Large Language Model (LLM) agents have recently shown strong potential in domains such as automated coding, deep research, and graphical user interface manipulation. However, training them to succeed on long-horizon, domain-specialized tasks remains challenging. Current methods primarily fall into two categories. The first relies on dense human annotations through behavior cloning, which is prohibitively expensive for long-horizon tasks that can take days or months. The second depends on outcome-driven sampling, which often collapses due to the rarity of valid positive trajectories on domain-specialized tasks. We introduce Apollo, a sampling framework that integrates asynchronous human guidance with action-level data filtering. Instead of requiring annotators to shadow every step, Apollo allows them to intervene only when the agent drifts from a promising trajectory, by providing prior knowledge, strategic advice, etc. This lightweight design makes it possible to sustain interactions for over 30 hours and produces valuable trajectories at a lower cost. Apollo then applies supervision control to filter out sub-optimal actions and prevent error propagation. Together, these components enable reliable and effective data collection in long-horizon environments. To demonstrate the effectiveness of Apollo, we evaluate it using InnovatorBench. Our experiments show that when applied to train the GLM-4.5 model on InnovatorBench, Apollo achieves more than a 50% improvement over the untrained baseline and a 28% improvement over a variant trained without human interaction. These results highlight the critical role of human-in-the-loop sampling and the robustness of Apollo's design in handling long-horizon, domain-specialized tasks.

Logical reasoning of text is an important ability that requires understanding the information present in the text, their interconnections, and then reasoning through them to infer new conclusions. Prior works on improving the logical reasoning ability of language models require complex processing of training data (e.g., aligning symbolic knowledge to text), yielding task-specific data augmentation solutions that restrict the learning of general logical reasoning skills. In this work, we propose APOLLO, an adaptively pretrained language model that has improved logical reasoning abilities. We select a subset of Wikipedia, based on a set of logical inference keywords, for continued pretraining of a language model. We use two self-supervised loss functions: a modified masked language modeling loss where only specific parts-of-speech words, that would likely require more reasoning than basic language understanding, are masked, and a sentence-level classification loss that teaches the model to distinguish between entailment and contradiction types of sentences. The proposed training paradigm is both simple and independent of task formats. We demonstrate the effectiveness of APOLLO by comparing it with prior baselines on two logical reasoning datasets. APOLLO performs comparably on ReClor and outperforms baselines on LogiQA. The code base has been made publicly available.

Importantly, the update and storage of the diagonal approximation of Hessian is as efficient as adaptive first-order optimization methods with linear complexity for both time and memory. To handle nonconvexity, we replace the Hessian with its rectified absolute value, which is guaranteed to be positive-definite. Nonconvex stochastic optimization is of core practical importance in many fields of machine learning, in particular for training deep neural networks (DNNs). First-order gradient-based optimization algorithms, conceptually attractive due to their linear efficiency on both the time and memory complexity, have led to tremendous progress and impressive successes. However, one disadvantage of SGD is that the gradients in different directions are scaled uniformly, resulting in limited convergence speed and sensitive choice of the learning rate, and thus has spawned a lot of recent interest in accelerating SGD from the algorithmic and practical perspectives. Recently, many adaptive first-order optimization methods have been proposed to achieve rapid training progress with element-wise scaled learning rates, and we can only mention a few here due to space limits. In their pioneering work, Duchi et al. (2011) proposed AdaGrad, which scales the gradient by the square root of the accumulative square gradients from the first iteration.