Scientific discovery increasingly entails long-horizon exploration of complex hypothesis spaces, yet most existing approaches emphasize final performance while offering limited insight into how scientific exploration unfolds over time, particularly balancing efficiency-diversity trade-offs and supporting reproducible, human-in-the-loop discovery workflows. We introduce SelfAI, a self-directed, multi-agent-enabled discovery system that automates scientific exploration as a strategic, trajectory-driven decision-making process. SelfAI translates high-level research intent into executable experiments, reasons over accumulated experimental trajectories to guide subsequent exploration, and applies adaptive stopping decisions to terminate unproductive search paths within a closed-loop workflow governed by explicit efficiency-diversity trade-offs. Evaluated using real-world experiments spanning domains from machine learning to drug discovery, SelfAI consistently discovers high-quality solutions with substantially fewer redundant trials than classical optimization and recent LLM-based baselines. The proposed methods establish a general framework for organizing long-horizon scientific discovery and adaptive decision-making in complex scientific and engineering systems.