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But these agents cannot learn on the fly at test time. Self-evolving agents address this by accumulating memory and reflection across episodes rather than requiring model-weight updates. However, these agents often suffer from exploration collapse: as memory grows, behavior concentrates around familiar high-reward routines, reducing the chance of discovering better alternatives. To address this problem, we propose Autonomous Policy EXploration (APEX), which builds and maintains an explicit strategy space through a strategy map-a directed acyclic graph of milestones with prerequisite dependency edges. In APEX, Fork Discovery expands the map with evidence-grounded unexplored directions, while Policy Selection balances exploration and exploitation during planning. 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In APEX, Fork Discovery expands the map with evidence-grounded unexplored directions, while Policy Selection balances exploration and exploitation during planning. 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