Towards Principled Efficient Rollout Allocation in Test-Time Training

Test-time training and test-time policy optimization have emerged as effective tools for improving the robustness of LLMs under distribution shift. A common approach constructs label-free reward signals from multiple sampled rollouts using majority voting, but existing methods typically rely on a fixed, large rollout budget for every query. This fixed allocation is inefficient because many queries reach consensus well before the rollout budget is exhausted. In this work, we introduce AdaPO, which replaces fixed-budget majority voting with an adaptive two-stage voting procedure that moves from electing to confirming when a leader is statistically dominant, and stops once the posterior error of accepting that leader is sufficiently low. AdaPO is plug-and-play with standard policy optimization algorithms such as PPO and GRPO, and it is also compatible with supervised fine-tuning at test time. Our rigorous theoretical results show that, under the symmetric categorical noise model with known likelihood parameters, AdaPO's electing-stage trigger coincides with the classical sequential probability ratio test (SPRT), while the confirming-stage rule yields a principled posterior-threshold stopping mechanism. Across representative reasoning benchmarks, AdaPO substantially reduces compute, achieving over 40% token savings on GPQA while maintaining competitive accuracy. The source code will be open upon acceptance at https://open-upon-acceptance.