Nz/WPnz4cE+GhP5mdWpqquTk5ES6KKhBM+jIkSNl69at4hdeq9PTT4scOHDo8axZlYeE0rOLu+8WadpUIoKgCBNtYho/fnyF8d26dZOHHnpIvObAgQNy8803y/Tp02XOnDmRLg6qSc9gZ8+eLT179pQtW7aIH3itTkuWHPr/cceJDBokUYugQI16bt14442SmZkpI0aMkGnaXQOeomez8+fPl9zcXLNj3bhxo3id1+q0ffuh/7dvLxIbsDfesOHg9Yrg4dZbI1JUrlGg+gYPHmx6bjVt2lRiYmJk1KhRIb1u9OjR0l63CBxVEyZMkN27d4c0bVJSkqxevVp69eolK1askA4dOkg08mOdAmkIRDOCAtW+LrF8+XLz/7y8PJk5c2bIr73++usJijDQpsDtgYerIdi5c6e51hStO1U/1umkk0Q+//zg//Wv3iPhBsbxxx/sEaUmTRIpLIxcORVNT6iW2NhY0523efPm0qxZM1m1apU4jhPSoNdpcPRt27YtpOXhds9WGRkZMnDgQIlWfqzTpZce+r92g9UeT67mzUV++9uDQ6R6OgUiKFBtF1xwgblRsF69epKcnCwrV66MdJFQTXv37pX+/fubs8OpU6fKxIkTxeu8VqeRI0WOOebQ47vuOnjPRDQiKFAjnTp1kmXLlsmxxx5rzjDgLZs3b5a1a9eaXmv333+/+IHX6tSxo0hgh0e9A7trV5GrrhJJTxd5+GGRO+8Uyc+XiOMaBWpMLxquW7dOWrZsGemioJo6d+5sdqx+WnZerFNamkijRgfvzi4qOnhfxT/+cXCojN6UFwkEBY6IlzZK+H/ZebFO996rPQkPfufT4sUi2qtXO3jVry/SqpWIXovv0UPk6qs1DCNTRoIiAubOnWsGAFD6LbHau0mHaMQ1CgCAFUEBALAiKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACsCAoAgBVBAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAAC185vZRUVFZnDl5+ebv7GxsWbwA7ceJSUl4gduPfxSn8C6pKamSn399Xmf1CkrK8uXy8mPdZo2bZqUlpaK1xUXF4c8bYzjOE4oE6anp0tGRkaF8ZmZmRIfH1+9EgIAIqqwsFBSUlIkLy9PEhISaueMIi0tTcaNG1fujCIxMVFycnKkQYMG4pcziqSkJElOTvbF0ap7pOqX+ijq5A1+rlN2dnadO6MIOSji4uLMEExnmB9mWiBdsf2ycvuxPoo6eYMf61Tqk31edergj4sLAICjhqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAABWBAUAwIqgAABYERQAACuCAgBgRVAAAKwICgCAFUEBALAiKMJs//79MnToUDnrrLNk06ZN4geer9OWLSKNG4vExBwcLr9cJPiHH/VxcvKhaRo1Evn880iVGH5Y7zyEoAjzL0oNHjzY/Hzsxo0bpXfv3rJhwwbxMl/U6fTTRZ544tDjrCyRmTPLT/PssyKLFx96/PjjIu3bh6+M8N965yEERZgUFRXJoEGDZN68eWW/T1tQUGBW8HXr1okX+apOw4eLDBhw6PH994u4R6n6Vx+7+vcXufvu8JcR/lvvPIKgCJMhQ4bIggULzG+PDxw40IxbtGiR7Nu3T/r06SPbtm0Tr/FdnWbPFmnR4uD/CwtFhg3TvZLIzTeL7Nt3cHzz5iIvvRTRYtZ1vlvvPICgCJMxY8bI5MmTZcqUKWXjunfvbn6sffjw4dK2bVvxGt/VqU0bkeeeO/R41SqRbt1E/v3vQ+P0+RNPFD803YwcOVK2bt0qXuO79c4D6kW6AHWFnhbrEKxbt25m8CI/1kkGDxYZOlTkT386+Pizzw49l5Ii8qtfiR+sWbNGZs+eLfPnz5elS5fK6XqdxiN8ud5FOc4ogGB64VrPLgKdcELFC9wepkfgGhK5ubnSs2dPc0EYqApnFEAwbeP+4Yfy4/Txl1+KnH++RLsJEybI7t27Q5o2KSlJVq9eLb169ZIVK1ZIhw4djnr54D0EBRCopOTgxWu9iF3Z+I8/FomLk2g2Z84c2b59e7Ves3PnTsnJySEoUCmanoBAkyaJfPLJocf33HPo/9nZIr//vUQ77fXjOM5hB7dLqcrIyCjrQQQEIygA18qVItOmHXp8++0Hr1fcccehcdOni3zwgXjd3r17pX///rJ8+XKZOnWqTJw4MdJFQhQjKAD1448it9wicuDAwcennCLy1FMH/69/Tzvt4P9LSw9OV1AgXrZ582ZZu3atTJ8+Xe4PvJkQqARBAajUVN17Hvx/bKzIyy+LNGly8LF+D9Qrr4gcc8zBx198ITJ2rHhZ586dTViM9Xg9EB4EBbBwocjzzx96rDvPnj3LT9OjR/mv8dC7uBcsEC9r2bJlpIsAjyAoImDu3LnmYqKfeLpO+t1NWnZ30C/8q8zDD5ef7oorwl1S+Gm98xCCAgBgRVAAAKwICgCAFUEBALAiKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACsCAoAgBVBAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArOpJiIqKiszgys/PN39jY2PN4AduPUpKSsQP3Hr4pT6KOnmDn+sU67P9XShinBB/cDY9PV0yMjIqjM/MzJT4+PjqlRAAEFGFhYWSkpIieXl5kpCQUDtnFGlpaTJu3LhyZxSJiYmSk5MjDRo0EL8kbFJSkmRnZ0tpaal4nd/qo6iTN1Cn6FdcXBzytCEHRVxcnBmC6Qzzw0zzc538Vh9FnbyBOkWv6tTBH41tAICjhqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAABWBAUAwIqgAABYERQAACuCAgBgRVAAAKwICgCAFUEBALAiKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACsCAoAgBVBAQCwIigAAFYEBQDAiqAAAFgRFAAAK4ICAGBFUAAArAgKAIAVQQEAsCIoAABWBAUAwIqgAABYERQAACuCAgBgRVAAAKwICgCAFUEBALAiKAAAVgQFAMCKoAAAWBEUAAArggIAYEVQAACsCAoAgBVBAQCwIigAAFYEBQDAqp6EqKioyAyuvLw887ekpET8IjY2VgoLC6W4uFhKS0vF6/xWH0WdvIE6RT933+04zuEndkI0adIkfTcGBgYGBvHPsGXLlsPu/2P0n5qcUezZs0f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",
