Thanks for the detailed and thoughtful feedback. We are encouraged that reviewer 339U appreciated our framework’s ability to learn expressive and agile humanoid skills and the strength of our real-world results. We address the raised concerns in detail below.

W1: ASAP

We agree that comparing the number of training stages with ASAP was imprecise. We will revise the text to avoid this unfair comparison. Additionally, we acknowledge that ASAP’s delta action policy addresses sim-to-real compensation in a different way, which is beyond the scope of our method. We will clarify this distinction in the paper.

W2: Threshold selection in motion filter

Our goal in motion filtering is not to establish an absolute notion of trackability, but rather to reliably distinguish clearly learnable motions from those that consistently fail under practical training settings. While some borderline cases might eventually succeed with more sophisticated methods, our thresholds serve the practical goal of enabling robust policy training at scale.

We selected the filtering thresholds based on small-scale preliminary experiments and then validated them on a larger set. To further justify the selected parameters, we provide ablations below. Each table sweeps one parameter with others fixed to default (asterisk, *) values. The results support the effectiveness of our chosen thresholds.

For the motion filtering thresholds, we report the F1 score $F_1= \frac{2*\text{Precision}\cdot{\text{Recall}}}{\text{Precision}+{\text{Recall}}}$ of classifying motions as trackable (Episode Length Ratio > 60%) on the same dataset as in Section 5.2, where $\epsilon_{\mathrm{stab}}$ defines the maximum CoM–CoP distance for a frame to be considered stable, and $\epsilon_N$ sets the maximum length of consecutive unstable frames allowed in a motion.

For the thresholds used in contact mask estimation, we evaluate the accuracy of correctly detecting both feet’s contact states, where the contact state of one feet is estimated according to $c_t=\mathbb{I}[\|\|p_{t+1}-p_t \|\|^2_2<\epsilon_{vel}]\cdot \mathbb{I}[ p_{t,z}<\epsilon_{height} ]$. The results are obtained from the same dataset as Appendix E.1 (Fig 9).

W3: Discussion about other motion filter methods

Thank you for the suggestion. We will add a discussion comparing our motion filtering with related approaches. Our method focuses on physically-plausible motion selection prior to training, aiming to reduce downstream learning difficulty. In contrast, progressive training and learning-progress curricula adaptively adjust training difficulty during learning. DOC retargets motions via differentiable optimization to obtain physically feasible motion, but has so far only succeeded on quadruped robots due to the complexity of humanoid dynamics.

W4: Formulation of adaptive tracking factor

While we did not explicitly formulate our method as a constrained MDP, the goal is indeed related—both aim to optimize final policy performance under certain constraints.

Our bi-level formulation separates concerns: the lower level corresponds a standard RL problem (MDP), while the upper level considers the tracking factor based on absolute policy performance. This separation makes our method compatible with off-the-shelf RL algorithms.

A constrained MDP formulation could express similar objectives by integrating external and internal objectives. While the formulation is more unified, solving CMDPs in practice is more complex and often requires custom algorithms such as Lagrangian relaxation or dual ascent.

W5: Reasonability of adaptive curriculum

We approximate the average tracking error using an exponential moving average of the instantaneous error during training. EMA provides a smooth and relatively stable estimate of the current policy’s average tracking error, and it gradually approaches the optimal tracking error as the policy converges.

Although the resulting update rule for sigma is simple in form, it is grounded in a principled formulation derived from our bi-level optimization. To our knowledge, ours is the first to provide a quantitative rule for determining sigma in motion tracking, supported by theoretical and empirical insights.

W6: Generality to multiple motions

Our formulation can be naturally extended to the multi-motion setting by concatenating the error sequences from all motions into a single sequence. The rest of the derivation remains unchanged.

We acknowledge that different motions may have different optimal tracking factors. In multi-motion training, however, a unified tracking factor is typically required, as in prior works such as OmniH2O $1$ , Exbody2 $2$ and GMT $3$ . In such cases, our formulation has the potential to offer an advantage by adaptively estimating a shared tracking factor, which may outperform manually tuned fixed values.

We focused on single-motion training in this work to better study highly dynamic and expressive motions. Extending the method to multi-motion training is a promising direction that we believe deserves a dedicated investigation.

$1$ T. He et al., “OmniH2O: Universal and Dexterous Human-to-Humanoid Whole-Body Teleoperation and Learning,” Jun. 13, 2024, arXiv: arXiv:2406.08858.

