v3/paper_source/05_experiment.tex

%In this section, we通过实验系统评估我们的算法SuP。我们需要回答：
% 1）
% 2）
\definecolor{HighLightColor}{rgb}{1.0, 0.92, 0.8}
\definecolor{lightgray}{gray}{0.9} % 定义置灰颜色
\newcommand{\cg}[1]{{\cellcolor{HighLightColor}#1}}
\newcommand{\bg}[1]{{\cellcolor{lightgray}#1}}
In this section, we conduct extensive experiments to evaluate the effectiveness of the proposed SuP framework. Specifically, we aim to investigate: (1) whether SuP can achieve significant execution speedup while preserving task success rates (Sec. \ref{sec:sim_exp}); (2) the versatility of SuP across different embodied architectures of $\pi_{\text{base}}$ (Sec. \ref{sec:sim_exp}); (3) SuP's empirical performance and reliability in real-world robotic experiments (Sec. \ref{sec:real_exp}); (4) the mechanism by which SuP dynamically selects appropriate downsampling ratios across diverse task scenarios (Sec. \ref{sec:case_exp}); and (5) the individual contributions of RWM, IQL, and different deviation threshold $\epsilon$ settings to the overall system performance (Sec. \ref{sec:ablation}).
    
\subsection{Simulation Task Experiments}
\label{sec:sim_exp}

\begin{figure}[h]
    \centering
% \vspace{-2mm}
\label{fig:simulation_task}
    \includegraphics[width=0.95\linewidth]{figures/simulation_tasks.pdf}
    \caption{\textbf{Simulation Tasks.} We systematically evaluate SuP across 20 tasks from Bigym and 4 task suites (40 tasks in total) from Libero.}
    \vspace{-5mm}
\end{figure}

\textbf{Compared methods.}~For the baseline methods considered in our comparative experiments, we select the following approaches:
\textbf{Vanilla Downsample(-ds*)}, which applies a fixed downsampling rate to all action chunks and 
\textbf{DemoSpeedup}, which speedup expert demonstration data with entropy estimation to \textbf{retrain} $\pi_{\text{base}}$.

\textbf{Task Setup.}~For simulation tasks, We validate the SuP algorithm with two benchmarks: \textbf{Bigym} \cite{chernyadev2025bigym}, a humanoid robot with kitchen/household manipulation that requires precise control and scene comprehension; \textbf{Libero} \cite{liu2023libero}, a robotic arm grasping benchmark for VLA models, covering 4 task suite, where policies need strong instruction-following abilities. For $\pi_{\text{base}}$, we evaluate our framework across diverse architectures: ACT \cite{zhao2023learning} and DP \cite{chi2025diffusion} trained on task-specific expert demonstrations for Bigym; pre-trained $\pi_{0.5}$ \cite{intelligence2025pi05} and VLA-Adapter \cite{wang2025vla} (weights can be directly downloads from Internet) for Libero. Regarding the scheduler training, we train task-specific SuP schedulers for each Bigym environment, while for Libero, a single scheduler is trained for each task suite.


\begin{table*}[t!]
    \centering
    
    \caption{SuP speedup results on Bigym Tasks compared with baselines. Each cell in the table reports two metrics: the success rate followed by the average steps to completion, where only successful trajectories are counted. Higher success rates and lower step counts indicate better performance. Cells highlighted in \colorbox{HighLightColor}{orange} denote the best success rate for each task, while those in \colorbox{lightgray}{gray} indicate a performance \textbf{drop exceeding 5\%} compared to the best success rate. 4 task results are shown, see \textbf{all task results in App.} 
    \ref{sec:whole_bigym}.}
    \label{tab:bigym_exp}
    