       "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
+       "<Figure size 640x480 with 2 Axes>"
       ]
      },
      "metadata": {},
@@ -1600,9 +1611,9 @@
     },
     {
      "data": {
-      "image/png": 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",
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",
       "text/plain": [
-       "<Figure size 640x480 with 2 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
      "metadata": {},
@@ -1610,11 +1621,23 @@
     }
    ],
    "source": [
-    "opt_policy, V = policy_iteration(random_policy, P, R, gamma)\n",
-    "print(\"Optimal policy found by Policy Iteration:\")\n",
+    "random_policy = rng.integers(low=0, high=len(ACTIONS), size=n_states)\n",
+    "print(random_policy)\n",
+    "\n",
+    "opt_policy, V_opt = policy_iteration(\n",
+    "    random_policy,\n",
+    "    P,\n",
+    "    R,\n",
+    "    gamma,\n",
+    "    theta=1e-6,\n",
+    "    max_iter=1000,\n",
+    ")\n",
     "print(opt_policy)\n",
-    "plot_policy(opt_policy, title=\"Optimal policy found by Policy Iteration\")\n",
-    "plot_values(V, title=\"Value function of the optimal policy\")"
+    "print(\"Optimal value function:\")\n",
+    "print(V_opt)\n",
+    "\n",
+    "plot_values(V_opt, title=\"Optimal value function (policy iteration)\")\n",
+    "plot_policy(opt_policy, title=\"Optimal policy (policy iteration)\")\n"
    ]
   },
   {
@@ -1650,7 +1673,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 105,
+   "execution_count": 29,
    "id": "293ba7fc-f9dc-41b0-ad78-677af1ac7e0f",
    "metadata": {},
    "outputs": [],
@@ -1688,37 +1711,41 @@
     "\n",
     "    \"\"\"\n",
     "    n_states = len(R)\n",
-    "    n_actions = len(P)\n",
+    "    n_actions = P.shape[0]\n",
     "    V = np.zeros(n_states)\n",
     "\n",
-    "    # Main value iteration loop\n",
     "    for _it in range(max_iter):\n",
     "        V_new = np.zeros_like(V)\n",
     "\n",
-    "        # Loop over all states\n",
     "        for s in range(n_states):\n",
     "            if is_terminal(s):\n",
     "                V_new[s] = R[s] / (1 - gamma)\n",
     "                continue\n",
     "\n",
-    "            Q_values = np.zeros(n_actions)\n",
+    "            Q_values = np.zeros(\n",
+    "                n_actions,\n",
+    "            )\n",
     "            for a in range(n_actions):\n",
-    "                Q_values[a] = R[s] + gamma * np.sum(P[a, s, :] * V)\n",
+    "                Q_values[a] = R[s] + gamma * np.dot(P[a, s, :], V)\n",
     "            V_new[s] = np.max(Q_values)\n",
     "\n",
     "        delta = np.max(np.abs(V_new - V))\n",
+    "        V = V_new\n",
     "        if delta < theta:\n",
     "            break\n",
     "\n",
-    "        V = V_new\n",
-    "    policy = policy_improvement(V, P, R, gamma)\n",
-    "\n",
+    "    policy = policy_improvement(\n",
+    "        V,\n",
+    "        P,\n",
+    "        R,\n",
+    "        gamma,\n",
+    "    )\n",
     "    return V, policy\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 106,
+   "execution_count": 30,
    "id": "9b6ff9d3-ccc9-4f35-a6c3-545aeed552f7",
    "metadata": {},
    "outputs": [
@@ -1799,7 +1826,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 107,
+   "execution_count": 31,
    "id": "cce78e3c-ca82-4002-9a8f-08af9457147c",
