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Zero-Shot Whole-Body Humanoid Control via Behavioral Foundation Models

Andrea Tirinzoni, Ahmed Touati, Jesse Farebrother, Mateusz Guzek, Anssi Kanervisto, Yingchen Xu, Alessandro Lazaric, Matteo Pirotta

arXiv:2504.11054v1cs.LG

TL;DR

Unsupervised RL lacks reliable zero-shot task generalization from unlabeled behavior data, especially for complex humanoid control. FB-CPR aligns unsupervised policy learning with unlabeled trajectories, producing Meta Motivo, a humanoid behavioral foundation model that solves diverse whole-body tasks zero-shot and outperforms unsupervised RL and model-based baselines.

  • Problem

    Existing unsupervised RL methods have limited zero-shot task alignment, requiring downstream training, broad transition datasets, or losses weakly correlated with target behaviors.

    Source: §1 · p. 2
  • Method

    FB-CPR embeds unlabeled trajectories into the forward-backward latent space and uses a latent-conditional discriminator to encourage policies to cover dataset states.

    Source: §1 · p. 2, §3 · pp. 4–5
  • Results

    FB-CPR trained a humanoid behavioral foundation model that solves motion tracking, goal reaching, and reward optimization zero-shot, with competitive task-specific performance and better unsupervised-RL and model-based baselines.

    Source: §1 · p. 2, §5 · p. 10
  • Takeaways & Limitations

    Unlabeled motion-capture behaviors can ground zero-shot humanoid control while preserving broad task coverage and human-like behavior.

    Source: §1 · p. 2, §5 · p. 10

    FB-CPR struggles on tasks far from motion-capture data and the resulting model is limited to proprioceptive observations, excluding navigation and object interaction.

    Source: §5 · p. 10

Abstract

from arXiv · show

Unsupervised reinforcement learning (RL) aims at pre-training agents that can solve a wide range of downstream tasks in complex environments. Despite recent advancements, existing approaches suffer from several limitations: they may require running an RL process on each downstream task to achieve a satisfactory performance, they may need access to datasets with good coverage or well-curated task-specific samples, or they may pre-train policies with unsupervised losses that are poorly correlated with the downstream tasks of interest. In this paper, we introduce a novel algorithm regularizing unsupervised RL towards imitating trajectories from unlabeled behavior datasets. The key technical novelty of our method, called Forward-Backward Representations with Conditional-Policy Regularization, is to train forward-backward representations to embed the unlabeled trajectories to the same latent space used to represent states, rewards, and policies, and use a latent-conditional discriminator to encourage policies to ``cover'' the states in the unlabeled behavior dataset. As a result, we can learn policies that are well aligned with the behaviors in the dataset, while retaining zero-shot generalization capabilities for reward-based and imitation tasks. We demonstrate the effectiveness of this new approach in a challenging humanoid control problem: leveraging observation-only motion capture datasets, we train Meta Motivo, the first humanoid behavioral foundation model that can be prompted to solve a variety of whole-body tasks, including motion tracking, goal reaching, and reward optimization. The resulting model is capable of expressing human-like behaviors and it achieves competitive performance with task-specific methods while outperforming state-of-the-art unsupervised RL and model-based baselines.

1 Introduction

This section motivates behavioral foundation models for humanoid whole-body control and introduces FB-CPR, which grounds zero-shot reinforcement learning in unlabeled behavior trajectories while retaining broad task-solving capabilities.

Motivation

  • Behavioral foundation models aim to extend promptable foundation-model capabilities to humanoid agents, enabling diverse responses to imitation, goal, and reward prompts in whole-body control.The target applications include robotics, virtual avatars, and non-player characters.Source: §1 · p. 2

Limitations

  • Existing zero-shot RL depends on broad exploratory transition datasets and unsupervised objectives with weak task alignment, limiting performance in high-dimensional systems with unstable dynamics.Alternative sequence-model approaches often reproduce demonstrated behaviors without generalizing to unseen tasks, while demonstration-regularized RL may still require hierarchical RL for downstream tasks.Source: §1 · p. 2

