ECO: Energy-Constrained Optimization with Reinforcement Learning for Humanoid Walking

Achieving stable and energy-efficient locomotion is essential for humanoid robots to operate continuously in real-world applications. Existing MPC and RL approaches often rely on energy-related metrics embedded within a multi-objective optimization framework, which require extensive hyperparameter tuning and often result in suboptimal policies. To address these challenges, we propose ECO (Energy-Constrained Optimization), a constrained RL framework that separates energy-related metrics from rewards, reformulating them as explicit inequality constraints. This method provides a clear and interpretable physical representation of energy costs, enabling more efficient and intuitive hyperparameter tuning for improved energy efficiency. ECO introduces dedicated constraints for energy consumption and reference motion, enforced by the Lagrangian method, to achieve stable, symmetric, and energy-efficient walking for humanoid robots. We evaluated ECO against MPC, standard RL with reward shaping, and four state-of-the-art constrained RL methods. Experiments, including sim-to-sim and sim-to-real transfers on the kid-sized humanoid robot BRUCE, demonstrate that ECO significantly reduces energy consumption compared to baselines while maintaining robust walking performance. These results highlight a substantial advancement in energy-efficient humanoid locomotion. All experimental demonstrations can be found on the project website: https://sites.google.com/view/eco-humanoid.

Enhance the Safety in Reinforcement Learning by ADRC Lagrangian Methods

Safe reinforcement learning (Safe RL) seeks to maximize rewards while satisfying safety constraints, typically addressed through Lagrangian-based methods. However, existing approaches, including PID and classical Lagrangian methods, suffer from oscillations and frequent safety violations due to parameter sensitivity and inherent phase lag. To address these limitations, we propose ADRC-Lagrangian methods that leverage Active Disturbance Rejection Control (ADRC) for enhanced robustness and reduced oscillations. Our unified framework encompasses classical and PID Lagrangian methods as special cases while significantly improving safety performance. Extensive experiments demonstrate that our approach reduces safety violations by up to 74%, constraint violation magnitudes by 89%, and average costs by 67\%, establishing superior effectiveness for Safe RL in complex environments.

Your Group-Relative Advantage Is Biased

Reinforcement Learning from Verifier Rewards (RLVR) has emerged as a widely used approach for post-training large language models on reasoning tasks, with group-based methods such as GRPO and its variants gaining broad adoption. These methods rely on group-relative advantage estimation to avoid learned critics, yet its theoretical properties remain poorly understood. In this work, we uncover a fundamental issue of group-based RL: the group-relative advantage estimator is inherently biased relative to the true (expected) advantage. We provide the first theoretical analysis showing that it systematically underestimates advantages for hard prompts and overestimates them for easy prompts, leading to imbalanced exploration and exploitation. To address this issue, we propose History-Aware Adaptive Difficulty Weighting (HA-DW), an adaptive reweighting scheme that adjusts advantage estimates based on an evolving difficulty anchor and training dynamics. Both theoretical analysis and experiments on five mathematical reasoning benchmarks demonstrate that HA-DW consistently improves performance when integrated into GRPO and its variants. Our results suggest that correcting biased advantage estimation is critical for robust and efficient RLVR training.

Constrained Language Model Policy Optimization via Risk-aware Stepwise Alignment

When fine-tuning pre-trained Language Models (LMs) to exhibit desired behaviors, maintaining control over risk is critical for ensuring both safety and trustworthiness. Most existing safety alignment methods, such as Safe RLHF and SACPO, typically operate under a risk-neutral paradigm that is insufficient to address the risks arising from deviations from the reference policy and offers limited robustness against rare but potentially catastrophic harmful behaviors. To address this limitation, we propose Risk-aware Stepwise Alignment (RSA), a novel alignment method that explicitly incorporates risk awareness into the policy optimization process by leveraging a class of nested risk measures. Specifically, RSA formulates safety alignment as a token-level risk-aware constrained policy optimization problem and solves it through a stepwise alignment procedure that yields token-level policy updates derived from the nested risk measures. This design offers two key benefits: (1) it mitigates risks induced by excessive model shift away from a reference policy, and (2) it explicitly suppresses low-probability yet high-impact harmful behaviors. Moreover, we provide theoretical analysis on policy optimality under mild assumptions. Experimental results demonstrate that our method achieves high levels of helpfulness while ensuring strong safety and significantly suppresses tail risks, namely low-probability yet high-impact unsafe responses.