    "metadata": {},
    "outputs": [
@@ -1817,12 +1844,12 @@
       "Same policy? True\n",
       "Same policy? True\n",
       "Same policy? True\n",
-      "Policy Iteration - outer iterations: [1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000]\n",
-      "Value Iteration  - iterations: [100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000, 100000]\n",
-      "Mean PI iterations: 1000.0\n",
-      "Mean VI iterations: 100000.0\n",
-      "Mean PI runtime: 0.01876246929168701\n",
-      "Mean VI runtime: 0.006057476997375489\n"
+      "Policy Iteration - outer iterations: [3, 3, 2, 3, 4, 3, 3, 3, 3, 4]\n",
+      "Value Iteration  - iterations: [34, 34, 34, 34, 34, 34, 34, 34, 34, 34]\n",
+      "Mean PI iterations: 3.1\n",
+      "Mean VI iterations: 34.0\n",
+      "Mean PI runtime: 0.033542495701112784\n",
+      "Mean VI runtime: 0.007521004001318943\n"
      ]
     }
    ],
@@ -1838,20 +1865,74 @@
     "    max_iter: int = 1_000,\n",
     "    seed: int = 0,\n",
     ") -> tuple[np.ndarray, np.ndarray, int, float]:\n",
-    "    \"\"\"Policy Iteration with iteration count and runtime.\"\"\"\n",
-    "    start_time = time.time()\n",
-    "    rng = np.random.default_rng(seed)\n",
-    "    policy = rng.integers(low=0, high=len(ACTIONS), size=n_states)\n",
-    "    for _it in range(max_iter):\n",
-    "        V = policy_evaluation(policy, P, R, gamma, theta)\n",
+    "    \"\"\"Policy Iteration that counts the number of outer iterations and runtime.\n",
     "\n",
-    "        new_policy = policy_improvement(V, P, R, gamma)\n",
+    "    Args:\n",
+    "        P: array of shape (n_actions, n_states, n_states)\n",
+    "        R: array of shape (n_states,)\n",
+    "        gamma: discount factor\n",
+    "        theta: convergence threshold for policy evaluation\n",
+    "        max_iter: maximum number of outer iterations\n",
+    "        seed: random seed for initial policy\n",
+    "\n",
+    "    Returns:\n",
+    "        policy: optimal policy found\n",
+    "        V: value function of the optimal policy\n",
+    "        n_iterations: number of outer iterations until convergence\n",
+    "        runtime: total runtime in seconds\n",
+    "\n",
+    "    \"\"\"\n",
+    "    rng = np.random.default_rng(\n",
+    "        seed,\n",
+    "    )\n",
+    "    n_states = len(R)\n",
+    "    n_actions = P.shape[0]\n",
+    "\n",
+    "    policy = rng.integers(\n",
+    "        low=0,\n",
+    "        high=n_actions,\n",
+    "        size=n_states,\n",
+    "    )\n",
+    "\n",
+    "    t0 = time.perf_counter()\n",
+    "\n",
+    "    for it in range(max_iter):\n",
+    "        V = policy_evaluation(\n",
+    "            policy,\n",
+    "            P,\n",
+    "            R,\n",
+    "            gamma,\n",
+    "            theta=theta,\n",
+    "        )\n",
+    "\n",
+    "        new_policy = policy_improvement(\n",
+    "            V,\n",
+    "            P,\n",
+    "            R,\n",
+    "            gamma,\n",
+    "        )\n",
+    "\n",
+    "        if np.array_equal(\n",
+    "            new_policy,\n",
+    "            policy,\n",
+    "        ):\n",
+    "            runtime = time.perf_counter() - t0\n",
+    "            return (\n",
+    "                policy,\n",
+    "                V,\n",
