Experience-based self-evolution enables language-model agents to improve their behavior by accumulating and updating experience at test time, yet existing evaluations often assume recurring task patterns and explicit success signals. We introduce \textsc{FinEvolveBench}, a benchmark for self-evolving agents on low-repetition tasks with implicit rewards. The benchmark reconstructs a daily financial information stream over 31 Chinese A-share industry indices and aligns 177,324 public news articles with market observations. Researchers can define prediction horizons over this stream; we evaluate predictive market-sentiment factors against delayed market-adjusted returns after 10, 20, and 40 trading days. Unlike static benchmarks that score each prediction independently, \textsc{FinEvolveBench} interleaves new decisions with delayed outcomes from earlier ones, testing whether agents can convert noisy real-world feedback into reusable experience at test time. Experiments with two backbone models show that the evaluated general-purpose memory systems do not consistently outperform the no-experience pipeline. A matched ablation further shows that feedback-driven utility updates help at shorter horizons on one backbone but hurt in most settings on the other. Together, these results position \textsc{FinEvolveBench} as a diagnostic testbed for experience-based self-evolution under noisy, delayed, and outcome-level feedback.

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