    \small
    \resizebox{\linewidth}{!}{
    \begin{tabular}{clcccc c c c} 
        \toprule
        \multicolumn{2}{c}{\textbf{Method}} & 
        {\small\textbf{\makecell{Sandwich\\Remove}}} & 
        {\small\textbf{\makecell{Take\\Cups}}} & 
        {\small\textbf{\makecell{Put\\Cups}}} & 
        {\small\textbf{\makecell{Drawers\\Close All}}} & 
        {\footnotesize\makecell{(15 more tasks)\\$\dots$}} & 
        {\small\textbf{\makecell{Cupboards\\Close All}}} & 
        \textbf{Average} \\ 
        \midrule
        \multirow{4}{*}{ACT} 
          & -base                & 0.45, 340.5 & 0.15, 288.3 & 0.28, 320.3 & 1.0, 100.0 & $\dots$ & 1.0, 449.8 & 0.66, 1.00$\times$ \\
          & -ds2                 & 0.48, 186.3 & 0.13, 178.0 & 0.36, 175.9 & 1.0, 52.0  & $\dots$ & 1.0, 234.0 & \bg{0.61, 1.65$\times$} \\
          & +\textit{DemoSpeedup}& 0.56, 171.5 & \bg{0.10, 183.9} & 0.33, 169.3 & 1.0, 54.0  & $\dots$ & \cg{1.0, \textbf{202.1}} & \bg{0.61, 2.21$\times$} \\
          & \textbf{+\textit{SuP(Ours)}}  & \cg{\textbf{0.64}, 155.9} & \cg{\textbf{0.20}, 176.6} & \cg{\textbf{0.38}, 156.0} & \cg{1.0, \textbf{40.0}}  & $\dots$ & 1.0, 212.1 & \cg{\textbf{0.67}, \textbf{2.01}$\times$} \\
        \midrule
        \multirow{4}{*}{DP}  
          & -base                & 0.40, 376.8 & 0.07, 284.6 & \cg{\textbf{0.28}, 307.7} & 0.66, 118.9& $\dots$ & 0.90, 544.0 & \cg{0.51, 1.00$\times$} \\
          & -ds2                 & 0.40, 209.6 & 0.12, 218.0 & \bg{0.22, 181.5} & \bg{0.54, 64.9} & $\dots$ & \bg{0.75, 270.3} & \bg{0.40, 1.42$\times$} \\
          & +\textit{DemoSpeedup}& \bg{0.35, 199.3} & \cg{\textbf{0.21}, 239.5} & 0.25, 143.9 & \bg{0.37, 49.2} & $\dots$ & \bg{0.60, 231.0} & \bg{0.46, 1.99$\times$} \\
          & \textbf{+\textit{SuP(Ours)}}  & \cg{\textbf{0.42}, 179.9} & 0.19, 203.0 & 0.27, 200.8 & \cg{0.66, \textbf{65.2}} & $\dots$ & \cg{\textbf{0.91}, 146.2} & \cg{\textbf{0.51}, 1.48$\times$} \\
        \bottomrule
    \end{tabular}
    }
\end{table*}
\begin{table*}[t!]
\centering
% 标题
\caption{SuP speedup results on Libero compared with baselines. Each cell in the table reports two metrics: the success rate followed by the average steps to completion, where only successful trajectories are counted. Higher success rates and lower step counts indicate better performance. Cells highlighted in \colorbox{HighLightColor}{orange} denote the best success rate for each task, while those in \colorbox{lightgray}{gray} indicate a performance \textbf{drop exceeding 1\%} compared to the best success rate.}
\label{tab:libero_exp}
\small
\resizebox{0.9\linewidth}{!}{
\begin{tabular}{clccccc}
    \toprule
    \multicolumn{2}{c}{\textbf{Method}} & \textbf{Spatial} & \textbf{Long} & \textbf{Goal} & \textbf{Object} & \textbf{Average} \\
    \midrule
    \multirow{4}{*}{$\pi_{0.5}$} & -base               & \cg{\textbf{0.988}, 105.3} & 0.924, 267.9 & 0.980, 113.1 & 0.982, 138.1 & 0.969, 1.00$\times$ \\
                            & -ds2                & \bg{0.914, 67.9} & \bg{0.874, 153.4} & \bg{0.952, 67.6} & \bg{0.970, 75.0} & \bg{0.928, 1.72$\times$} \\
                            & +\textit{DemoSpeedup} & \bg{0.964, 88.1} & 0.932, 221.4 & \bg{0.968, 88.7} & 0.988, 114.1 & 0.963, 1.22$\times$ \\
                            & \textbf{+\textit{SuP(Ours)}} & \bg{0.972, 70.4} & \cg{\textbf{0.940}, 215.2} & \cg{\textbf{0.986}, 93.4} & \cg{\textbf{0.994}, 83.0} & \cg{\textbf{0.973}, \textbf{1.35}$\times$}\\
    \midrule
    \multirow{4}{*}{\makecell{VLA-\\Adapter}} & -base                & \cg{\textbf{0.922}, 99.6} & \cg{\textbf{0.936}, 255.1} & \cg{\textbf{0.970}, 107.0} & 0.942, 136.2 & \textbf{0.942}, 1.00$\times$ \\
                         & -ds2                 & \bg{0.802, 57.1} & \bg{0.834, 147.6} & \bg{0.930, 57.1} & \bg{0.882, 76.3} & \bg{0.862, 1.77$\times$} \\
                         & +\textit{DemoSpeedup} & - & - & - & - & - \\
                         & \textbf{+\textit{SuP(Ours)}}  & 0.912, 77.3 & 0.934, 204.6 & \bg{0.956, 74.2} & \cg{\textbf{0.944}, 91.4} & \cg{0.937, \textbf{1.34}$\times$}\\
    \bottomrule
\end{tabular}
}
\end{table*}

