AI 速览：该论文从支撑估计角度刻画基于采样端点估计可达集的几何（Hausdorff）误差，并给出样本复杂度上界与匹配的极小极大下界。
Sampling-based reachability estimates reachable sets from finitely many simulated trajectory endpoints. Existing guarantees often control missed probability mass or approximation error relative to the convex hull of the reachable set, leaving the geometric error relative to the reachable set incompletely characterized. We study this error as a problem of support estimation under flow distortion. Our assumptions combine a uniform lower bound on the local volume density of the initial set, a lower bound on the sampling density, and a one-sided Lipschitz constant $μ$ for the vector field. These conditions admit initial sets with corners and dynamics that may expand or contract. In the fine-accuracy regime, $\tilde{\mathcal O}\bigl(2^ne^{nμT}(R/r)^n/(ρκ)\bigr)$ independent endpoint samples suffice for Hausdorff accuracy $r$ using the endpoint cloud. Here, $n$ is the state dimension, $T$ is the horizon, $R$ is the volume-equivalent radius, and $ρ$ and $κ$ quantify sampling density and local volume density. For $n\ge2$ and sufficiently small $κ$, a minimax lower bound over all estimators based only on independent endpoints matches these dependencies up to a dimension-dependent factor $2\cdot4^n$ and logarithmic factors, within the stated parameter range and when the state domain accommodates the construction. The exponential burden in dimension, and in the horizon for expanding systems, is therefore intrinsic to this observation model. Planar experiments illustrate the predicted effects of corners and contraction; robot-arm experiments show how empirical accuracy deteriorates with dimension.
SWEET-RL: Training Multi-Turn LLM Agents on Collaborative Reasoning Tasks
Yifei Zhou, Song Jiang, Yuandong Tian, Jason Weston, Sergey Levine, Sainbayar Sukhbaatar, Xian Li
AI 速览：提出 ColBench 多轮人机协作基准与 SWEET-RL 算法，利用训练时额外信息训练评论家模型提供步级奖励，以改进多轮 LLM 智能体的信用分配。
Large language model (LLM) agents need to perform multi-turn interactions in real-world tasks. However, existing multi-turn RL algorithms for optimizing LLM agents fail to perform effective credit assignment over multiple turns while leveraging the generalization capabilities of LLMs and it remains unclear how to develop such algorithms. To study this, we first introduce a new benchmark, ColBench, where an LLM agent interacts with a human collaborator over multiple turns to solve realistic tasks in backend programming and frontend design. Building on this benchmark, we propose a novel RL algorithm, SWEET-RL (RL with Step-WisE Evaluation from Training-time information), that uses a carefully designed optimization objective to train a critic model with access to additional training-time information. The critic provides step-level rewards for improving the policy model. Our experiments demonstrate that SWEET-RL achieves a 6% absolute improvement in success and win rates on ColBench compared to other state-of-the-art multi-turn RL algorithms, enabling Llama-3.1-8B to match or exceed the performance of GPT4-o in realistic collaborative content creation.