It is often suggested that decisions are made when accumulated sensory information reaches a fixed accuracy criterion. This is supported by many studies showing a gradual build up of neural activity to a threshold. However, the proposal that this build up is caused by sensory accumulation is challenged by findings that decisions are based on information from a time window much shorter than the build-up process. Here, we propose that in natural conditions where the environment can suddenly change, the policy that maximizes reward rate is to estimate evidence by accumulating only novel information and then compare the result to a decreasing accuracy criterion. We suggest that the brain approximates this policy by multiplying an estimate of sensory evidence with a motor-related urgency signal and that the latter is primarily responsible for neural activity build up. We support this hypothesis using human behavioral data from a modified random-dot motion task in which motion coherence changes during each trial.