return
/ ree-TURN /
The return is the grand total — the sum of all the rewards an agent collects from some moment onward, not just the next one. A single reward is one step's pay; the return is the whole paycheck for the rest of the episode. This distinction is the soul of reinforcement learning: the agent isn't trying to maximize the next reward, it's trying to maximize the return, the long-run total.
Usually the return is discounted, meaning later rewards are shrunk by the discount factor before being added in, so a reward now counts more than the same reward far in the future. That is why a chess player will happily sacrifice a pawn (a small immediate loss) to win the game (a large future gain): the move that hurts the next reward can be exactly the move that maximizes the return.
Keep return and value distinct, because they are easy to blur. The return is what actually happened — the real total you got from one particular play-through, known only in hindsight. The value is the prediction — the average return you'd expect over many play-throughs, estimated in advance. Value functions exist precisely to forecast the return before you've lived it; the return is the ground truth they are trying to guess.
An episode yields rewards: 0, 0, -1 (lose a pawn), 0, +10 (checkmate). The undiscounted return from the start is 0+0-1+0+10 = 9. The pawn sacrifice lowered an early reward but raised the total return — which is what the agent actually cares about.
Return = the whole future sum of rewards. A move that lowers the next reward can raise the return.
Reward is one step; return is the long-run sum; value is the expected return. Mixing these up is the single most common confusion in RL. The agent never maximizes the immediate reward — it always maximizes the return, which is exactly why short-term sacrifices for long-term gain are possible.