Two earlier sweeps in research/lowcomm-training said that DiLoCo-style training (four workers, sync every H steps) beat synchronous AdamW on a 14k parameter character model: H=16 by 0.1 nats, and H=1 with a large outer step by 0.2. Both used an inner learning rate of 3e-3 that nobody had tuned, on a model still under-trained after 640 steps.
Milestone 2e tunes the inner lr per H (and for synchronous AdamW) from four values, with the outer step set to plain averaging. Held-out loss, five seeds: synchronous 2.159, H=1 2.149, H=4 2.167, H=16 2.183, H=64 2.210, H=160 2.218. The inner lr alone moved every loss by about 0.2 nats, more than any effect of H. The earlier "wins" were under-training, and the U-shape went with them: loss rises gently with H, and H of 16 or less sits within two standard deviations of synchronous (H=16 only just).
Limits: the best lr for H of 16 or less is the top of the grid, so those picks are probably under-tuned; the model is far below the scale the programme targets; outer momentum is off. The log and results file are in the programme directory.