Humanoid robots are drawing significant attention as versatile platforms for complex motor control, human-robot interaction, and general-purpose physical intelligence. However, achieving efficient whole-body control (WBC) in humanoids remains a fundamental challenge due to sophisticated dynamics, underactuation, and diverse task requirements. While learning-based controllers have shown promise for complex tasks, their reliance on labor-intensive and costly retraining for new scenarios limits real-world applicability. To address these limitations, behavior(al) foundation models (BFMs) have emerged as a new paradigm that leverages large-scale pre-training to learn reusable primitive skills and broad behavioral priors, enabling zero-shot or rapid adaptation to a wide range of downstream tasks. In this paper, we present a comprehensive overview of BFMs for humanoid WBC, tracing their development across diverse pre-training pipelines. Furthermore, we discuss real-world applications, current limitations, urgent challenges, and future opportunities, positioning BFMs as a key approach toward scalable and general-purpose humanoid intelligence. Finally, we provide a curated and regularly updated collection of BFM papers and projects to facilitate further research, which is available at https://github.com/yuanmingqi/awesome-bfm-papers.

As rapidly growing AI computational demands accelerate the need for new hardware installation and maintenance, this work explores optimal data center resource management by balancing operational efficiency with fault tolerance through strategic rack positioning considering diverse resources and locations. Traditional mixed-integer programming (MIP) approaches often struggle with scalability, while heuristic methods may result in significant sub-optimality. To address these issues, this paper presents a novel two-tier optimization framework using a high-level deep reinforcement learning (DRL) model to guide a low-level gradient-based heuristic for local search. The high-level DRL agent employs Leader Reward for optimal rack type ordering, and the low-level heuristic efficiently maps racks to positions, minimizing movement counts and ensuring fault-tolerant resource distribution. This approach allows scalability to over 100,000 positions and 100 rack types. Our method outperformed the gradient-based heuristic by 7% on average and the MIP solver by over 30% in objective value. It achieved a 100% success rate versus MIP's 97.5% (within a 20-minute limit), completing in just 2 minutes compared to MIP's 1630 minutes (i.e., almost 4 orders of magnitude improvement). Unlike the MIP solver, which showed performance variability under time constraints and high penalties, our algorithm consistently delivered stable, efficient results—an essential feature for large-scale data center management.

Skills are effective temporal abstractions established for sequential decision making, which enable efficient hierarchical learning for long-horizon tasks and facilitate multi-task learning through their transferability. Despite extensive research, research gaps remain in multi-agent scenarios, particularly for automatically extracting subgroup coordination patterns in a multi-agent task. In this case, we propose two novel auto-encoder schemes: VO-MASD-3D and VO-MASD-Hier, to simultaneously capture subgroup- and temporal-level abstractions and form multi-agent skills, which firstly solves the aforementioned challenge. An essential algorithm component of these schemes is a dynamic grouping function that can automatically detect latent subgroups based on agent interactions in a task. Further, our method can be applied to offline multi-task data, and the discovered subgroup skills can be transferred across relevant tasks without retraining. Empirical evaluations on StarCraft tasks indicate that our approach significantly outperforms existing hierarchical multi-agent reinforcement learning (MARL) methods. Moreover, skills discovered using our method can effectively reduce the learning difficulty in MARL scenarios with delayed and sparse reward signals. The codebase is available at: https://github.com/LucasCJYSDL/VOMASD.

Monte Carlo Tree Search (MCTS), which leverages Upper Confidence Bound for Trees (UCTs) to balance exploration and exploitation through randomized sampling, is instrumental to solving complex planning problems. However, for multi-agent planning, MCTS is confronted with a large combinatorial action space that often grows exponentially with the number of agents. As a result, the branching factor of MCTS during tree expansion also increases exponentially, making it very difficult to efficiently explore and exploit during tree search. To this end, we propose MALinZero, a new approach to leverage low-dimensional representational structures on joint-action returns and enable efficient MCTS in complex multi-agent planning. Our solution can be viewed as projecting the joint-action returns into the low-dimensional space representable using a contextual linear bandit problem formulation. We solve the contextual linear bandit problem with convex and $\mu$-smooth loss functions -- in order to place more importance on better joint actions and mitigate potential representational limitations -- and derive a linear Upper Confidence Bound applied to trees (LinUCT) to enable novel multi-agent exploration and exploitation in the low-dimensional space. We analyze the regret of MALinZero for low-dimensional reward functions and propose an $(1-\tfrac1e)$-approximation algorithm for the joint action selection by maximizing a sub-modular objective. MALinZero demonstrates state-of-the-art performance on multi-agent benchmarks such as matrix games, SMAC, and SMACv2, outperforming both model-based and model-free multi-agent reinforcement learning baselines with faster learning speed and better performance.