$2$ M. Ji et al., “ExBody2: Advanced Expressive Humanoid Whole-Body Control,” Mar. 12, 2025, arXiv: arXiv:2412.13196.

$3$ Z. Chen et al., “GMT: General Motion Tracking for Humanoid Whole-Body Control,” Jun. 17, 2025, arXiv: arXiv:2506.14770.

W7: Baseline on single-motion tracking

We clarify that all baselines, including OmniH2O and Exbody2, are trained individually for each motion, rather than using a multi-motion training setup, therefore ensures a fair comparison. Our MaskedMimic baseline in fact corresponds to the first-stage policy of the original paper only, which is equivalent to DeepMimic you mentioned.

Additionally, we conducted additional ablation experiments to enable a fairer comparison with MaskedMimic’s oracle setting. Specifically, we trained our method with privileged information and without domain randomization, which we refer to as Ours (Oracle). The results are presented in the table below.

It demonstrates that our method achieves competitive or superior performance to MaskedMimic under identical oracle settings.

We thank the reviewer again for the detailed, valuable feedback. We hope our responses have addressed all concerns, and we remain happy to answer any further questions.

We thank Reviewer qDky for the detailed and insightful feedback. We appreciate your recognition of the theoretical contribution, real-world results, and clarity of presentation. Below, we respond to your questions and concerns:

W1: Limited to single motion

We thank the reviewer for highlighting this important limitation. While our current framework trains separate policies per motion, it can be naturally extended to multi-motion settings by incorporating reference motion states as inputs and modestly expanding the network architecture. We view this as a valuable direction for future work.

Q1: Statistical significance

We have revised the Table 1 to report mean $\pm$ standard error (instead of standard deviation) and include statistical significance testing between our methods and each baseline method. Specifically, we conducted two-sided permutation tests (as recommended) to assess whether the observed differences in means are statistically significant.

Significant improvements (p < 0.05) by Ours over baselines are marked with asterisks (*) in the table for clarity. The additional results of Ours(Oracle), suggested by other reviewers, are also reported to compare with MaskedMimic(Oracle).

Across many metrics and difficulty levels, Ours shows statistically significant improvements over prior methods, confirming the robustness of our approach.

Q2: Intuition of theoretical derivation

Why you are shrinking sigma in training time but talking about the converged policy for theoretical derivation?

In short, our strategy of shrinking sigma during training is for approximately solving the theoretical formulation.

In our theoretical derivation, we do care about the converged policy, and consider the problem as a bi-level optimization, where the lower level corresponding to RL training and the upper level corresponding to reward tuning. Meanwhile, in the implementation, we integrate these two levels into a single-stage RL training process with a practical adaptive mechanism (Sec.3.2.3).

This integration is for practical considerations. While accessing to the precise performance of a specific sigma requires a converged policy, and iteratively train multiple policies to explore the suitable sigma is expensive, we use the EMA of tracking error during training to roughly access the converged performance. This provides a tractable and gradually accurate signal for adjusting sigma. As training proceeds and the policy converges, this approximation becomes increasingly reliable. Hence the converged policy trained with adaptive module should reflect the theoretical optimal solution.

Why isn’t sigma for the optimal policy arbitrarily large?

While a larger sigma makes the $J^{in}$ mimicking the linear objective $J^{ex}$, this does not imply that the converged policy from the inner RL optimization will minimize $J^{ex}$. The bi-level formulation explicitly models this distinction.

From a theoretical perspective, the lower level problem is subject to complex factors, including environment dynamics and implicit regularization, modelled by $R(x)$. These factors will bias the solution and prevent the learned policy from exactly minimizing $J^{ex}$. The upper level problem chooses sigma to improve the actual tracking outcome—not to match the functional form of the reward.

From a practical perspective, setting sigma too large makes the reward too flat, weakening the learning signal. This makes the RL agent focus more on other rewards and leads to training failure. This is aligned with the above theoretical analysis.

Thank you again for the thoughtful feedback and for recognizing the contributions of this work. If there are any questions you would like to discuss, please let us know.

We sincerely thank the reviewer for their thoughtful and constructive feedback. We are glad that the reviewer found our proposed pipeline practical, well-motivated, and effective in enabling robust humanoid imitation of highly dynamic motions. We appreciate the positive comments on our real-world results, reward adaptation mechanism, and detailed implementation. We address the concerns raised point-by-point below.

