Running Average Algorithm Produces Monotonic Envelope

A researcher developing a hybrid reinforcement-learning and gradient-descent optimizer for a gamma-ray observatory reports a statistical issue with running averages while smoothing time-series data. They show that enforcing a monotonically nondecreasing running-average envelope creates multiple-testing bias that flattens slow growth; they propose using significance thresholds and an adaptive k (e.g., k = sqrt(log N)) to reduce false downward updates but note no universal fix exists.