Contributions

  • FB-CPR grounds forward-backward unsupervised RL representations toward unlabeled behaviors by embedding trajectories in the policy latent space and using a latent-conditional discriminator to encourage state coverage.The method regularizes online policy learning toward observation-only trajectories without requiring action labels.Source: §1 · p. 2
  • The resulting humanoid behavioral foundation model solves motion tracking, goal reaching, and reward optimization zero-shot while expressing human-like behaviors and outperforming unsupervised RL and model-based baselines.It is trained on SMPL-based humanoid control with the uncurated AMASS motion-capture dataset and is competitive with task-specific methods.Source: §1 · p. 2

2 Preliminaries

This section formalizes reward-free discounted MDPs and introduces successor measures and Forward-Backward representations as the basis for zero-shot evaluation, optimization, and inference. It also identifies finite-rank and poor-coverage limitations that can cause policy collapse and weak downstream performance.

  • The framework considers a reward-free discounted MDP with state and action spaces, transition kernel, initial-state distribution, discount factor, and stochastic policies.State-action trajectories follow the transition kernel and policy from an initial state-action pair.Source: §2 · p. 3

Successor measures for zero-shot RL

  • Successor measures represent discounted future-state distributions under a policy and factor action values into environment dynamics and task rewards.This factorization enables evaluating a policy for any reward without further training.Source: §2 · p. 3

Forward-Backward (FB) representations

  • Low-rank successor-measure decompositions yield Forward-Backward representations that support both zero-shot policy evaluation and zero-shot policy optimization.Forward and backward embeddings approximate successor measures, with action values expressed as F(s, a)^⊤z and reward information mapped through the backward embedding.Source: §2 · p. 3
  • For multiple policies, FB shares a task encoding z across the forward representation and policy, with training based on Bellman-residual criteria and actor optimization for continuous actions.In practice, FB models are often trained offline using transition datasets collected by unsupervised exploration.Source: §2 · p. 3

Zero-shot inference

  • Pre-trained FB models infer reward-maximizing, goal-reaching, and imitation policies in zero-shot fashion without additional task-specific learning, planning, or fine-tuning.Reward and goal tasks use backward-embedding-derived encodings, while demonstrations can be embedded through ERFB for imitation.Source: §2 · p. 4
  • With finite representation rank or poor dataset coverage, FB lacks sufficient inductive bias or offline support, causing collapse to a few policies with poor downstream performance.Optimality for arbitrary rewards and imitation is guaranteed only in the limit of full rank and full coverage of ρ.Source: §2 · p. 4

3 FB with Conditional Policy Regularization

FB-CPR steers latent-conditioned unsupervised policies toward unlabeled trajectories by embedding each trajectory into the policy latent space and matching joint state-latent distributions. A conditional discriminator supplies tractable density-ratio rewards, while a mixed latent distribution balances trajectory reproduction, goal reaching, and broad task coverage.

3 FB with Conditional Policy Regularization

  • FB-CPR interleaves environment rollouts with off-policy updates to forward-backward representations, discriminator, critic, and actor using the online replay buffer.The method samples multiple latent-conditioned policies during interaction and stores their unsupervised transitions in a finite-capacity buffer.Source: §3 · pp. 4–5
  • FB-CPR represents each unlabeled trajectory with an inferred latent z using ERFB, producing the dataset joint distribution pM(s, z) alongside FB’s pπ(s, z).The latent z is inferred so its policy would visit the trajectory’s states; this follows the single-trajectory embedding approach discussed with Pirotta et al. (2024).Source: §3 · pp. 4–5
  • The actor is regularized by minimizing the discrepancy between pπ(s, z) and pM(s, z), with α controlling the regularization strength.This distribution matching aligns FB policies with behaviors represented in the unlabeled dataset while retaining the latent-conditioned policy space.Source: §3 · p. 5
  • A latent-conditioned discriminator estimates the Jensen–Shannon variational objective, yielding the density-ratio reward log pM(s, z)/pπ(s, z) ≈ log D/(1−D).An off-policy critic then estimates action values for this approximate reward, which produces the final FB-CPR actor loss.Source: §3 · p. 5
  • The latent distribution mixes ERFB trajectory latents, backward-representation latents for online states, and hyperspherical uniform samples to support reproduction, goal reaching, and broader task coverage.The three components respectively generate challenging discriminator samples, focus capacity on observed-state goals, and cover the latent space exhaustively.Source: §3 · p. 5
  • Unlike state-marginal imitation schemes, conditional matching can reproduce trajectories; directly using ERFB avoids ad-hoc end-to-end trajectory encoding and binds policy and FB training consistently.The discussion contrasts this design with Peng et al. (2022), Vlastelica et al. (2024), and Tessler et al. (2023).Source: §3 · pp. 5–6