\textbf{Metrics.} To evaluate performance, we report the success rate and the average episode length of successful rollouts as a measure of efficiency. We conduct 100 evaluation trials for each task in BiGym, and 500 trials per task suite in Libero. More details of simulation can be found in App. \ref{app:sim_exp_detail}.

\textbf{Speedup Performance.}~The main experimental results on Bigym are presented in Tab. \ref{tab:bigym_exp}, and those on Libero are summarized in Tab. \ref{tab:libero_exp}. Across both challenging benchmarks, SuP demonstrates a superior capability to accelerate inference while maintaining, and often enhancing performance. Unlike baselines such as standard downsampling (-ds2) and DemoSpeedup, which frequently suffer from performance degradation—evidenced by the gray cells indicating a noticeable performance drop—SuP consistently maintains the original performance $\pi_{\text{base}}$. On Bigym, SuP achieves substantial average speedups (e.g., $2.01\times$ for ACT) while maintaining its success rate. Similarly, on Libero, SuP yields a $1.35\times$ speedup for $\pi_{0.5}$ with a peak average success rate of 0.973, effectively decoupling inference speed from performance loss and proving its robustness in numerous simulation tasks.

\textbf{Universality across Architectures.}~SuP exhibits strong generalizability across diverse policy backbones, ranging from ACT and DP to VLAs. For the ACT architecture, SuP not only doubles the inference speed but also improves the average success rate compared to the base policy. Crucially, on DP—which is sensitive to temporal modifications—SuP successfully mitigates the severe performance collapse observed in other acceleration methods (where -ds2 drops success to 0.4), recovering the success rate to 0.51 with a $1.48\times$ speedup. This consistent efficacy extends to VLA architectures while Demospeedup faces \textbf{compatibility issues}, which is inapplicable to VLA-Adapter due to the architecture's lack of support for entropy estimation. In contrast, SuP outperforms naive downsampling strategies on both VLA-Adapter and $\pi_{0.5}$, delivering stable acceleration without compromising decision-making precision.

