docs: `ElasticsearchCache` in cache integrations documentation (#20790)

The package for LangChain integrations with Elasticsearch
https://github.com/langchain-ai/langchain-elastic is going to contain a
LLM cache integration in the next release (see
https://github.com/langchain-ai/langchain-elastic/pull/14). This is the
documentation contribution on the page dedicated to cache integrations

docs/docs/integrations/llms/llm_caching.ipynb

@@ -1428,6 +1428,15 @@
   },
   {
    "cell_type": "code",
+   "execution_count": 82,
+   "id": "14ca942820e8140c",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2024-03-12T00:12:57.462226Z",
+     "start_time": "2024-03-12T00:12:55.166201Z"
+    },
+    "collapsed": false
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -1439,7 +1448,9 @@
     },
     {
      "data": {
-      "text/plain": "'\\n\\nWhy was the math book sad? Because it had too many problems.'"
+      "text/plain": [
+       "'\\n\\nWhy was the math book sad? Because it had too many problems.'"
+      ]
      },
      "execution_count": 82,
      "metadata": {},
@@ -1450,16 +1461,7 @@
     "%%time\n",
     "# The first time, it is not yet in cache, so it should take longer\n",
     "llm(\"Tell me a joke\")"
-   ],
-   "metadata": {
-    "collapsed": false,
-    "ExecuteTime": {
-     "end_time": "2024-03-12T00:12:57.462226Z",
-     "start_time": "2024-03-12T00:12:55.166201Z"
-    }
-   },
-   "id": "14ca942820e8140c",
-   "execution_count": 82
+   ]
   },
   {
    "cell_type": "code",
@@ -1482,7 +1484,9 @@
     },
     {
      "data": {
-      "text/plain": "'\\n\\nWhy was the math book sad? Because it had too many problems.'"
+      "text/plain": [
+       "'\\n\\nWhy was the math book sad? Because it had too many problems.'"
+      ]
      },
      "execution_count": 83,
      "metadata": {},
@@ -1495,6 +1499,141 @@
     "llm(\"Tell me a joke\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "306ff47b",
+   "metadata": {},
+   "source": [
+    "## `Elasticsearch` Cache\n",
+    "A caching layer for LLMs that uses Elasticsearch.\n",
+    "\n",
+    "First install the LangChain integration with Elasticsearch."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9ee5cd3e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%pip install -U langchain-elasticsearch"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9e70b0a0",
+   "metadata": {},
+   "source": [
+    "Use the class `ElasticsearchCache`.\n",
+    "\n",
+    "Simple example:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1762c9c1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from elasticsearch import Elasticsearch\n",
+    "from langchain.globals import set_llm_cache\n",
+    "from langchain_elasticsearch import ElasticsearchCache\n",
+    "\n",
+    "es_client = Elasticsearch(hosts=\"http://localhost:9200\")\n",
+    "set_llm_cache(\n",
+    "    ElasticsearchCache(\n",
+    "        es_connection=es_client,\n",
+    "        index_name=\"llm-chat-cache\",\n",
+    "        metadata={\"project\": \"my_chatgpt_project\"},\n",
+    "    )\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d4fac5d6",
+   "metadata": {},
+   "source": [
+    "The `index_name` parameter can also accept aliases. This allows to use the \n",
+    "[ILM: Manage the index lifecycle](https://www.elastic.co/guide/en/elasticsearch/reference/current/index-lifecycle-management.html)\n",
+    "that we suggest to consider for managing retention and controlling cache growth.\n",
+    "\n",
+    "Look at the class docstring for all parameters."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eaf9dfd7",
+   "metadata": {},
+   "source": [
+    "### Index the generated text\n",
+    "\n",
+    "The cached data won't be searchable by default.\n",
+    "The developer can customize the building of the Elasticsearch document in order to add indexed text fields,\n",
+    "where to put, for example, the text generated by the LLM.\n",
+    "\n",
+    "This can be done by subclassing end overriding methods.\n",
+    "The new cache class can be applied also to a pre-existing cache index:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5104c2c0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import json\n",
+    "from typing import Any, Dict, List\n",
+    "\n",
+    "from elasticsearch import Elasticsearch\n",
+    "from langchain.globals import set_llm_cache\n",
+    "from langchain_core.caches import RETURN_VAL_TYPE\n",
+    "from langchain_elasticsearch import ElasticsearchCache\n",
+    "\n",
+    "\n",
+    "class SearchableElasticsearchCache(ElasticsearchCache):\n",
+    "    @property\n",
+    "    def mapping(self) -> Dict[str, Any]:\n",
+    "        mapping = super().mapping\n",
+    "        mapping[\"mappings\"][\"properties\"][\"parsed_llm_output\"] = {\n",
+    "            \"type\": \"text\",\n",
+    "            \"analyzer\": \"english\",\n",
+    "        }\n",
+    "        return mapping\n",
+    "\n",
+    "    def build_document(\n",
+    "        self, prompt: str, llm_string: str, return_val: RETURN_VAL_TYPE\n",
+    "    ) -> Dict[str, Any]:\n",
+    "        body = super().build_document(prompt, llm_string, return_val)\n",
+    "        body[\"parsed_llm_output\"] = self._parse_output(body[\"llm_output\"])\n",
+    "        return body\n",
+    "\n",
+    "    @staticmethod\n",
+    "    def _parse_output(data: List[str]) -> List[str]:\n",
+    "        return [\n",
+    "            json.loads(output)[\"kwargs\"][\"message\"][\"kwargs\"][\"content\"]\n",
+    "            for output in data\n",
+    "        ]\n",
+    "\n",
+    "\n",
+    "es_client = Elasticsearch(hosts=\"http://localhost:9200\")\n",
+    "set_llm_cache(\n",
+    "    SearchableElasticsearchCache(es_connection=es_client, index_name=\"llm-chat-cache\")\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "db0dea73",
+   "metadata": {},
+   "source": [
+    "When overriding the mapping and the document building, \n",
+    "please only make additive modifications, keeping the base mapping intact."
+   ]
+  },
   {
    "cell_type": "markdown",
    "id": "0c69d84d",