W1: No ablation study on reward vectorization

We conducted ablation studies comparing performance with and without reward vectorization on representative motions, each with 3 seeds. The results across different training steps are summarized below. Overall, reward vectorization facilitates training and consistently improves early learning performance, especially noticeable in the first 10K steps.

W2: Loss from regularization and privilege information

As suggested, we conducted additional ablation experiments to enable a fairer comparison with MaskedMimic’s oracle setting. Specifically, we trained our method with privileged information and without domain randomization, which we refer to as Ours (Oracle). The results are presented in the table below.

It demonstrates that our method achieves competitive or superior performance to MaskedMimic under identical oracle settings.

W3: Unrealizable motion

We identify two main sources of “unrealizable” motions:

1. Tracking artifacts: Motions from video or mocap may contain artifacts (e.g., teleporting, ground penetration, floating feet) due to reconstruction errors, which violate physical constraints and hinder learning. Imperfect motion retargeting can further exacerbate these issues.
2. Robot limitations: Even with perfect tracking, some motions are infeasible due to mechanical capacity limitations, such as high-speed action, excessive torque, or unstable contact transitions. (e.g., toe balancing in ballet or rapid one-leg spins).

Q1: Sim2real gap

In our experiments, while our DR strategy effectively cover a wide range of scenarios, sim2real gap still exists, particularly for motions that heavily rely on ankle and waist pitch/roll actuation. We suspect this is partly due to the parallel-joint mechanical design of these modules, which introduces structural discrepancies between simulation and hardware. We also observe that robot-specific factors, including manufacturing variation and wear, influence sim2real performance.

We view the ASAP paper as a valuable and complementary approach. Its delta action model effectively mitigates sim2real discrepancies—especially at the ankle—and could potentially improve success rates and tracking accuracy. However, our results show that even without such corrections, our method achieves strong sim2real performance across dynamic skills, suggesting that ASAP addresses an important but not exclusive aspect of the sim2real challenge.

We hope the additional explanations helped address your concern. We will include the suggested analysis and comparison in the revised manuscript. We are happy to answer further questions that you may have.

We sincerely thank the reviewer for their thoughtful and constructive feedback. We are encouraged that the reviewer found our real-world validation strong, the dynamic tracking weight adjustment intuitive, and appreciated our detailed implementation and ablation studies. We address your concerns point by point below::

W1: Reward maximization != good policy

We agree with your observation: simply increasing scalar reward values via reward shaping does not necessarily lead to a better policy, as policy learning is driven by TD errors and relative action advantages.

However, we would like to clarify a possible misunderstanding of our formulation. Our method does not attempt to achieve a higher scalar reward by simply adjusting sigma. Rather, in our theoretical formulation (Sec.3.2.2), we model both the RL training and reward shaping into a bi-level optimization problem where:

• The lower-level optimization, expressed as a simplified motion tracking problem, corresponds to the standard RL process, aiming to train a policy that maximizes the fixed tracking reward and other reward terms, given a specific sigma.
• The upper-level optimization, which is not part of the RL loop, seeks the optimal sigma that minimizes the accumulated tracking error of the final converged policy. This outer optimization is not reward maximization but a performance-driven objective based on absolute external metrics.

In short, sigma is chosen not to maximize reward per se, but to guide the RL process such that the resulting policy achieves better external performance.

In the implementation, we integrate these two levels into a single-stage RL training process with a practical adaptive mechanism (Sec.3.2.3).

W2: Reliance on contact mask

We agree that our current framework is best suited for motions involving foot-ground contact, and this is a limitation for tasks such as climbing or rolling. However, the contact mask formulation is inherently generalizable. In principle, the same technique can be extended to detect and handle contacts for other body parts (e.g., hands, pelvis, head). We believe this simple yet general technique holds promise for enabling the imitation of a broader range of contact-rich behaviors.

Q1: Learning curve and training time

Thank you for the suggestion. We have provided training curves and wall-clock training times for representative motions in the following tables.

Training Time: Aggregated across all main experiments since it's motion-agnostic.

Learning curve of typical motions: Each row summarizes mean $\pm$ standard error over 3 seeds.

We hope this addresses your concerns. We will revise the paper to clarify our formulation, and include the requested training analysis. Let us know if there is any other clarification we can provide.

Thank you! My concerns have been addressed.