+    "                it + 1,\n",
+    "                runtime,\n",
+    "            )\n",
     "\n",
-    "        if np.array_equal(new_policy, policy):\n",
-    "            break\n",
     "        policy = new_policy\n",
-    "    runtime = time.time() - start_time\n",
-    "    return policy, V, max_iter, runtime\n",
+    "\n",
+    "    runtime = time.perf_counter() - t0\n",
+    "    return (\n",
+    "        policy,\n",
+    "        V,\n",
+    "        max_iter,\n",
+    "        runtime,\n",
+    "    )\n",
     "\n",
     "\n",
     "def value_iteration_count(\n",
@@ -1861,33 +1942,72 @@
     "    theta: float = 1e-6,\n",
     "    max_iter: int = 100_000,\n",
     ") -> tuple[np.ndarray, np.ndarray, int, float]:\n",
-    "    \"\"\"Value Iteration with iteration count and runtime.\"\"\"\n",
-    "    start_time = time.time()\n",
+    "    \"\"\"Value Iteration that counts the number of iterations and runtime.\n",
+    "\n",
+    "    Args:\n",
+    "        P: array of shape (n_actions, n_states, n_states)\n",
+    "        R: array of shape (n_states,)\n",
+    "        gamma: discount factor\n",
+    "        theta: convergence threshold\n",
+    "        max_iter: maximum number of iterations\n",
+    "\n",
+    "    Returns:\n",
+    "        V: array of shape (n_states,)\n",
+    "            Approximation of the optimal value function V*.\n",
+    "        policy: array of shape (n_states,)\n",
+    "            Greedy policy derived from V.\n",
+    "        n_iterations: number of iterations until convergence\n",
+    "        runtime: total runtime in seconds\n",
+    "\n",
+    "    \"\"\"\n",
     "    n_states = len(R)\n",
-    "    n_actions = len(P)\n",
+    "    n_actions = P.shape[0]\n",
+    "\n",
     "    V = np.zeros(n_states)\n",
-    "    for _it in range(max_iter):\n",
+    "    t0 = time.perf_counter()\n",
+    "\n",
+    "    for it in range(max_iter):\n",
     "        V_new = np.zeros_like(V)\n",
+    "\n",
     "        for s in range(n_states):\n",
     "            if is_terminal(s):\n",
     "                V_new[s] = R[s] / (1 - gamma)\n",
     "                continue\n",
-    "            Q_values = np.zeros(n_actions)\n",
-    "            for a in range(n_actions):\n",
-    "                Q_values[a] = R[s] + gamma * np.sum(P[a, s, :] * V)\n",
-    "            V_new[s] = np.max(Q_values)\n",
-    "        delta = np.max(np.abs(V_new - V))\n",
-    "        if delta < theta:\n",
-    "            break\n",
-    "        V = V_new\n",
-    "    runtime = time.time() - start_time\n",
-    "    policy = policy_improvement(V, P, R, gamma)\n",
     "\n",
-    "    return V, policy, max_iter, runtime\n",
+    "            Q = np.zeros(n_actions)\n",
+    "            for a in range(n_actions):\n",
+    "                Q[a] = R[s] + gamma * np.dot(P[a, s, :], V)\n",
+    "            V_new[s] = np.max(Q)\n",
+    "\n",
+    "        delta = np.max(np.abs(V_new - V))\n",
+    "        V = V_new\n",
+    "\n",
+    "        if delta < theta:\n",
+    "            runtime = time.perf_counter() - t0\n",
+    "            policy = policy_improvement(V, P, R, gamma)\n",
+    "            return (\n",
+    "                V,\n",
+    "                policy,\n",
+    "                it + 1,\n",
+    "                runtime,\n",
+    "            )\n",
+    "\n",
