Songjun Tu

Di He, Songjun Tu, Keyu Wang et al.

Learning rate configuration is a fundamental aspect of modern deep learning. The prevailing practice of applying a uniform learning rate across all layers overlooks the structural heterogeneity of Transformers, potentially limiting their effectiveness as the backbone of Large Language Models (LLMs). In this paper, we introduce Layerwise Learning Rate (LLR), an adaptive scheme that assigns distinct learning rates to individual Transformer layers. Our method is grounded in Heavy-Tailed Self-Regularization (HT-SR) theory, which characterizes the empirical spectral density (ESD) of weight correlation matrices to quantify heavy-tailedness. Layers with weaker heavy-tailedness are assigned larger learning rates to accelerate their training, while layers with stronger heavy-tailedness receive smaller learning rates. By tailoring learning rates in this manner, LLR promotes balanced training across layers, leading to faster convergence and improved generalization. Extensive experiments across architectures (from LLaMA to GPT-nano), optimizers (AdamW and Muon), and parameter scales (60M-1B) demonstrate that LLR achieves up to 1.5x training speedup and outperforms baselines, notably raising average zero-shot accuracy from 47.09% to 49.02%. A key advantage of LLR is its low tuning overhead: it transfers nearly optimal LR settings directly from the uniform baseline. Code is available at https://github.com/hed-ucas/Layer-wise-Learning-Rate.

Yaocheng Zhang, Jiajun Chai, Songjun Tu et al.

On-policy distillation (OPD) provides dense teacher feedback along rollouts generated by the student and has emerged as a promising post-training paradigm for long-horizon reasoning. However, standard OPD typically generates full rollouts during training, which is computationally expensive and may expose the student to unreliable teacher feedback at late rollout positions, especially during early training. We identify the rollout horizon as a key bottleneck in OPD that substantially impacts training efficiency. Unlike Reinforcement Learning with Verifiable Rewards (RLVR), OPD does not require a complete trajectory or a final answer reward to provide learning signals. This observation suggests that full rollouts may not always be necessary for effective OPD. Motivated by this insight, we propose two simple horizon-control strategies: Progressive OPD (POPD), which gradually expands the rollout horizon during training, and Truncated OPD (TOPD), which permanently performs distillation on reliable truncated rollouts. Experiments on mathematical reasoning show that POPD improves the training efficiency of OPD by up to 3$\times$, while TOPD matches OPD performance using only 10\% of the rollout horizon, leading to substantial wall-clock and memory reductions. These results demonstrate that controlling the rollout horizon offers a simple and practical path to more efficient OPD.

Songjun Tu, Chengdong Xu, Qichao Zhang et al.

Agentic reinforcement learning (RL) can benefit substantially from reusable experience, yet existing skill-based methods mainly extract trajectory-level guidance and often lack principled mechanisms for maintaining an evolving skill memory. We propose D2Skill, a dynamic dual-granularity skill bank for agentic RL that organizes reusable experience into task skills for high-level guidance and step skills for fine-grained decision support and error correction. D2Skill jointly trains the policy and skill bank through paired baseline and skill-injected rollouts under the same policy, using their performance gap to derive hindsight utility signals for both skill updating and policy optimization. Built entirely from training-time experience, the skill bank is continuously expanded through reflection and maintained with utility-aware retrieval and pruning. Experiments on ALFWorld and WebShop with Qwen2.5-7B-Instruct and Qwen3-4B-Instruct-2507 show that D2Skill consistently improves success rates over skill-free baselines by 10-20 points. Further ablations and analyses show that both dual-granularity skill modeling and dynamic skill maintenance are critical to these gains, while the learned skills exhibit higher utility, transfer across evaluation settings, and introduce only modest training overhead.

Yaocheng Zhang, Yuanheng Zhu, Wenyue Chong et al.

