Although the decisions of our daily lives often occur in the context of temporal and reward structures, the impact of such regularities on decision-making strategy is poorly understood. Here, to explore how temporal and reward context modulate strategy, we trained 2 male rhesus monkeys to perform a novel perceptual decision-making task with asymmetric rewards and time-varying evidence reliability. To model the choice and response time patterns, we developed a computational framework for fitting generalized drift-diffusion models, which flexibly accommodate diverse evidence accumulation strategies. We found that a dynamic urgency signal and leaky integration, in combination with two independent forms of reward biases, best capture behavior. We also tested how temporal structure influences urgency by systematically manipulating the temporal structure of sensory evidence, and found that the time course of urgency was affected by temporal context. Overall, our approach identified key components of cognitive me...