+    "    runtime = time.perf_counter() - t0\n",
+    "    policy = policy_improvement(\n",
+    "        V,\n",
+    "        P,\n",
+    "        R,\n",
+    "        gamma,\n",
+    "    )\n",
+    "    return (\n",
+    "        V,\n",
+    "        policy,\n",
+    "        max_iter,\n",
+    "        runtime,\n",
+    "    )\n",
     "\n",
     "\n",
     "# Next, run the comparison over several seeds\n",
-    "\n",
     "gamma = 0.9\n",
     "theta = 1e-6\n",
     "seeds = list(range(10))\n",
@@ -1898,7 +2018,6 @@
     "vi_times = []\n",
     "\n",
     "for seed in seeds:\n",
-    "    # Policy iteration\n",
     "    pi_policy, pi_V, n_pi, t_pi = policy_iteration_count(  # noqa: N816\n",
     "        P,\n",
     "        R,\n",
@@ -1906,7 +2025,6 @@
     "        theta=theta,\n",
     "        seed=seed,\n",
     "    )\n",
-    "    # Value iteration\n",
     "    vi_V, vi_policy, n_vi, t_vi = value_iteration_count(P, R, gamma, theta=theta)  # noqa: N816\n",
     "\n",
     "    pi_iters.append(n_pi)\n",
@@ -1914,9 +2032,9 @@
     "    pi_times.append(t_pi)\n",
     "    vi_times.append(t_vi)\n",
     "\n",
-    "    # Optional: check both found the same final policy\n",
     "    print(\"Same policy?\", np.array_equal(pi_policy, vi_policy))\n",
     "\n",
+    "\n",
     "print(\"Policy Iteration - outer iterations:\", pi_iters)\n",
     "print(\"Value Iteration  - iterations:\", vi_iters)\n",
     "\n",
@@ -1950,10 +2068,19 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 108,
+   "execution_count": 32,
    "id": "0b3469a6",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Same policy? True\n",
+      "Async iterations: 22\n"
+     ]
+    }
+   ],
    "source": [
     "def asynchronous_value_iteration(\n",
     "    P: np.ndarray,\n",
@@ -1962,36 +2089,60 @@
     "    theta: float = 1e-6,\n",
     "    max_iter: int = 200_000,\n",
     ") -> tuple[np.ndarray, np.ndarray, int]:\n",
-    "    \"\"\"Asynchronous (in-place) value iteration: updates V[s] immediately inside the loop.\"\"\"\n",
+    "    \"\"\"Asynchronous Value Iteration.\n",
+    "\n",
+    "    Args:\n",
+    "        P: array of shape (n_actions, n_states, n_states)\n",
+    "        R: array of shape (n_states,)\n",
+    "        gamma: discount factor\n",
+    "        theta: convergence threshold\n",
+    "        max_iter: maximum number of iterations\n",
+    "\n",
+    "    Returns:\n",
+    "        V: array of shape (n_states,)\n",
+    "            Approximation of the optimal value function V*.\n",
+    "        policy: array of shape (n_states,)\n",
+    "            Greedy policy derived from V.\n",
+    "        n_iterations: number of iterations until convergence\n",
+    "\n",
+    "    \"\"\"\n",
     "    n_states = len(R)\n",
-    "    n_actions = len(P)\n",
+    "    n_actions = P.shape[0]\n",
     "    V = np.zeros(n_states)\n",
     "\n",
     "    for _it in range(max_iter):\n",
-    "        delta = 0\n",
+    "        delta = 0.0\n",
+    "\n",
     "        for s in range(n_states):\n",
+    "            v_old = V[s]\n",
+    "\n",
     "            if is_terminal(s):\n",
     "                V[s] = R[s] / (1 - gamma)\n",
-    "                continue\n",
+    "            else:\n",
+    "                Q = np.zeros(n_actions)\n",
+    "                for a in range(n_actions):\n",