This paper addresses the challenge of achieving order-optimal sample complexity in reinforcement learning for discounted Markov Decision Processes (MDPs) with general policy parameterization and multi-layer neural network critics. Existing approaches either fail to achieve the optimal rate or assume a linear critic. We introduce Natural Actor-Critic with Data Drop (NAC-DD) algorithm, which integrates Natural Policy Gradient methods with a Data Drop technique to mitigate statistical dependencies inherent in Markovian sampling. NAC-DD achieves an optimal sample complexity of $\tilde{\mathcal{O}}(1/\epsilon^2)$, marking a significant improvement over the previous state-of-the-art guarantee of $\tilde{O}(1/\epsilon^3)$. The algorithm employs a multi-layer neural network critic with differentiable activation functions, aligning with real-world applications where tabular policies and linear critics are insufficient. Our work represents the first to achieve order-optimal sample complexity for actor-critic methods with neural function approximation, continuous state and action spaces, and Markovian sampling. Empirical evaluations on benchmark tasks confirm the theoretical findings, demonstrating the practical efficacy of the proposed method.

Online optimization of resource management for large-scale data centers and infrastructures to meet dynamic capacity reservation demands and various practical constraints (e.g., feasibility and robustness) is a very challenging problem. Mixed Integer Programming (MIP) approaches suffer from recognized limitations in such a dynamic environment, while learning-based approaches may face with prohibitively large state/action spaces. To this end, this paper presents a novel two-tiered online optimization to enable a learning-based Resource Allowance System (RAS). To solve optimal server-to-reservation assignment in RAS in an online fashion, the proposed solution leverages a reinforcement learning (RL) agent to make high-level decisions, e.g., how much resource to select from the Main Switch Boards (MSBs), and then a low-level Mixed Integer Linear Programming (MILP) solver to generate the local server-to-reservation mapping, conditioned on the RL decisions. We take into account fault tolerance, server movement minimization, and network affinity requirements and apply the proposed solution to large-scale RAS problems. To provide interpretability, we further train a decision tree model to explain the learned policies and to prune unreasonable corner cases at the low-level MILP solver, resulting in further performance improvement. Extensive evaluations show that our two-tiered solution outperforms baselines such as pure MIP solver by over 15% while delivering$100\times $speedup in computation.

Sepsis, a life-threatening condition triggered by the body's exaggerated response to infection, demands urgent intervention to prevent severe complications. Existing machine learning methods for managing sepsis struggle in offline scenarios, exhibiting suboptimal performance with survival rates below 50%. This paper introduces thePosNegDM— “Reinforcement Learning with Positive and Negative Demonstrations for Sequential Decision-Making” framework utilizing an innovative transformer-based model and a feedback reinforcer to replicate expert actions while considering individual patient characteristics. A mortality classifier with 96.7% accuracy guides treatment decisions towards positive outcomes. ThePosNegDMframework significantly improves patient survival, saving 97.39% of patients, outperforming established machine learning algorithms (Decision Transformer and Behavioral Cloning) with survival rates of 33.4% and 43.5%, respectively. Additionally, ablation studies underscore the critical role of the transformer-based decision maker and the integration of a mortality classifier in enhancing overall survival rates. In summary, our proposed approach presents a promising avenue for enhancing sepsis treatment outcomes, contributing to improved patient care and reduced healthcare costs.

Imitation learning (IL) has been proposed to recover the expert policy from demonstrations. However, it would be difficult to learn a single monolithic policy for highly complex long-horizon tasks of which the expert policy usually contains subtask hierarchies. Therefore, hierarchical IL (HIL) has been developed to learn a hierarchical policy from expert demonstrations through explicitly modeling the activity structure in a task with the option framework. Existing HIL methods either overlook the causal relationship between the subtask structure and the learned policy, or fail to learn the high-level and low-level policy in the hierarchical framework in conjuncture, which leads to suboptimality. In this work, we propose a novel HIL algorithm-hierarchical adversarial inverse reinforcement learning (H-AIRL), which extends a state-of-the-art (SOTA) IL algorithm-AIRL, with the one-step option framework. Specifically, we redefine the AIRL objectives on the extended state and action spaces, and further introduce a directed information term to the objective function to enhance the causality between the low-level policy and its corresponding subtask. Moreover, we propose an expectation-maximization (EM) adaption of our algorithm so that it can be applied to expert demonstrations without the subtask annotations which are more accessible in practice. Theoretical justifications of our algorithm design and evaluations on challenging robotic control tasks are provided to show the superiority of our algorithm compared with SOTA HIL baselines. The codes are available at https://github.com/LucasCJYSDL/HierAIRL.