\textbf{Computational Efficiency.}~As shown in Tab. \ref{tab:compute}, SuP achieves high computational efficiency in both training and inference time. Unlike DemoSpeedup, which incurs high computational costs by training on the massive parameters of VLA models and requiring frequent base policy queries, SuP is exceptionally lightweight with only 5.12M trainable parameters. Crucially, our training strategy completely decouples policy learning from base policy inference; instead of querying $\pi_{\text{base}}$, we optimize our light-weight world model and scheduler using only offline data. This design drastically reduces training time, and the scheduler’s inference overhead (1 ms) is negligible compared with the 50 ms inference latency of the $\pi_{0.5}$.

\begin{table}[h]
  \centering  % 表格居中
  \caption{Computational Efficiency of SuP in Libero.}  % 表格标题
  \label{tab:compute}
  \small
  \begin{tabular}{lccc}
    \toprule
    \textbf{Method} & \textbf{\makecell{Training\\Params}} & \textbf{\makecell{Training\\Time}} & \textbf{\makecell{Inference\\Overhead}} \\
    \midrule
    DemoSpeedup       & 4B     & 20h  &  -  \\
    SuP (Ours)         & 5.12M  & 2h  &  1ms (2\%)  \\
    \bottomrule
  \end{tabular}
\end{table}

% 【直接加速的不可行+wm的准确性+state deviation】
\subsection{Real-world Task Experiments}
\label{sec:real_exp}

\begin{figure*}[h!]
    \centering
    \vspace{-2mm}
    \includegraphics[width=0.98\linewidth]{figures/real_tasks.pdf}
    \caption{Real-world Tasks Illustration. We illustrate the procedure of 3 real-world tasks: (a) \textit{Arange Table} (b) \textit{Fold Towel} (c) \textit{Stack Plates}.}
    \label{fig:real_task}
    \vspace{-3mm}
\end{figure*}

\begin{table*}[h!]
\centering
% 标题
\caption{SuP speedup results on Real-world Tasks compared with baselines.}
\label{tab:real_exp}
\small
\begin{tabular}{clcccc}
    \toprule
    \multicolumn{2}{c}{\textbf{Method}} & \textbf{Arrange Table} & \textbf{Fold Towel} & \textbf{Stack Plates}  & \textbf{Average} \\
    \midrule
    \multirow{4}{*}{$\pi_{0.5}$} & -base  & 11/30, 537.8 & 15/30, 519.5 & 27/30, 221.5  & 0.589, 1.00$\times$ \\
                            & +\textit{ds2} & 10/30, 291.9 & 14/30, 326.3 & 27/30, 177.1  & 0.567, 1.61$\times$\\
                            & +\textit{ds3} & \bg{3/30, 247.2} & \bg{8/30, 187.7} & \bg{21/30, 148.4}  & \bg{0.356, 2.19$\times$}\\
                            & +\textit{DemoSpeedup} & 12/30, 267.4 & 14/30, 223.2 & \cg{\textbf{28/30}, 124.4}  & 0.600, 2.07$\times$\\
                            & +\textit{SuP(Ours)} & \cg{\textbf{13/30}, 258.5} & \cg{\textbf{16/30}, 192.5} & 26/30, 138.5  & \cg{\textbf{0.611}, \textbf{2.17}}$\times$\\
    \bottomrule
\end{tabular}
% 156.1   91.0 128.1 115.5
\end{table*}


To evaluate the practical efficacy of SuP in physical environments, we deployed SuP on a dual-arm robotic platform—similar to the Aloha setup \cite{zhao2023learning}—focusing on manipulation tasks with multiple steps that require a balance between execution speed and operational success. Our evaluation suite consists of three tasks (Fig. \ref{fig:real_task}): \textit{Arrange Table}, \textit{Fold Towel} and \textit{Stack Plates}. Among these, \textit{Arrange Table} and \textit{Stack Plates} are conducted as single-arm setting, while \textit{Fold Towel} serves as a bimanual task involving deformable object manipulation. Detailed descriptions of the experimental hardware and task setup are provided in App. \ref{app:real_exp}. 