Deep search agents have emerged as a promising paradigm for addressing complex information-seeking tasks, but their training remains challenging due to sparse rewards, weak credit assignment, and limited labeled data. Self-play offers a scalable route to reduce data dependence, but conventional self-play optimizes students only through sparse outcome rewards, leading to low learning efficiency. In this work, we observe that self-play naturally produces a question construction path (QCP) during task generation, an intermediate artifact that captures the reverse solution process. This reveals a new source of privileged information for self-distillation: self-play can itself provide high-quality privileged context for the teacher model in a low-cost and scalable manner, without relying on human feedback or curated privileged information. Leveraging this insight, we propose Privileged Information Self-Play ($π$-Play), a multi-agent self-evolution framework. In $π$-Play, an examiner generates tasks together with their QCPs, and a teacher model leverages QCP as privileged context to densely supervise a student via self-distillation. This design transforms conventional sparse-reward self-play into a dense-feedback self-evolution loop. Extensive experiments show that data-free $π$-Play surpasses fully supervised search agents and improves evolutionary efficiency by 2-3$\times$ over conventional self-play.

Jingbo Sun, Wenyue Chong, Songjun Tu et al.

Agentic retrieval-augmented generation (RAG) systems enable large language models (LLMs) to solve complex tasks through multi-step interaction with external retrieval tools. However, such multi-step interaction often involves redundant search steps, incurring substantial computational cost and latency. Prior work limits search depth (i.e., the number of search steps) to reduce cost, but this often leads to underexploration of complex questions. To address this, we first investigate how search depth affects accuracy and find a minimal sufficient search depth that defines an accuracy-efficiency trade-off, jointly determined by question complexity and the agent's capability. Furthermore, we propose AutoSearch, a reinforcement learning (RL) framework that evaluates each search step via self-generated intermediate answers. By a self-answering mechanism, AutoSearch identifies the minimal sufficient search depth and promotes efficient search by rewarding its attainment while penalizing over-searching. In addition, reward mechanisms are introduced to stabilize search behavior and improve answer quality on complex questions. Extensive experiments on multiple benchmarks show that AutoSearch achieves a superior accuracy-efficiency trade-off, alleviating over-searching while preserving search quality.

Jiarui Su, Songjun Tu, Bei Sun et al.

LLM-based equation discovery offers a promising route to recovering symbolic laws from data, but many systems still rely on generation-centered loops that propose candidates, fit parameters, score results, and reuse selected examples. Such loops can misjudge useful skeletons under unreliable fitting, discard near-correct equations that require repair, and accumulate redundant memories that provide limited guidance. We propose STRIDE, a self-reflective agent framework that improves reliability by coordinating data-aware generation, mixed-fitting evaluation, critic--executor repair, and diversity-preserving semantic memory. By turning fitted scores and candidate behavior into shared feedback, STRIDE enables equations to be proposed, assessed, refined, and reused within a closed-loop discovery process. Experiments on representative symbolic-regression benchmarks and LSR-Synth suites show that STRIDE improves accuracy, OOD robustness, and structural recovery across multiple LLM backbones, with ablations and analyses confirming the contribution of its core components.

Di He, Songjun Tu, Ajay Jaiswal et al.

Weight decay is a standard regularization technique for training large language models (LLMs). While it is common to assign a uniform decay rate to every layer, this approach overlooks the structural diversity of LLMs and the varying spectral properties across modules. In this paper, we introduce AlphaDecay, a simple yet effective method that adaptively assigns different weight decay strengths to each module of an LLM. Our approach is guided by Heavy-Tailed Self-Regularization (HT-SR) theory, which analyzes the empirical spectral density (ESD) of weight correlation matrices to quantify "heavy-tailedness." Modules exhibiting more pronounced heavy-tailed ESDs, reflecting stronger feature learning, are assigned weaker decay, while modules with lighter-tailed spectra receive stronger decay. Our method leverages tailored weight decay assignments to balance the module-wise differences in spectral properties, leading to improved performance. Extensive pre-training tasks with various model sizes from 60M to 1B demonstrate that AlphaDecay achieves better perplexity and generalization than conventional uniform decay and other adaptive decay baselines. Our code is available at https://github.com/hed-ucas/AlphaDecay.

Yuqian Fu, Tinghong Chen, Jiajun Chai et al.