Multi-task Imitation Learning (MIL) aims to train a policy capable of performing a distribution of tasks based on multi-task expert demonstrations, which is essential for general-purpose robots. Existing MIL algorithms suffer from low data efficiency and poor performance on complex long-horizontal tasks. We develop Multi-task Hierarchical Adversarial Inverse Reinforcement Learning (MH-AIRL) to learn hierarchically-structured multi-task policies, which is more beneficial for compositional tasks with long horizons and has higher expert data efficiency through identifying and transferring reusable basic skills across tasks. To realize this, MH-AIRL effectively synthesizes context-based multi-task learning, AIRL (an IL approach), and hierarchical policy learning. Further, MH-AIRL can be adopted to demonstrations without the task or skill annotations (i.e., state-action pairs only) which are more accessible in practice. Theoretical justifications are provided for each module of MH-AIRL, and evaluations on challenging multi-task settings demonstrate superior performance and transferability of the multi-task policies learned with MH-AIRL as compared to SOTA MIL baselines.

Hierarchical Imitation Learning (HIL) has been proposed to recover highly-complex behaviors in long-horizon tasks from expert demonstrations by modeling the task hierarchy with the option framework. Existing methods either overlook the causal relationship between the subtask and its corresponding policy or cannot learn the policy in an end-to-end fashion, which leads to suboptimality. In this work, we develop a novel HIL algorithm based on Adversarial Inverse Reinforcement Learning and adapt it with the Expectation-Maximization algorithm in order to directly recover a hierarchical policy from the unannotated demonstrations. Further, we introduce a directed information term to the objective function to enhance the causality and propose a Variational Autoencoder framework for learning with our objectives in an end-to-end fashion. Theoretical justifications and evaluations on challenging robotic control tasks are provided to show the superiority of our algorithm. The codes are available at https://github.com/LucasCJYSDL/HierAIRL.

Learning rich skills under the option framework without supervision of external rewards is at the frontier of reinforcement learning research. Existing works mainly fall into two distinctive categories: variational option discovery that maximizes the diversity of the options through a mutual information loss (while ignoring coverage) and Laplacian-based methods that focus on improving the coverage of options by increasing connectivity of the state space (while ignoring diversity). In this paper, we show that diversity and coverage in unsupervised option discovery can indeed be unified under the same mathematical framework. To be specific, we explicitly quantify the diversity and coverage of the learned options through a novel use of Determinantal Point Process (DPP) and optimize these objectives to discover options with both superior diversity and coverage. Our proposed algorithm, ODPP, has undergone extensive evaluation on challenging tasks created with Mujoco and Atari. The results demonstrate that our algorithm outperforms state-of-the-art baselines in both diversity- and coverage-driven categories.

Covering option discovery has been developed to improve the exploration of RL in single-agent scenarios with sparse reward signals, through connecting the most distant states in the embedding space provided by the Fiedler vector of the state transition graph. Given that joint state space grows exponentially with the number of agents in multi-agent systems, existing researches still relying on single-agent option discovery either become prohibitive or fail to directly discover joint options that improve the connectivity of the joint state space. In this paper, we show how to directly compute multi-agent options with collaborative exploratory behaviors while still enjoying the ease of decomposition. Our key idea is to approximate the joint state space as a Kronecker graph, based on which we can directly estimate its Fiedler vector using the Laplacian spectrum of individual agents' transition graphs. Further, considering that directly computing the Laplacian spectrum is intractable for tasks with infinite-scale state spaces, we further propose a deep learning extension of our method by estimating eigenfunctions through NN-based representation learning techniques. The evaluation on multi-agent tasks built with simulators like Mujoco, shows that the proposed algorithm can successfully identify multi-agent options, and significantly outperforms the state-of-the-art. Codes are available at: https://github.itap.purdue.edu/Clan-labs/ScalableMAODvia_KP.

Making decisions in complex driving environments is a challenging task for autonomous agents. Imitation learning methods have great potentials for achieving such a goal. Adversarial Inverse Reinforcement Learning (AIRL) is one of the state-of-art imitation learning methods that can learn both a behavioral policy and a reward function simultaneously, yet it is only demonstrated in simple and static environments where no interactions are introduced. In this paper, we improve and stabilize AIRL’s performance by augmenting it with semantic rewards in the learning framework. Additionally, we adapt the augmented AIRL to a more practical and challenging decision-making task in a highly interactive environment in autonomous driving. The proposed method is compared with four baselines and evaluated by four performance metrics. Simulation results show that the augmented AIRL outperforms all the baseline methods, and its performance is comparable with that of the experts on all of the four metrics.

This work studies a supervised learning method using 3D LiDAR data for autonomous driving applications. A system of semantic segmentation, including range image segmentation, sample generation, track-level annotation and supervised learning, is developed. The formation and content of a data sample is studied intensively to address the specialty of 3D LiDAR data, which can be represented at a Cartesian or a 2D polar coordinate system, and composed of a segment as the foreground and/or the neighborhood points as the background. A CNN-based classifier is trained to map a given sample to an object label. Qualitative and quantitative experiments show that the background information and multiple feature map fusion significantly improve the performance of the classifier.