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While Large Language Models (LLM) are able to accumulate and restoreknowledge, they are still prone to hallucination. Especially when faced withfactual questions, LLM cannot only rely on knowledge stored in parameters toguarantee truthful and correct answers. Augmenting these models with theability to search on external information sources, such as the web, is apromising approach to ground knowledge to retrieve information. However,searching in a large collection of documents introduces additionalcomputational/time costs. An optimal behavior would be to query externalresources only when the LLM is not confident about answers. In this paper, wepropose a new LLM able to self-estimate if it is able to answer directly orneeds to request an external tool. We investigate a supervised approach byintroducing a hallucination masking mechanism in which labels are generatedusing a close book question-answering task. In addition, we propose to leverageparameter-efficient fine-tuning techniques to train our model on a small amountof data. Our model directly provides answers for $78.2\%$ of the known queriesand opts to search for $77.2\%$ of the unknown ones. This results in the APIbeing utilized only $62\%$ of the time.

Navigating Uncertainty: Optimizing API Dependency for Hallucination Reduction in Closed-Book Question Answering