Large language models (LLMs) have achieved remarkable progress in reasoning tasks, yet the optimal integration of Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) remains a fundamental challenge. Through comprehensive analysis of token distributions, learning dynamics, and integration mechanisms from entropy-based perspectives, we reveal key differences between these paradigms: SFT induces coarse-grained global changes to LLM policy distributions, while RL performs fine-grained selective optimizations, with entropy serving as a critical indicator of training effectiveness. Building on these observations, we propose Supervised Reinforcement Fine-Tuning (SRFT), a single-stage method that unifies both fine-tuning paradigms through entropy-aware weighting mechanisms. Our approach simultaneously applies SFT and RL to directly optimize the LLM using demonstrations and self-exploration rollouts rather than through two-stage sequential methods. Extensive experiments show that SRFT achieves 59.1% average accuracy, outperforming zero-RL methods by 9.0% on five mathematical reasoning benchmarks and 10.9% on three out-of-distribution benchmarks.

Songjun Tu, Jiahao Lin, Xiangyu Tian et al.

Recent advancements in post-training methodologies for large language models (LLMs) have highlighted reinforcement learning (RL) as a critical component for enhancing reasoning. However, the substantial computational costs associated with RL-based approaches have led to growing interest in alternative paradigms, such as Direct Preference Optimization (DPO). In this study, we investigate the effectiveness of DPO in facilitating self-improvement for LLMs through iterative preference-based learning. We demonstrate that a single round of DPO with coarse filtering significantly enhances mathematical reasoning performance, particularly for strong base model. Furthermore, we design an iterative enhancement framework for both the generator and the reward model (RM), enabling their mutual improvement through online interaction across multiple rounds of DPO. Finally, with simple verifiable rewards, our model DPO-VP achieves RL-level performance with significantly lower computational overhead. These findings highlight DPO as a scalable and cost-effective alternative to RL, offering a practical solution for enhancing LLM reasoning in resource-constrained situations.

Songjun Tu, Jingbo Sun, Qichao Zhang et al.

Preference-based reinforcement learning (PbRL) provides a powerful paradigm to avoid meticulous reward engineering by learning rewards based on human preferences. However, real-time human feedback is hard to obtain in online tasks. Most work suppose there is a "scripted teacher" that utilizes privileged predefined reward to provide preference feedback. In this paper, we propose a RL Self-augmented Large Language Model Feedback (RL-SaLLM-F) technique that does not rely on privileged information for online PbRL. RL-SaLLM-F leverages the reflective and discriminative capabilities of LLM to generate self-augmented trajectories and provide preference labels for reward learning. First, we identify an failure issue in LLM-based preference discrimination, specifically "query ambiguity", in online PbRL. Then LLM is employed to provide preference labels and generate self-augmented imagined trajectories that better achieve the task goal, thereby enhancing the quality and efficiency of feedback. Additionally, a double-check mechanism is introduced to mitigate randomness in the preference labels, improving the reliability of LLM feedback. The experiment across multiple tasks in the MetaWorld benchmark demonstrates the specific contributions of each proposed module in RL-SaLLM-F, and shows that self-augmented LLM feedback can effectively replace the impractical "scripted teacher" feedback. In summary, RL-SaLLM-F introduces a new direction of feedback acquisition in online PbRL that does not rely on any online privileged information, offering an efficient and lightweight solution with LLM-driven feedback.

Jingbo Sun, Qichao Zhang, Songjun Tu et al.

Zero-shot unsupervised reinforcement learning (URL) offers a promising direction for building generalist agents capable of generalizing to unseen tasks without additional supervision. Among existing approaches, successor representations (SR) have emerged as a prominent paradigm due to their effectiveness in structured, low-dimensional settings. However, SR methods struggle to scale to high-dimensional visual environments. Through empirical analysis, we identify two key limitations of SR in visual URL: (1) SR objectives often lead to suboptimal representations that attend to dynamics-irrelevant regions, resulting in inaccurate successor measures and degraded task generalization; and (2) these flawed representations hinder SR policies from modeling multi-modal skill-conditioned action distributions and ensuring skill controllability. To address these limitations, we propose Saliency-Guided Representation with Consistency Policy Learning (SRCP), a novel framework that improves zero-shot generalization of SR methods in visual URL. SRCP decouples representation learning from successor training by introducing a saliency-guided dynamics task to capture dynamics-relevant representations, thereby improving successor measure and task generalization. Moreover, it integrates a fast-sampling consistency policy with URL-specific classifier-free guidance and tailored training objectives to improve skill-conditioned policy modeling and controllability. Extensive experiments on 16 tasks across 4 datasets from the ExORL benchmark demonstrate that SRCP achieves state-of-the-art zero-shot generalization in visual URL and is compatible with various SR methods.