+    "                    Q[a] = R[s] + gamma * np.dot(P[a, s, :], V)\n",
+    "                V[s] = np.max(Q)\n",
     "\n",
-    "            Q_values = np.zeros(n_actions)\n",
-    "            for a in range(n_actions):\n",
-    "                Q_values[a] = R[s] + gamma * np.sum(P[a, s, :] * V)\n",
-    "            v_new = np.max(Q_values)\n",
-    "\n",
-    "            delta = max(delta, abs(v_new - V[s]))\n",
-    "            V[s] = v_new\n",
+    "            delta = max(\n",
+    "                delta,\n",
+    "                abs(V[s] - v_old),\n",
+    "            )\n",
     "\n",
     "        if delta < theta:\n",
     "            break\n",
     "\n",
-    "        pi = policy_improvement(V, P, R, gamma)\n",
+    "    pi = policy_improvement(V, P, R, gamma)\n",
+    "    return V, pi, _it + 1\n",
     "\n",
-    "    return (\n",
-    "        V,\n",
-    "        pi,\n",
-    "        _it,\n",
-    "    )  # return final value function, greedy policy from V, and number of iteration performed\n"
+    "\n",
+    "gamma = 0.9\n",
+    "V_sync, pi_sync = value_iteration(P, R, gamma, theta=1e-6)\n",
+    "V_async, pi_async, it_async = asynchronous_value_iteration(P, R, gamma, theta=1e-6)\n",
+    "\n",
+    "\n",
+    "print(\"Same policy?\", np.array_equal(pi_sync, pi_async))\n",
+    "print(\"Async iterations:\", it_async)\n"
    ]
   },
   {
@@ -2015,28 +2166,71 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 109,
+   "execution_count": 33,
    "id": "b64a1e78",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "fails: 0 out of 50\n"
+     ]
+    }
+   ],
    "source": [
     "def T_opt(V: np.ndarray, P: np.ndarray, R: np.ndarray, gamma: float) -> np.ndarray:\n",
-    "    \"\"\"Bellman optimality operator in the maze: (T* V)(s) = max_a [ R[s] + gamma * sum_{s'} P[a,s,s'] V[s'] ].\"\"\"\n",
+    "    \"\"\"Compute the optimal Bellman operator T^* applied to V.\n",
+    "\n",
+    "    Args:\n",
+    "        V: array of shape (n_states,)\n",
+    "        P: array of shape (n_actions, n_states, n_states)\n",
+    "        R: array of shape (n_states,)\n",
+    "        gamma: discount factor\n",
+    "\n",
+    "    Returns:\n",
+    "        out: array of shape (n_states,)\n",
+    "\n",
+    "    \"\"\"\n",
     "    n_states = len(R)\n",
-    "    n_actions = len(P)\n",
-    "    V_new = np.zeros_like(V)\n",
+    "    n_actions = P.shape[0]\n",
+    "    out = np.zeros(n_states)\n",
     "\n",
     "    for s in range(n_states):\n",
     "        if is_terminal(s):\n",
-    "            V_new[s] = R[s] / (1 - gamma)\n",
-    "            continue\n",
+    "            out[s] = R[s] / (1 - gamma)\n",
+    "        else:\n",
+    "            Q = np.zeros(n_actions)\n",
+    "            for a in range(n_actions):\n",
+    "                Q[a] = R[s] + gamma * np.dot(P[a, s, :], V)\n",
+    "            out[s] = np.max(Q)\n",
     "\n",
-    "        Q_values = np.zeros(n_actions)\n",
-    "        for a in range(n_actions):\n",
-    "            Q_values[a] = R[s] + gamma * np.sum(P[a, s, :] * V)\n",
-    "        V_new[s] = np.max(Q_values)\n",
+    "    return out\n",
     "\n",
-    "    return V_new\n"
+    "\n",
+    "def sup_norm(x: np.ndarray) -> float:\n",
+    "    \"\"\"Compute the sup norm (infinity norm) of vector x.\"\"\"\n",
+    "    return np.max(np.abs(x))\n",
+    "\n",
