When Should Humans Step In? Optimal Human Dispatching in AI-Assisted Decisions

AI systems increasingly assist human decision making by producing preliminary assessments of complex inputs. However, such AI-generated assessments can often be noisy or systematically biased, raising a central question: how should costly human effort be allocated to correct AI outputs where it matters the most for the final decision? We propose a general decision-theoretic framework for human-AI collaboration in which AI assessments are treated as factor-level signals and human judgments as costly information that can be selectively acquired. We consider cases where the optimal selection problem reduces to maximizing a reward associated with each candidate subset of factors, and turn policy design into reward estimation. We develop estimation procedures under both nonparametric and linear models, covering contextual and non-contextual selection rules. In the linear setting, the optimal rule admits a closed-form expression with a clear interpretation in terms of factor importance and residual variance. We apply our framework to AI-assisted peer review. Our approach substantially outperforms LLM-only predictions and achieves performance comparable to full human review while using only 20-30% of the human information. Across different selection rules, we find that simpler rules derived under linear models can significantly reduce computational cost without harming final prediction performance. Our results highlight both the value of human intervention and the efficiency of principled dispatching.

Accelerate Langevin Sampling with Birth-Death process and Exploration Component

Sampling a probability distribution with known likelihood is a fundamental task in computational science and engineering. Aiming at multimodality, we propose a new sampling method that takes advantage of both birth-death process and exploration component. The main idea of this method is \textit{look before you leap}. We keep two sets of samplers, one at warmer temperature and one at original temperature. The former one serves as pioneer in exploring new modes and passing useful information to the other, while the latter one samples the target distribution after receiving the information. We derive a mean-field limit and show how the exploration process determines sampling efficiency. Moreover, we prove exponential asymptotic convergence under mild assumption. Finally, we test on experiments from previous literature and compared our methodology to previous ones.