Songjun Tu, Jingbo Sun, Qichao Zhang et al.

Offline preference-based reinforcement learning (PbRL) typically operates in two phases: first, use human preferences to learn a reward model and annotate rewards for a reward-free offline dataset; second, learn a policy by optimizing the learned reward via offline RL. However, accurately modeling step-wise rewards from trajectory-level preference feedback presents inherent challenges. The reward bias introduced, particularly the overestimation of predicted rewards, leads to optimistic trajectory stitching, which undermines the pessimism mechanism critical to the offline RL phase. To address this challenge, we propose In-Dataset Trajectory Return Regularization (DTR) for offline PbRL, which leverages conditional sequence modeling to mitigate the risk of learning inaccurate trajectory stitching under reward bias. Specifically, DTR employs Decision Transformer and TD-Learning to strike a balance between maintaining fidelity to the behavior policy with high in-dataset trajectory returns and selecting optimal actions based on high reward labels. Additionally, we introduce an ensemble normalization technique that effectively integrates multiple reward models, balancing the tradeoff between reward differentiation and accuracy. Empirical evaluations on various benchmarks demonstrate the superiority of DTR over other state-of-the-art baselines.

Songjun Tu, Qichao Zhang, Jingbo Sun et al.

While multimodal large language models excel at tasks that integrate visual perception with symbolic reasoning, their performance is often undermined by a critical vulnerability: perception-induced errors that propagate through the reasoning chain. Current reinforcement learning (RL) fine-tuning methods, while enhancing reasoning abilities, largely fail to address the underlying misalignment between visual grounding and the subsequent reasoning process. To address this challenge, we propose \textbf{Caption-Regularized Policy Optimization (CapPO)}, a novel RL framework that explicitly enforces perceptual consistency during policy optimization. CapPO integrates two key mechanisms: (1) a caption-based consistency regularization, which minimizes the divergence between responses conditioned on raw images and those conditioned on captions, thereby anchoring reasoning to semantically faithful visual content; and (2) a KL-weighted advantage estimation scheme, which adaptively scales reinforcement signals to strengthen perceptually consistent trajectories while suppressing spurious correlations. Extensive experiments on five math-focused and five general reasoning benchmarks demonstrate that CapPO achieves competitive performance, yielding gains of +6.0% accuracy on math-related tasks and +2.4% on general reasoning tasks over the base Qwen2.5-VL-7B model. Moreover, ablation studies further confirm the effectiveness of each component, while error analysis reveals that CapPO significantly reduces perception-related mistakes compared with baselines. Overall, CapPO provides a simple yet effective framework for improving multimodal reasoning.

Jingbo Sun, Songjun Tu, Qichao Zhang et al.

Generalizing policies to unseen scenarios remains a critical challenge in visual reinforcement learning, where agents often overfit to the specific visual observations of the training environment. In unseen environments, distracting pixels may lead agents to extract representations containing task-irrelevant information. As a result, agents may deviate from the optimal behaviors learned during training, thereby hindering visual generalization.To address this issue, we propose the Salience-Invariant Consistent Policy Learning (SCPL) algorithm, an efficient framework for zero-shot generalization. Our approach introduces a novel value consistency module alongside a dynamics module to effectively capture task-relevant representations. The value consistency module, guided by saliency, ensures the agent focuses on task-relevant pixels in both original and perturbed observations, while the dynamics module uses augmented data to help the encoder capture dynamic- and reward-relevant representations. Additionally, our theoretical analysis highlights the importance of policy consistency for generalization. To strengthen this, we introduce a policy consistency module with a KL divergence constraint to maintain consistent policies across original and perturbed observations.Extensive experiments on the DMC-GB, Robotic Manipulation, and CARLA benchmarks demonstrate that SCPL significantly outperforms state-of-the-art methods in terms of generalization. Notably, SCPL achieves average performance improvements of 14\%, 39\%, and 69\% in the challenging DMC video hard setting, the Robotic hard setting, and the CARLA benchmark, respectively.Project Page: https://sites.google.com/view/scpl-rl.