Selecting Long-Horizon Trajectories for Reliable and Efficient Terminal-Agent Training

Terminal agents are commonly trained by imitating long teacher trajectories, yet how much of each trajectory to supervise remains unexplored. We study the supervision horizon, the number of trajectory tokens retained for training, and show that it is a key design axis for reliability and cost. Reliability improves with longer horizons but saturates: on Terminal-Bench, a 12K-token horizon solves more tasks than 16K (29 plus or minus0.7 vs. 26 plus or minus0.8) while requiring 30% less training time. The horizon also shapes agent behavior: short horizons cause premature termination, intermediate horizons yield productive error recovery, and long horizons induce over-persistence. We analyze this saturation through a bias--complexity bound, in which longer supervision reduces temporal supervision bias but increases finite-sample estimation error from more heterogeneous late-stage histories. Guided by this analysis, we propose selective long-horizon refinement, which first trains on short prefixes and then refines only on continuations that are most likely under the warm-start model. It consistently outperforms full long-horizon training. At 16K, it raises successful attempts from 110 plus or minus2.7 to 126 plus or minus2.1 and tasks solved in at least six of eight attempts from 9 plus or minus0.7 to 14 plus or minus0.6; with half of the long-horizon data, it still reaches 122 plus or minus2.4 while cutting training time by 23%. The gains transfer across benchmarks, from 64 plus or minus2.6 to 73 plus or minus2.1 on Terminal-Bench v2.0 and from 137 plus or minus2.7 to 155 plus or minus2.2 on OpenThoughts-TBLite. For long-horizon supervision, selecting the right trajectories matters more than training on all of them.