4 Experiments on Humanoid

Experiments evaluate FB-CPR on physically plausible whole-body humanoid control using observation-only AMASS motions across reward optimization, goal reaching, and tracking. FB-CPR achieves strong zero-shot performance, while ablations show benefits from online conditional regularization, unsupervised value maximization, and scaling.

4 Experiments on Humanoid

  • The humanoid suite uses a 24-body SMPL skeleton with 23 actuated bodies, normalized proprioception, bounded PD targets, joint limits, torque limits, and MuJoCo simulation at 450 Hz.Experiments use 8,902 training motions and 990 test motions from AMASS, totaling approximately 29 and 3 hours, respectively, and evaluate 45 rewards, 50 goals, and motion tracking.Source: §4 · p. 6

4.1 Main Results

  • FB-CPR reaches 73.4% of top-line performance across reward, goal-reaching, and tracking tasks, outperforming ASE by more than 1.4× in every category while requiring no downstream training or planning.It matches or surpasses specialized unsupervised RL methods and performs zero-shot inference.Source: §4.1 · p. 7, Table 1 · p. 7
  • FB-CPR achieves 61% of TD3’s reward-task performance, 177% of DIFFUSER’s performance, and 70% greater performance than ASE across reward tasks.Oracle MPPI improves over FB-CPR by 17.8% but requires at least 30 minutes per episode, compared with 12 seconds for FB-CPR.Source: §4.1 · p. 7
  • On goal reaching, FB-CPR performs similarly to specialized Goal-GAIL and Goal-TD3, while improving over ASE by 48% on proximity and 118% on success.It achieves higher proximity but lower success than planning-based approaches, indicating more persistent proximity but less reliable stable goal attainment.Source: §4.1 · pp. 7–8
  • For tracking, FB-CPR reaches about 80% and 88% of top-line EMD and success performance, respectively, with 83% success on the test dataset.It outperforms zero-shot and planning baselines; only Goal-TD3 performs better among multi-task baselines on average.Source: §4.1 · p. 8

4.2 Ablations

  • Ablations show that online FB-CPR substantially outperforms offline FB-AW, including the unsupervised value term improves reward and tracking, and latent-conditioned discrimination improves tracking over state-only matching.Larger models benefit more from larger motion datasets, with a 2× model significantly outperforming the 1× model.Source: §4.2 · pp. 9–10

5 Conclusions … C.3 Tasks and Metrics

The paper presents FB-CPR as a behavior-grounded unsupervised RL method for zero-shot humanoid control, while documenting its algorithmic regularizers, environment design, data construction, related work, and remaining limitations. The resulting behavioral foundation model achieves broad task performance but remains constrained by motion-capture coverage, proprioceptive observations, and imperfect behaviors.

5 Conclusions

  • FB-CPR combines FB-model zero-shot control with unlabeled behavior regularization, producing the first behavioral foundation model for zero-shot control of a complex humanoid agent with state-of-the-art performance across varied tasks.The method grounds online training and policy learning in behavior trajectories while retaining zero-shot capabilities.Source: §5 · p. 10
  • The method’s main limitations are weak performance on tasks far from motion-capture data, occasional unnatural behaviors, proprioceptive-only observations, and reliance on expensive motion-capture datasets.Future directions include richer perception, video-based training, test-time planning or adaptation, and more direct language-policy alignment.Source: §5 · p. 10