+    "\n",
+    "gamma = 0.9\n",
+    "n_states = len(R)\n",
+    "rng = np.random.default_rng()\n",
+    "\n",
+    "num_tests = 50\n",
+    "fails_numbers = 0\n",
+    "\n",
+    "for _ in range(num_tests):\n",
+    "    V = rng.standard_normal(n_states)\n",
+    "    W = rng.standard_normal(n_states)\n",
+    "\n",
+    "    lhs = sup_norm(T_opt(V, P, R, gamma) - T_opt(W, P, R, gamma))\n",
+    "    rhs = gamma * sup_norm(V - W)\n",
+    "\n",
+    "    if lhs > rhs + 1e-10:\n",
+    "        fails_numbers += 1\n",
+    "\n",
+    "print(\"fails:\", fails_numbers, \"out of\", num_tests)"
    ]
   },
   {
@@ -2057,7 +2251,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 110,
+   "execution_count": 34,
    "id": "47219cdc-b99b-4b73-a3d1-c133afb0e215",
    "metadata": {},
    "outputs": [
@@ -2065,35 +2259,126 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Max difference between V_opt and V_vi: 18.749999999999982\n",
-      "Asynchronous VI iterations for gamma = 0.2 : 9\n",
-      "Max difference between V_async and V_vi: 18.749999999999982\n",
-      "Same policy between async VI and VI? True\n",
-      "Max difference between V_opt and V_vi: 17.999999999999982\n",
-      "Asynchronous VI iterations for gamma = 0.5 : 14\n",
-      "Max difference between V_async and V_vi: 17.999999999999982\n",
-      "Same policy between async VI and VI? True\n",
-      "Max difference between V_opt and V_vi: 9.99999999999998\n",
-      "Asynchronous VI iterations for gamma = 0.9 : 21\n",
-      "Max difference between V_async and V_vi: 9.99999999999998\n",
-      "Same policy between async VI and VI? True\n",
-      "Max difference between V_opt and V_vi: 79.99999999999993\n",
-      "Asynchronous VI iterations for gamma = 0.99 : 25\n",
-      "Max difference between V_async and V_vi: 79.99999999999993\n",
-      "Same policy between async VI and VI? True\n"
+      "gamma=0.2: computed V* and pi*\n"
      ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "gamma=0.5: computed V* and pi*\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "gamma=0.9: computed V* and pi*\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "gamma=0.99: computed V* and pi*\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
-    "for gamma in [0.2, 0.5, 0.9, 0.99]:\n",
-    "    V_opt = T_opt(V_vi, P, R, gamma)\n",
-    "    print(\"Max difference between V_opt and V_vi:\", np.max(np.abs(V_opt - V_vi)))\n",
+    "gammas = [0.2, 0.5, 0.9, 0.99]\n",
+    "theta = 1e-6\n",
     "\n",
-    "    V_async, pi_async, n_async = asynchronous_value_iteration(P, R, gamma, theta=theta)\n",
-    "    print(\"Asynchronous VI iterations for gamma =\", gamma, \":\", n_async)\n",
+    "results = {}\n",
     "\n",
-    "    print(\"Max difference between V_async and V_vi:\", np.max(np.abs(V_async - V_vi)))\n",
-    "    print(\"Same policy between async VI and VI?\", np.array_equal(pi_async, policy_vi))"
+    "for gamma in gammas:\n",
+    "    print(f\"gamma={gamma}: computed V* and pi*\")\n",
+    "\n",
+    "    V_star, pi_star = value_iteration(P, R, gamma, theta=theta)\n",
+    "\n",
+    "    results[gamma] = {\"V\": V_star, \"pi\": pi_star}\n",
+    "\n",
+    "    plot_values(V_star, title=f\"Optimal Value Function (gamma={gamma})\")\n",
+    "    plot_policy(pi_star, title=f\"Optimal Policy (gamma={gamma})\")\n"
    ]
   },
   {