VLA-Arena: An Open-Source Framework for Benchmarking Vision-Language-Action Models

While Vision-Language-Action models (VLAs) are rapidly advancing towards generalist robot policies, it remains difficult to quantitatively understand their limits and failure modes. To address this, we introduce a comprehensive benchmark called VLA-Arena. We propose a novel structured task design framework to quantify difficulty across three orthogonal axes: (1) Task Structure, (2) Language Command, and (3) Visual Observation. This allows us to systematically design tasks with fine-grained difficulty levels, enabling a precise measurement of model capability frontiers. For Task Structure, VLA-Arena's 170 tasks are grouped into four dimensions: Safety, Distractor, Extrapolation, and Long Horizon. Each task is designed with three difficulty levels (L0-L2), with fine-tuning performed exclusively on L0 to assess general capability. Orthogonal to this, language (W0-W4) and visual (V0-V4) perturbations can be applied to any task to enable a decoupled analysis of robustness. Our extensive evaluation of state-of-the-art VLAs reveals several critical limitations, including a strong tendency toward memorization over generalization, asymmetric robustness, a lack of consideration for safety constraints, and an inability to compose learned skills for long-horizon tasks. To foster research addressing these challenges and ensure reproducibility, we provide the complete VLA-Arena framework, including an end-to-end toolchain from task definition to automated evaluation and the VLA-Arena-S/M/L datasets for fine-tuning. Our benchmark, data, models, and leaderboard are available at https://vla-arena.github.io.

RoboSafe: Safeguarding Embodied Agents via Executable Safety Logic

Embodied agents powered by vision-language models (VLMs) are increasingly capable of executing complex real-world tasks, yet they remain vulnerable to hazardous instructions that may trigger unsafe behaviors. Runtime safety guardrails, which intercept hazardous actions during task execution, offer a promising solution due to their flexibility. However, existing defenses often rely on static rule filters or prompt-level control, which struggle to address implicit risks arising in dynamic, temporally dependent, and context-rich environments. To address this, we propose RoboSafe, a hybrid reasoning runtime safeguard for embodied agents through executable predicate-based safety logic. RoboSafe integrates two complementary reasoning processes on a Hybrid Long-Short Safety Memory. We first propose a Backward Reflective Reasoning module that continuously revisits recent trajectories in short-term memory to infer temporal safety predicates and proactively triggers replanning when violations are detected. We then propose a Forward Predictive Reasoning module that anticipates upcoming risks by generating context-aware safety predicates from the long-term safety memory and the agent's multimodal observations. Together, these components form an adaptive, verifiable safety logic that is both interpretable and executable as code. Extensive experiments across multiple agents demonstrate that RoboSafe substantially reduces hazardous actions (-36.8% risk occurrence) compared with leading baselines, while maintaining near-original task performance. Real-world evaluations on physical robotic arms further confirm its practicality. Code will be released upon acceptance.

SportsGPT: An LLM-driven Framework for Interpretable Sports Motion Assessment and Training Guidance

Existing intelligent sports analysis systems mainly focus on "scoring and visualization," often lacking automatic performance diagnosis and interpretable training guidance. Recent advances in Large Language Models (LLMs) and motion analysis techniques provide new opportunities to address the above limitations. In this paper, we propose SportsGPT, an LLM-driven framework for interpretable sports motion assessment and training guidance, which establishes a closed loop from motion time-series input to professional training guidance. First, given a set of high-quality target models, we introduce MotionDTW, a two-stage time series alignment algorithm designed for accurate keyframe extraction from skeleton-based motion sequences. Subsequently, we design a Knowledge-based Interpretable Sports Motion Assessment Model (KISMAM) to obtain a set of interpretable assessment metrics (e.g., insufficient extension) by contrasting the keyframes with the target models. Finally, we propose SportsRAG, a RAG-based training guidance model built upon Qwen3. Leveraging a 6B-token knowledge base, it prompts the LLM to generate professional training guidance by retrieving domain-specific QA pairs. Experimental results demonstrate that MotionDTW significantly outperforms traditional methods with lower temporal error and higher IoU scores. Furthermore, ablation studies validate the KISMAM and SportsRAG, confirming that SportsGPT surpasses general LLMs in diagnostic accuracy and professionalism.

