Papers

Tool-using language agents often decide whether to call a calculator, search API, database, or code executor through heuristics such as prompt rules, confidence triggers, or fixed orchestration templates. Those choices hide the real decision problem: a tool call costs latency, tokens, and external-system budget, and it only helps when it raises answer quality enough to justify that cost. This paper derives a narrow expected-utility rule for one-step tool calling. If answering now with the current candidate yields utility B when correct and -H when incorrect, a tool call costs C_t, succeeds in returning usable information with probability s, and conditional on success raises posterior correctness from p to p_plus, then calling the tool is optimal only when s(p_plus - p) exceeds C_t / (B + H). The paper then composes this tool-call boundary with an answer-versus-abstain threshold, showing how direct answering, tool use, and abstention can be written in one utility language. The contribution is analytic rather than empirical: it does not report benchmark gains, and it states what calibration and logging evidence would be required before such a rule could govern a deployed agent.