Fix LATS select to choose the best child at each level until reaching…

… leaf child (#1723)

docs/docs/tutorials/lats/lats.ipynb

@@ -152,14 +152,6 @@
     "        return not self.children\n",
     "\n",
     "    @property\n",
-    "    def best_child(self):\n",
-    "        \"\"\"Select the child with the highest UCT to search next.\"\"\"\n",
-    "        if not self.children:\n",
-    "            return None\n",
-    "        all_nodes = self._get_all_children()\n",
-    "        return max(all_nodes, key=lambda child: child.upper_confidence_bound())\n",
-    "\n",
-    "    @property\n",
     "    def best_child_score(self):\n",
     "        \"\"\"Return the child with the highest value.\"\"\"\n",
     "        if not self.children:\n",
@@ -589,11 +581,23 @@
    "source": [
     "from collections import defaultdict\n",
     "\n",
+    "def select(root: Node) -> dict:\n",
+    "    \"\"\"Starting from the root node a child node is selected at each tree level until a leaf node is reached.\"\"\"\n",
+    "\n",
+    "    if not root.children:\n",
+    "        return root\n",
+    "    \n",
+    "    node = root\n",
+    "    while node.children:\n",
+    "        max_child = max(node.children, key=lambda child: child.upper_confidence_bound())\n",
+    "        node = max_child\n",
+    "\n",
+    "    return node\n",
     "\n",
     "def expand(state: TreeState, config: RunnableConfig) -> dict:\n",
     "    \"\"\"Starting from the \"best\" node in the tree, generate N candidates for the next step.\"\"\"\n",
     "    root = state[\"root\"]\n",
-    "    best_candidate: Node = root.best_child if root.children else root\n",
+    "    best_candidate: Node = select(root)\n",
     "    messages = best_candidate.get_trajectory()\n",
     "    # Generate N candidates from the single child candidate\n",
     "    new_candidates = expansion_chain.invoke(\n",