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However, existing web agents often rely on handcrafted execution pipelines or expensive expert trajectories, limiting their adaptability to complex, dynamic environments. To address these challenges, we propose SCALE (Self-Cognitive-Aware Learning and Exploration), which leverages three adversarial roles, Selector, Predictor, and Judger to autonomously discover the agent's limitations and expand its cognitive boundaries through environmental exploration. Moreover, we propose SCALE-Hop, a graph exploration strategy that facilitates global planning and helps agents avoid local exploration traps. To further support learning, we construct SCALE-20k, a large-scale dataset collected from 19 real-world websites, containing diverse task types and structured demonstrations generated from SCALE's exploration traces. 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