A Related Work

  • Prior humanoid-control work spans behavior cloning, imitation-regularized RL, motion tracking, and task-specific control, but lacks an established platform, dataset, or benchmark for multi-task whole-body humanoid control.Existing simulators use different skeletons and offer few reward-based tasks, while broader suites require task-specific observations for navigation or object interaction.Source: A Related Work · p. 19
  • Unsupervised RL pre-trains representations or diverse policies from interaction or passive data, but downstream tasks generally still require training a full RL model from scratch.Zero-shot RL instead uses goal-conditioned policies, successor features, generalized occupancy models, world models, or reward encodings, each with limitations such as restricted behavior scope, planning, or task-aware training.Source: A Related Work · p. 19
  • Demonstration-learning approaches use behavioral cloning, diffusion or transformer trajectory generation, discriminator-based RL, tracking, hierarchical RL, and internet-scale control datasets.FB-CPR differs by integrating unlabeled demonstrations into a zero-shot RL framework rather than relying solely on curated expert data, action labels, or downstream planning.Source: A Related Work · pp. 19–20, B Algorithmic details · p. 20

B Algorithmic details

  • FB-CPR adds orthonormality and temporal-difference regularization to stabilize FB representations and focus F on latent directions relevant to policy optimization.The orthonormality loss prevents B from becoming ill-conditioned or collapsing, while the temporal-difference loss aligns F(s, a, z)^Tz with the corresponding action-value function.Source: B Algorithmic details · p. 20

C.1 The SMPL MuJoCo Model

  • The refined SMPL MuJoCo humanoid uses more natural joint ranges and PD controllers derived from the dm_control CMU humanoid definition, improving stability and defining a more reasonable control space.The design addresses instability associated with unconstrained, over-actuated motion-tracking controllers, though reward-only policies can still produce non-natural behaviors.Source: §C.1 · p. 22

C.2 Data

  • AMASS-Act converts kinematic AMASS motions into action-labeled trajectories by training Goal-GAIL policies, while the experiments retain a filtered subset that excludes object interactions and redundant or removed datasets.AMASS unifies 15 motion-capture datasets into a single SMPL-based dataset, and the paper reports dataset statistics in Table 2.Source: §C.2 · p. 22, Table 2 · p. 22

C.3.1 Reward-based evaluation

Reward-based evaluation uses normalized [0, 1] rewards spanning eight whole-body behavior categories and assesses policies on 55 representative tasks by cumulative return over 300-step episodes. Test initial states mix random falling positions with AMASS data, differing from training, while FB-CPR infers rewards from state information and relies on pre-training to avoid rapid movements.

Reward categories

  • The reward suite normalizes rewards to [0, 1] and covers locomotion, standing, handstands, arm raising, rotation, jumping, ground poses, and crawling.Tasks specify targets such as velocity, height, posture, hand position, angular velocity, or ground configuration, often with control penalties.Source: §C.3.1 · pp. 22–23

Task design

  • Locomotion, rotation, jumping, and crawling require controlled movement targets, while standing, handstands, arm raising, and ground poses evaluate stable whole-body configurations.Movement tasks constrain speeds, directions, heights, or angular velocities; configuration tasks include balance, hand placement, and sitting, crouching, lying, or splitting.Source: §C.3.1 · pp. 23–24

FB-CPR limitation

  • FB-CPR infers rewards only from state-based information through B(s), so regularized pre-training must learn to avoid high-speed movements.This limitation arises because the method does not use action information for reward inference, despite explicit action penalties in some task definitions.Source: §C.3.1 · p. 23

Evaluation protocol

  • 55 representative tasks are evaluated using cumulative episode return over H = 300 steps, with test initial states mixing random falling positions and AMASS samples unlike training.The suite can generate virtually infinite tasks, but evaluation extracts 55 representative tasks.Source: §C.3.1 · p. 24

C.3.2 Motion tracking evaluation … D Additional Experimental Results

The appendices define motion-tracking and goal-based evaluation protocols, training procedures, and implementations for the compared humanoid-control algorithms. They also document shared architectures, inference methods, offline datasets, and additional experimental analysis.

C.3.2 Motion tracking evaluation

  • Motion tracking uses strict per-step success at threshold ξ = 0.5 and Earth Mover’s Distance to accommodate temporal misalignment, discontinuities, and physically unrealizable motions.Success requires accurate alignment at each step, whereas EMD can remain low when trajectories are slightly time-shifted.Source: §C.3.2 · pp. 24–25

C.3.3 Goal-based evaluation

  • Goal-based evaluation manually selects 50 attainable poses and measures both shortest-path success and soft proximity over 300-step episodes from randomly sampled test states.The poses include 38 training motions and 12 test motions, spanning different heights and body-part positions; distance uses positions and rotations while ignoring velocities.Source: §C.3.3 · p. 25, Figure 5 · p. 25

