Completeness and Cost of Retrieval Structures for Multi-Tool Requests in LLM Agents

Abstract

An agent that must call several tools to fulfill a request fails when the tool retriever omits any one of them, yet tool retrievers are mostly built and evaluated on queries requiring a single tool. We compare representatives of six retrieval structures (flat lexical and dense retrieval, LLM query decomposition, LLM-navigated hierarchies, server-then-tool matching, dependency graphs, and trained set-level retrievers) across two multi-tool testbeds: 345 AppWorld queries with expert dependency labels and 103 MCP-Bench tasks over 257 MCP tools. We measure completeness@k, the share of queries whose entire required tool set appears in the top k, alongside the LLM calls, tokens, and latency that each structure incurs at retrieval time. A motivating analysis on all 7,961 ToolRet queries shows that aggregate completeness mixes two regimes: completeness at 10 is .58 to .67 on single-target queries and .08 to .17 on queries with four or more targets, and the ordering of retrievers on single-target queries reverses on multi-target ones. Across the two testbeds, none of the compared structures that is untrained on the testbed and makes at most one LLM call per query completes more than 10% of AppWorld queries at k = 16. The two structures that do better incur different costs: a set-level retriever trained on 75 to 90 in-domain queries reaches .33 on AppWorld and .58 on MCP-Bench with no LLM calls, while an LLM-navigated hierarchy reaches .30 and .40 with a median of 31 to 38 LLM calls and about five minutes per query. Their failure modes also differ: the trained retriever mostly ranks the missing tools just below the cutoff, whereas the hierarchy finds the target API and stops before collecting its prerequisites. In a downstream check with the official AppWorld agent, tasks with a complete retrieved set succeeded 21 of 21 times, whereas incomplete ones succeeded 2 of 39 times.