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.

Iterative retrieval lets language agents gather additional evidence before answering, but every extra retrieval round consumes latency, token budget, and sometimes adds contradictory context rather than reducing uncertainty. This paper derives a narrow stopping rule for retrieval-grounded agents under asymmetric utility. Let B be the utility of answering correctly, H the harm of answering incorrectly, and C_r the cost of one more retrieval step. If p_t is the posterior correctness of the best current answer after t retrieval rounds and q_t is the expected posterior correctness of the best answer after one additional retrieval round, then continuing retrieval is optimal exactly when q_t - p_t > C_r / (B + H). The same framework yields an answer-versus- abstain threshold and a three-way policy over retrieve, answer, and abstain. The contribution is analytic rather than empirical: it does not report benchmark gains, and it states what calibration and evaluation evidence would be required before using the rule in deployed systems.