Trajectory Segment — is summed without discount by → Bradley-Terry Model

Equation 1 turns a trajectory segment into a single number by summing predicted reward across every observation-action pair in the segment, with no discount factor applied to later timesteps (deep-rl-human-prefs, §"2.2.3 Fitting the Reward Function", p. 5). The paper flags this as a modeling choice rather than a neutral default: undiscounted summation can be read as assuming the human is indifferent to when within a one-to-two-second clip something good or bad happens, treating an event at the start of the segment as equally decisive as the same event at the end. The paper explicitly notes that using explicit discounting, or trying to infer a human's discount function from their comparisons, would also have been a reasonable alternative, which it simply did not pursue. So the trajectory segment is not just a fixed-length window the Bradley-Terry model happens to operate on; the choice of segment length interacts with this no-discounting assumption, since the assumption becomes less plausible the longer a segment is allowed to run.