To thrive in complex environments, animals and artificial agents must learn to act adaptively to maximize fitness and rewards. Such adaptive behaviour can be learned through reinforcement learning, a class of algorithms that has been successful at training artificial agents and at characterizing the firing of dopaminergic neurons in the midbrain. In classical reinforcement learning, agents discount future rewards exponentially according to a single timescale, known as the discount factor. Here we explore the presence of multiple timescales in biological reinforcement learning. We first show that reinforcement agents learning at a multitude of timescales possess distinct computational benefits. Next, we report that dopaminergic neurons in mice performing two behavioural tasks encode reward prediction error with a diversity of discount time constants. Our model explains the heterogeneity of temporal discounting in both cue-evoked transient responses and slower timescale fluctuations known as dopamine ramps. Crucially, the measured discount factor of individual neurons is correlated across the two tasks, suggesting that it is a cell-specific property. Together, our results provide a new paradigm for understanding functional heterogeneity in dopaminergic neurons and a mechanistic basis for the empirical observation that humans and animals use non-exponential discounts in many situations, and open new avenues for the design of more-efficient reinforcement learning algorithms.