As summarized in Tab. \ref{tab:real_exp}, the results demonstrate that SuP consistently maintains high success rates while achieving significant temporal speedups across all tasks. Specifically, SuP achieves an average speedup of $2.17\times$ over the base policy $\pi_{0.5}$, outperforming the $2.07\times$ of Demospeedup while simultaneously maintaining the original success rate. This performance stands in sharp contrast to naive acceleration strategies; as highlighted in gray, the aggressive ds3 strategy leads to a catastrophic collapse in manipulation capability, dropping the success rate to 0.356. Notably, in the challenging bimanual \textit{Fold Towel} task—which requires precise coordination for deformable objects—SuP attains the highest success rate and the lowest step count, validating its robustness in improving real-world task efficiency.

\subsection{Case Study}
\label{sec:case_exp}
To analyze how SuP dynamically selects the downsampling rate, we visualize the selected rates during the \textit{Fold Towel} task (Fig. \ref{fig:case_study_real}). In the plot, the blue-shaded regions correspond to phases where the model strictly predicts a low downsampling rate ($k=2$), while red-shaded regions highlight periods of accelerated execution ($k=4$). We observe that this behavior is highly interpretable: the model maintains the low rate during precision-critical phases such as ``Approach \& Contact''. Conversely, during gross motion phases like Push \& Move'' or ``Flip'', the model increases the rate to exploit temporal redundancy. This demonstrates that SuP effectively distinguishes between key decision points and translational phases, accelerating execution without sacrificing control where it matters most.
\begin{figure*}[h!]
    \centering
    \vspace{-2mm}
    \includegraphics[width=0.95\linewidth]{figures/case_study_real.pdf}
    \caption{Case study. We visualize the adaptive downsampling strategy during a \textit{Fold Towel} task. The plot tracks the predicted downsampling rate over the episode timesteps. Shaded regions annotate distinct task phases.}
    \label{fig:case_study_real}
    \vspace{-3mm}
\end{figure*}



% \subsection{Generalizable Transferability of SuP}   

% % transfer exp to other task suite
% % SuP通过训练一个scheduler policy，无需对base policy进行精调，实现了整体策略的动作加速。我们思考这个scheduler policy是否具备跨不同任务、跨base policy模型的泛化能力。
% We investigate whether this scheduler policy possesses the generalization ability across different tasks and various base policies.

% % 我们在libero上进行实验，通过只在其中某个task suite训练SuP，然后把它用在另外一个task suite上训练的base policy上进行加速。我们发现将SuP直接部署到其他任务的base policy都可以带来一个稳定的加速效果，至少能实现1.13的加速能力，对于部分任务（libero-object）上训练的scheduler策略在其他task suite上做加速，甚至至少能实现1.59的加速比。同时，迁移之后成功率保持不变或者上升的几率为56%，任务成功率损失最多不超过2.4%。这验证了SuP能够在学习加速的过程中，学到跨任务的加速、动作相关知识，具备一定程度的across task泛化能力。
% \textbf{Cross-Task.}  We conduct experiments on Libero, where SuP is trained exclusively on a single task suite and then applied to accelerate base policies trained on other task suites.
% \begin{figure}[!h]
%     \centering
% % \vspace{-2mm}
% \label{fig:state_deviation}
%     \includegraphics[width=0.95\linewidth]{figures/libero_combined_heatmaps.pdf}
%     \caption{\textbf{Task transfer.}}
%     \label{fig:libero_task_gen}
%     % \vspace{-7mm}
% \end{figure}
% As shown in the Fig.\ref{fig:libero_task_gen}, we observe that directly deploying SuP to base policies of unseen tasks consistently yields stable acceleration gains, achieving a minimum speedup of 1.13$\times$. Notably, the scheduler policy trained on a specific task suite (Libero-Object) delivers an even higher minimum speedup of 1.59$\times$ when transferred to other task suites. Meanwhile, the success rate remains unchanged or improves in 56\% of transfer scenarios, with the maximum success rate degradation capped at merely 2.4\%. These results verify that SuP can learn task-agnostic acceleration and action-related knowledge during the acceleration learning process, thus demonstrating a notable level of cross-task generalization capability.

