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However, the fundamental cognitive faculties essential for problem solving, including perception, reasoning, and memory, remain the stable core of intelligence. Unlike memorizing specific patterns, humans succeed in novel environments by applying these intrinsic faculties to adapt and optimize. Yet, whether LLMs possess this essential capacity, namely the ability to continuously refine solutions in response to dynamic environmental feedback, remains underexplored. To address this challenge, we introduce OPT-BENCH, a benchmark for evaluating self-improvement capabilities in large-scale search spaces. By combining 20 machine learning tasks with 10 classic NP-hard problems, OPT-BENCH provides a rigorous setting to assess whether agents can adapt through intrinsic self-reflection rather than rote tool application. 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