C.4 Training Protocols

  • Online training runs 50 parallel environments for 300-step episodes, mixes fall and motion-capture initialization, and prioritizes sampled motions using periodically updated tracking performance.Fall initialization is selected with probability 0.2; offline methods instead use an approximately 8.1M-transition combination of AMASS-Act and an FB-CPR replay buffer.Source: §C.4 · pp. 25–26

C.5.1 Shared configurations

  • Shared implementations use 5M-transition replay buffers, 1024-sample minibatches, eight-step unlabeled segments, state normalization, and MLP policies with fixed actor standard deviation 0.2.Online updates alternate 500-transition rollouts with 50 network updates, while Adam uses β1 = 0.9, β2 = 0.999, and ϵ = 10^-8.Source: §C.5.1 · pp. 26–27

C.5.1 Shared configurations; C.5.2 TD3

  • The shared discriminator is a three-layer, 1024-unit MLP conditioned on state and latent variables, trained with cross-entropy, learning rate 10^-5, and a Wasserstein-GAN gradient penalty of coefficient 10.TD3-based methods replace target-network minimization with an ensemble-Q absolute-difference penalty, using reported coefficients 0 or 0.5.Source: §C.5.1 · p. 27, §C.5.2 · pp. 27–28

C.5.3 FB-CPR; C.5.4 ASE; C.5.5 CALM; C.5.7 GOAL-GAIL

  • FB-CPR infers reward, goal, and tracking latents through weighted regression, goal-state representations, and per-timestep motion encodings, respectively.ASE, CALM, and GOAL-GAIL use off-policy TD3-based variants with learned representations or goal-conditioned discriminators, while ASE adds orthonormality regularization to prevent encoder collapse.Source: §C.5.3 · p. 28, §C.5.4 · pp. 28–29, §C.5.5 · p. 29

C.5.6 PHC; C.5.8 GOAL-TD3; C.5.9 MPPI

  • PHC performs one-step tracking by treating the next motion state as a forced goal, whereas GOAL-TD3 uses position-based rewards with dataset and hindsight goals, and MPPI plans under real dynamics and rewards.PHC uses reward −d_smpl(g, s′); GOAL-TD3 and MPPI use joint-position distance rewards while ignoring velocities.Source: §C.5.6 · p. 30, §C.5.8 · p. 31, §C.5.9 · p. 31

C.5.10 Diffuser; C.5.11 H-GAP; D Additional Experimental Results

  • Diffuser learns a diffusion model over state-action sequences for reward-guided sampling, while H-GAP discretizes trajectories with VQ-VAE and uses a Prior Transformer within MPC; the appendix then reports additional experimental analysis.Both offline methods train on the FB-CPR replay buffer and AMASS-Act dataset and select trajectories using task-specific rewards.Source: §C.5.10 · p. 32, §C.5.11 · p. 32, D Additional Experimental Results · p. 34

D.1 Detailed Results

The detailed results organize humanoid evaluation across reward optimization, goal reaching, and motion tracking, with dedicated tables for each metric and task grouping. Additional experiments report poor performance from H-GAP and learned-model MPPI baselines.

Reward optimization

  • Results are reported for reward-based tasks using average return per task and category.Tables 18 and 19 provide the corresponding task-level and category-level evaluations.Source: §D.1 · p. 34, Table 19 · p. 35

Goal reaching

Motion tracking

  • Tracking evaluation reports train and test EMD and success rate across subsets of the AMASS datasets.Table 22 groups the average tracking performance by AMASS subset.Source: §D.1 · p. 34, Table 22 · p. 38

Baseline results

  • H-GAP achieved 0.05 average normalized performance on a subset of stand and locomotion reward tasks despite hyper-parameter and model-scaling efforts.The method was not evaluated on the other modalities, and Table 23 contains the detailed comparison.Source: §D.1 · p. 35, Table 23 · p. 35
  • MPPI with a learned next-state model achieved a 0.03 normalized return on the same stand-and-locomotion subset.The reported explanation is distribution shift and compounding errors from out-of-distribution action plans; pessimistic planning is suggested as necessary for learned models.Source: §D.1 · p. 35, Table 23 · p. 35

D.2 Ablations · D.3 Qualitative Evaluation

The ablations show that Wasserstein gradient penalties, mixed latent sampling, conditional CPR regularization, and a 256-dimensional latent space each improve FB-CPR’s stability, coverage, or performance. Removing unlabeled-data regularization causes near-zero performance, demonstrating that CPR is essential for discovering diverse behaviors.