Prismatic World Model: Learning Compositional Dynamics for Planning in Hybrid Systems

Model-based planning in robotic domains is fundamentally challenged by the hybrid nature of physical dynamics, where continuous motion is punctuated by discrete events such as contacts and impacts. Conventional latent world models typically employ monolithic neural networks that enforce global continuity, inevitably over-smoothing the distinct dynamic modes (e.g., sticking vs. sliding, flight vs. stance). For a planner, this smoothing results in catastrophic compounding errors during long-horizon lookaheads, rendering the search process unreliable at physical boundaries. To address this, we introduce the Prismatic World Model (PRISM-WM), a structured architecture designed to decompose complex hybrid dynamics into composable primitives. PRISM-WM leverages a context-aware Mixture-of-Experts (MoE) framework where a gating mechanism implicitly identifies the current physical mode, and specialized experts predict the associated transition dynamics. We further introduce a latent orthogonalization objective to ensure expert diversity, effectively preventing mode collapse. By accurately modeling the sharp mode transitions in system dynamics, PRISM-WM significantly reduces rollout drift. Extensive experiments on challenging continuous control benchmarks, including high-dimensional humanoids and diverse multi-task settings, demonstrate that PRISM-WM provides a superior high-fidelity substrate for trajectory optimization algorithms (e.g., TD-MPC), proving its potential as a powerful foundational model for next-generation model-based agents.

Boosting In-Silicon Directed Evolution with Fine-Tuned Protein Language Model and Tree Search

Protein evolution through amino acid sequence mutations is a cornerstone of life sciences. While current in-silicon directed evolution algorithms largely focus on designing heuristic search strategies, they overlook how to integrate the transformative protein language models, which encode rich evolutionary patterns, with reinforcement learning to learn to directly evolve proteins. To bridge this gap, we propose AlphaDE, a novel framework to optimize protein sequences by harnessing the innovative paradigms of large language models such as fine-tuning and test-time inference. First, AlphaDE fine-tunes pretrained protein language models using masked language modeling on homologous protein sequences to activate the evolutionary plausibility for the interested protein class. Second, AlphaDE introduces test-time inference based on Monte Carlo tree search, which effectively evolves proteins with evolutionary guidance from the fine-tuned protein language model. Extensive benchmark experiments show that AlphaDE remarkably outperforms previous state-of-the-art methods even with few-shot fine-tuning. A further case study demonstrates that AlphaDE supports condensing the protein sequence space of avGFP through computational evolution.

Finding Kissing Numbers with Game-theoretic Reinforcement Learning

Since Isaac Newton first studied the Kissing Number Problem in 1694, determining the maximal number of non-overlapping spheres around a central sphere has remained a fundamental challenge. This problem represents the local analogue of Hilbert's 18th problem on sphere packing, bridging geometry, number theory, and information theory. Although significant progress has been made through lattices and codes, the irregularities of high-dimensional geometry and exponentially growing combinatorial complexity beyond 8 dimensions, which exceeds the complexity of Go game, limit the scalability of existing methods. Here we model this problem as a two-player matrix completion game and train the game-theoretic reinforcement learning system, PackingStar, to efficiently explore high-dimensional spaces. The matrix entries represent pairwise cosines of sphere center vectors; one player fills entries while another corrects suboptimal ones, jointly maximizing the matrix size, corresponding to the kissing number. This cooperative dynamics substantially improves sample quality, making the extremely large spaces tractable. PackingStar reproduces previous configurations and surpasses all human-known records from dimensions 25 to 31, with the configuration in 25 dimensions geometrically corresponding to the Leech lattice and suggesting possible optimality. It achieves the first breakthrough beyond rational structures from 1971 in 13 dimensions and discovers over 6000 new structures in 14 and other dimensions. These results demonstrate AI's power to explore high-dimensional spaces beyond human intuition and open new pathways for the Kissing Number Problem and broader geometry problems.