% \textbf{Cross-Model.} We verify whether our SuP method achieves robust acceleration across diverse base policy architectures. As shown in Fig.\ref{tab:bigym main result}, SuP demonstrates consistent and stable acceleration capability across different large-scale Vision-Language-Action (VLA) models. Our results confirm that the proposed SuP approach achieves cross-model generalization, despite the discrepancies in architecture, inference workflow, and inductive bias across different models.
% 这个结果验证了我们的方法SuP能够做到across model的迁移，即使这些模型具备不同的结构、不同的推理流程、不同的inductive bias。
\subsection{Ablation Study}
\label{sec:ablation}

\begin{figure}[h]
    \centering
    \includegraphics[width=0.99\linewidth]{figures/rnn-mlp-contrast.png}
    \caption{Comparison between ADM-based and MLP-based world model. (a) Visualization of task success rates against predicted violation counts in the Spatial suite. (b) Spearman correlation scores across four LIBERO suites.}
    \label{fig:ablate_adm}
\end{figure}
\textbf{Impact of ADM-based world model.}~To validate the effectiveness of our design, we compare our ADM-based world model against a standard MLP baseline on the Libero benchmark. As illustrated in Fig.~\ref{fig:ablate_adm}, MLP model exhibits inconsistent, non-monotonic behavior in the Spatial suite, failing to correctly associate high violation counts with task failure. In contrast, ADM maintains a monotonic decrease in success rates as violations increase. Furthermore, quantitative analysis across all suites confirms that ADM achieves consistently stronger negative Spearman correlations \cite{spearman1961proof}, demonstrating its superior capability in capturing the inverse relationship between safety violations and task success.


\textbf{Impact of IQL.} We compare SuP with the MPC baseline, which greedily select the highest downsample rate without violation $h_{\epsilon}$. As shown in Tab. \ref{tab:ablation}, the MPC exhibits inferior performance in both success rate and task efficiency. This is because MPC's greedy selection only considers immediate constraints, leading to cumulative errors that compromise long-term stability.

\textbf{Sensitivity on $\epsilon$.}  We evaluate the performance under different deviation thresholds. As shown in Tab. \ref{tab:ablation}, a small threshold ($\epsilon=0.01$) results in conservative behavior and sub-optimal efficiency. Conversely, a large threshold ($\epsilon=0.02$) prioritizes speed but allows excessive deviations, leading to a decline in success rates. Our framework achieves the most robust performance at $\epsilon=0.015$, demonstrating that a moderate threshold effectively triggers RL intervention at the right moment to maintain both stability and optimality across varying tasks.
\begin{table}[h]
\centering
\caption{Ablation study on SuP. We compare the performance impact of the IQL module and different deviation thresholds $\epsilon$.}
\label{tab:ablation}
\small
\begin{tabular}{lcccc}
\toprule
\textbf{Ablation} & \textbf{\makecell{Sandwich\\Remove}} & \textbf{\makecell{Put\\Cup}} & \textbf{Long}\\
\midrule
$\pi_{base}$ & 0.45, 340.5 & 0.28, 320.3 & 0.924, 267.9 \\
\midrule
SuP-0.01 & 0.59, 187.5 & 0.35, 159.8 & \cg{\textbf{0.940}, 215.2} \\
SuP-0.015  &  \cg{\textbf{0.64}, 155.9} & \cg{\textbf{0.38}, 156.0} & 0.922, 191.8 \\
SuP-0.02  & 0.46, 157.6 & \bg{0.21, 143.3} & \bg{0.904, 168.4} \\
\midrule
MPC-0.01 & 0.54, 181.4 & 0.32, 154.8 & 0.936, 225.2  \\
MPC-0.015  &  0.59, 173.3 & 0.3, 146.1 & 0.924, 205.6 \\
MPC-0.02  & \bg{0.35, 162.1} & \bg{0.19, 148.4} & 0.922, 173.7 \\
\bottomrule
\end{tabular}
\vspace{-3mm}
\end{table}