D.2 Ablations

  • The Wasserstein gradient penalty performs best for discriminator stabilization, with λGP = 10 optimal for both tested penalty methods.Without a gradient penalty, training is unstable and performance is subpar; results were averaged over five independent seeds.Source: §D.2 · p. 39
  • Performance improves nearly monotonically with latent dimension through d = 128 and d = 256, while d = 32 and d = 64 cannot represent the hardest behaviors and goals.At saturation, d = 256 is slightly better on reward tasks, whereas d = 128 is slightly better on tracking and goal reaching.Source: Figure 7 · p. 40, §D.2 · p. 40
  • Mixed latent sampling balances tracking and reward optimization, whereas hypersphere-only sampling substantially degrades performance across the board.Using only ERFB-encoded subtrajectories harms reward evaluation without improving tracking, while mixed sampling best leverages the motion dataset.Source: §D.2 · pp. 39–40
  • FB-CPR’s action-free conditional discriminator outperforms behavior-cloning regularization in both reward and tracking evaluation, even when action labels are available.The best settings were αBC = 0.2 and αCPR = 0.01, averaged over five seeds.Source: §D.2 · p. 40
  • Very large latent spaces can collapse the learned representation: d = 512 reduces performance because the default network and batch-size configuration are inadequate.Overall, d = 256 provides the best trade-off between capacity, succinctness, and training stability while learning harder behaviors than d = 128.Source: §D.2 · pp. 40–41
  • Removing CPR leaves the plain FB algorithm with near-zero performance across tasks, showing that unlabeled-data regularization directs agents toward diverse useful behaviors.Without CPR, FB only learns to roughly stand up and cannot maintain standing, because myopic action-noise exploration fails in large state and action spaces.Source: §D.2 · p. 41

D.3.1 Human Evaluation

Human raters compared zero-shot FB-CPR with task-specific TD3 on reward and goal tasks, finding that FB-CPR was generally judged more human-like while achieving better perceived success on goal tasks.

Evaluation protocol

  • The evaluation compared TD3 and FB-CPR across 45 reward tasks and 50 goal tasks, selecting the best-metric TD3 agent among three random seeds per task against FB-CPR’s zero-shot policy.This qualitative study complemented the quantitative analysis in Sect. 4.Source: §D.3.1 · p. 41
  • For each task, 50 raters watched paired videos with randomized positions and undisclosed agent identities, then scored success and human-likeness.Human-likeness allowed preference for either behavior, a draw, or neither; success rate and average human-likeness were computed as positive responses divided by total replies.Source: §D.3.1 · p. 41

Results

  • FB-CPR was considered more human-like than TD3 in the large majority of evaluated cases, sometimes despite raters judging it unsuccessful.Its human-likeness could come at the cost of lower reward scores.Source: §D.3.1 · pp. 41–42
  • FB-CPR achieved a better success rate than TD3 on goal tasks, without reducing perceived success despite differences in behavioral style.Raters evaluated whether each behavior achieved the assigned objective, using target poses for goal tasks and natural-language descriptions for reward tasks.Source: §D.3.1 · pp. 41–42

D.3.2 Reward-based tasks

FB-CPR composes locomotion and arm-raising behaviors while preserving human-like motion, achieving 74% of individually trained TD3 performance and being judged more natural by about 98% of evaluators. On under-specified, human-inspired rewards, FB-CPR solves tasks with natural behaviors and recovers motion tendencies from dataset bias, whereas TD3 produces unnatural behaviors and ASE cannot solve all tasks.

