We study proactive exploration in LLM agents, i.e., the ability to explore an environment to acquire information that improves future decision-making. In this regard, we first identify two fundamental bottlenecks that hinder this capability and then propose \ours, a novel method designed to instill and refine proactive exploration. Specifically, \ours\ consists of two components: (1) Exploratory Data Construction, which synthesizes exploration-rich trajectories to mitigate the hindsight bias of standard demonstrations; and (2) RL Optimization with Contrastive Signal Guidance, which leverages contrastive trajectory pairs to distinguish productive exploration from redundant wandering. Extensive experiments demonstrate the effectiveness of \ours\ and provide insights into the characteristics of proactive exploration. Our code is available at: https://github.com/GuanZhizhao/SAFARI.