Behavior composition

  • FB-CPR achieves 74% of individually trained TD3 performance on combined locomotion and arm-raising tasks, while producing natural motions that about 98% of evaluators prefer over TD3.The combined rewards balance conflicting movement and stillness objectives; Fig. 11 contrasts FB-CPR’s natural behavior with TD3’s high-performing but unnatural behavior, and Fig. 12 reports the human evaluation.Source: §D.3.2 · pp. 42–43, Figure 11 · p. 45, Figure 12 · p. 45

Under-specified rewards

  • For under-specified human-inspired rewards, FB-CPR produces human-like solutions, distinguishes medium and high standing goals, and recovers forward running from motion-data bias.The evaluated tasks include running, walking with the left hand raised, and standing with the right foot raised; FB-CPR identifies a simple policy sufficient for each specified goal.Source: §D.3.2 · pp. 43–44
  • Traditional RL rewards are too vague for learning from scratch without behavioral bias, and TD3 consequently exhibits completely unnatural behaviors on these tasks.The reward descriptions specify broad outcomes such as high speed, low-speed walking with a raised hand, and upright standing with a raised foot.Source: §D.3.2 · pp. 43–44
  • ASE fails to solve all under-specified reward tasks, while FB-CPR solves them in ways closely resembling human behavior.The comparison highlights FB-CPR’s alignment with behavioral data rather than only reward maximization.Source: §D.3.2 · p. 44, Figure 13 · p. 46

D.4 Comparison to Unsupervised Skill Discovery Methods · E Understanding the Behavioral Latent Space

FB-CPR uses unlabeled behavior data to bias unsupervised learning toward human-like behavior manifolds, avoiding failures observed for unconstrained skill discovery in humanoid control. The learned latent space simultaneously represents states, trajectories, and policies, enabling qualitative analysis of behavioral structure.

D.4 Comparison to Unsupervised Skill Discovery Methods

  • The comparison tests METRA as the current state-of-the-art unsupervised skill-discovery method and argues that its high-dimensional humanoid failure may extend to existing USD methods.The paper frames unlabeled datasets as an inductive bias toward the behavior manifold, unlike USD objectives targeting the full behavior space.Source: §D.4 · p. 47
  • The METRA implementation replaces SAC with TD3 and selects latent dimension d = 16 after searching dimensions from 2 through 256.Other representation-learning parameters follow Park et al. (2024c), while TD3 settings match those used across the paper’s baselines.Source: §D.4 · p. 47
  • METRA’s zero-shot inference uses normalized representation differences for goals and tracking, while reward inference regresses on transition features.The authors caution that METRA’s self-supervised reward telescopes over time, making poor cumulative-reward performance expected.Source: §D.4 · p. 48
  • METRA achieves near-zero performance across all humanoid tasks, learning to fall and remain still despite optimizing its diversity objectives.The authors attribute this collapse to the lack of an inductive bias favoring complex skills such as locomotion.Source: §D.4 · p. 48
  • Restricting METRA’s representation to pelvis linear velocities prevents skill collapse and yields locomotion behaviors moving in different x,y,z directions.This manipulation supplies an inductive bias toward controlling selected locomotion variables.Source: §D.4 · p. 48
  • METRA-ASE significantly improves goal-reaching and tracking over METRA and is competitive with DIAYN-ASE, but both remain significantly worse than FB-CPR.METRA-ASE learns directional navigation while avoiding some over-actuated movements through unlabeled-data regularization.Source: §D.4 · pp. 48–49

E Understanding the Behavioral Latent Space

  • FB-CPR’s behavioral latent space simultaneously embeds states through B(s), trajectories through ERFB, and policies through πz.Section E qualitatively investigates the structure of this shared latent space.Source: E Understanding the Behavioral Latent… · p. 49

E.1 Diversity, Dataset Coverage and Transitions · E.2 Dimensionality Reduction of the Behavioral Latent Space · E.3 Behavior Interpolation

FB-CPR learns diverse, broadly dataset-covering behaviors that can transition between motions while extending beyond strict imitation. Its latent space aligns semantically similar motions and rewards, and interpolation produces smooth compositions of behaviors.

E.1 Diversity, Dataset Coverage and Transitions

  • FB-CPR achieves the highest behavioral diversity, with consistently larger trajectory EMD distances than ASE and CALM.ASE concentrates on less diverse behaviors, whereas CALM combines clustered motions with a wider high-EMD tail.Source: §E.1 · p. 49, Figure 15
  • FB-CPR has the highest dataset coverage across matching thresholds and a flatter top-motion frequency distribution than CALM and ASE.ASE exhibits a skewed distribution indicating coverage collapse, while FB-CPR covers motions more evenly.Source: Figure 17 · p. 50, Figure 18 · p. 50, §E.1 · p. 51
  • All algorithms achieve similar overall pairwise transition coverage when stitching source and destination motions.Transitions are evaluated by generating 200-step source and destination segments and measuring conditional destination-matching probabilities.Source: §E.1 · p. 51, Figure 19 · p. 51
  • Most FB-CPR trajectories are not tightly connected to training motions, indicating policy capacity beyond reproducing the dataset.CALM and ASE show smaller closest-motion EMD distances, consistent with allocating more capacity to accurate motion reproduction.Source: §E.1 · p. 51

E.2 Dimensionality Reduction of the Behavioral Latent Space

  • UMAP reveals that semantically similar motions cluster together and that reward embeddings fall within corresponding motion clusters.Motion embeddings use ERFB, while reward embeddings come from weighted regression; behavior classes include jumping, running, walking, crawling, and headstands or cartwheels.Source: §E.2 · pp. 51–52, Figure 21 · p. 53
  • The aligned latent space places reward tasks and motion behaviors in common regions, supporting a shared representation of motions and rewards.The analysis embeds representative motion subsequences and reward functions for behavior categories selected using EMD-based grouping.Source: §E.2 · p. 52

E.3 Behavior Interpolation

  • Linear interpolation between reward embeddings varies behavior smoothly and often composes the original tasks into more complex motions.For reward embeddings z1 and z2, the method uses zα = αz1 + (1 − α)z2 with α in [0, 1], producing behaviors such as running with the left hand raised.Source: §E.3 · pp. 52–53

F Ablations on Bipedal Walker

The Walker ablation evaluates FB variants across 90 reward tasks, 147 poses, and held-out reward, imitation, and goal-reaching tasks. Online FB with policy regularization performs best overall, while discriminator conditioning matters most for goal reaching.

  • The study expands Walker evaluation to 90 parameterized run, spin, and crawl tasks plus 147 stable poses, with held-out tasks used for evaluation.Evaluation uses 42 unseen reward and imitation tasks, one imitation demonstration, and 25 unseen goals.Source: F Ablations on Bipedal Walker · p. 54
  • Online FB with policy regularization performs best overall; FB-CPR outperforms alternatives, while unconditional FB-MPR is better on reward and imitation but significantly worse on goal reaching.Results are averaged over 10 seeds across reward-based, imitation-learning, and goal-reaching evaluations.Source: Table 28 · p. 53, F Ablations on Bipedal Walker · p. 54
  • Adding demonstrations to RND improves FB by 15% for reward-based tasks, 30% for imitation learning, and 60% for goal-reaching, though FB-CPR remains significantly better.RND provides broad coverage in Walker, while curated demonstrations bias learning toward dataset behaviors.Source: Table 28 · p. 53, F Ablations on Bipedal Walker · p. 54
  • Online FB without demonstrations performs worst, indicating that representation collapse from insufficient useful samples harms exploration and downstream policy performance.Offline FB with RND performs well when the dataset has good coverage, whereas FB-AWAC provides limited or task-dependent gains.Source: F Ablations on Bipedal Walker · p. 54

G Ablations on AntMaze

On AntMaze, the ablation compares online FB, offline FB with AWAC, and online FB-CPR under a stitch-dataset goal-reaching protocol; FB-CPR performs best on both success rate and proximity.

Data

  • The ablation uses AntMaze stitch datasets containing short goal-reaching demonstrations designed to test stitching across subgoals.AntMaze controls an eight-degree-of-freedom quadrupedal Ant agent.Source: G Ablations on AntMaze · p. 55

Evaluation

  • The evaluation averages success rate and goal proximity across three random-seed models, using five target-reaching tasks per domain and 50 episodes per goal.Each task specifies a target (x, y) location while randomly generating the remaining state components.Source: G Ablations on AntMaze · p. 55

Results

  • FB-CPR achieves the strongest AntMaze performance, significantly outperforming online FB and offline FB-AWAC in both success rate and proximity.Online FB achieves zero success because of insufficient exploration, while FB-AWAC is competitive with non-hierarchical offline goal-conditioned RL methods.Source: G Ablations on AntMaze · p. 55
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