Expert-Play Contouring Control Faster-than-Demonstration Planning from Slow Expert and Fast Play

Anonymous AuthorsUnder review

Expert demonstrations define the task geometry, play data trains the dynamics; a slow imitation policy succeeds in 22 s, naive acceleration fails, EPCC succeeds in 13 s.

TL;DR

EPCC executes tasks faster than its demonstrations by pairing slow expert demonstrations with fast, non-expert play. Key idea: demonstrations say what to do; play shows how fast it can be done. Key result: 2.0× the throughput of the IL baseline on average, with gains concentrated in contact-sensitive phases, driven by play-trained dynamics and actions optimized beyond temporal rescaling.

Throughput (1/s) ↑	PushT	Cube	Slippery-PushT
DP[1]	.033	.137	.021
SkiP[2]	.021	.146	−.003
SAIL[3]	.037	.241	.018
SuP[4]	.062	.318	.017
EPCC (ours)	.068	.282	.039

DP: IL baseline; SkiP, SAIL, SuP: acceleration baselines. TP rewards fast successes and penalizes failures.

Try Play + Expert

Read the full abstract

Expert demonstrations often specify what a robot should do, but not how fast it can do it. Imitation Learning (IL) inherits demonstration timing, while directly accelerating the learned motion can fail when faster execution changes the robot–object dynamics. We study faster-than-demonstration execution as a dynamics-aware control problem and introduce Expert-Play Contouring Control (EPCC), which combines slow expert demonstrations with fast, non-expert play. Expert demonstrations train a latent trajectory generator whose predictions are reparameterized into a time-independent contour of successful task progression, while play trains a world model (WM) of fast-action outcomes. At deployment, our proposed planner uses the WM to optimize actions that maximize progress along the expert-derived contour while penalizing deviation from the intended task evolution. Averaged across three visuomotor manipulation tasks, EPCC achieves 2.0× the throughput of the IL baseline, including 2.2× the throughput of the strongest acceleration baseline on a task with interaction-sensitive object dynamics. Our analysis shows that the gains concentrate where faster execution changes robot–object evolution. Together, our results highlight a simple yet effective principle: demonstrations provide task intent, while play data provides the dynamic coverage needed to execute that intent faster. Our project page is available at https://expert-play-contouring.netlify.app/.

Real robot

Real-world demonstration

Task

Push-T on a low-friction surface, where faster execution makes object motion more sensitive to contact dynamics.

Rollout

EPCC and a Flow Matching (IL) policy rollout from the same initial state, in real time. The timer stops when the task is completed.

Deep diveVisualizing planner inference

EPCC planning on the robot, at 2× speed. Gradient line: the task contour. Thin lines: candidate plans sampled by the optimizer. White line: the optimized plan. Yellow T: the predicted block pose. Left: camera view; right: the same plan, zoomed around the end effector.

Try it

Play + Expert = ?

Does faster play lead to faster execution? Pick a play pace and see for yourself.

i Play data trains the world model; the four equal-budget sets differ in pace (×demo). demos: the expert demonstrations are also used as play (Expert-Only, not EPCC).
Expert demonstrations give the contour of successful task progression.
Initial state: ★ marks the recommended one. Clips play at 2× speed.
SR / TTC / TP: over the same 50 initial conditions. Success on PushT tasks: block within 20 px and 20° of the goal for 5 s (amber bar: the hold in progress); on Cube: within 7 cm.

Play data

Expert demos

EPCC

EPCC across play paces

Deep diveSurprising: can expert demos from plain PushT guide EPCC on a slippery table?

Expert demonstrations come only from plain PushT (τ = 0). On every slippery table, EPCC gets zero expert demonstrations, only play collected on that table.

Coasting sweep

i After contact the block velocity decays with coasting time τ (τ = 0: quasi-static PushT). Clips play at 2× speed from the chosen initial state. SR, TTC and TP: over the same 50 initial conditions.

Play data

Expert demos

EPCC

EPCC across coasting times

01 Problem

Faster-than-demonstration execution

TL;DR

Expert demonstrations often specify what a robot should do, but not how fast it can do it. Directly accelerating the learned motion can fail when faster execution changes the robot–object dynamics. EPCC uses fast, non-expert play to provide the missing fast-regime action–outcome evidence.

Policies trained from human demonstrations often inherit their slow and cautious execution, limiting throughput. Most prior work identifies phases during which the motion generated by the policy can be executed faster without changing outcome. It uses proxy cues for precision, such as motion complexity or semantic phase, and temporally compresses the identified segments through action downsampling, faster tracking or retiming[3][5][2][6][7]. These cues do not directly predict how robot–object dynamics change under faster execution.

For example, a careful push that stops an object at its target on a low-friction surface may instead send it diverging away from the target when executed faster (see the real-robot clip). Speeding up there requires understanding robot–object dynamics.

Our key insight is to separate task intent from fast-execution dynamics: slow expert demonstrations define the successful task evolution to preserve, whereas fast play reveals how actions change the robot–object evolution at higher speed.

02 Method

Expert-Play Contouring Control

TL;DR

EPCC learns a latent world model from fast play to predict robot–object dynamics, and a contour generator from expert demonstrations to produce an expert-derived latent contour from the current observation. It combines them through receding-horizon contouring control, which optimizes actions to maximize progress along the latent contour while keeping predicted rollouts close to it.

Overview of EPCC: training on play and demonstrations (left) and latent contouring control at inference (right). — **Overview of EPCC.** **Training (left):** play data \(\mathcal{D}_{\mathrm{p}}\) trains a latent world model, consisting of an encoder \(h_\phi\) and an action-conditioned predictor \(f_{\theta}\), with the next-latent prediction objective \(\mathcal{L}_{\mathrm{WM}}\) (Sec. IV-A). Expert demonstrations \(\mathcal{D}_{\mathrm{e}}\) are encoded with the frozen \(h_\phi\) and used to train a latent trajectory generator \(G_\psi\); the path reparameterization \(\mathcal{P}\) removes the demonstrations' timing, yielding a time-independent contour \(\bar{z}_t(s)\), \(s \in [0,1]\) (Sec. IV-B). **Inference (right):** from the current observation, the contour generator \(C_\psi\) produces the reference contour, and the controller jointly optimizes the action sequence \(A_t\) and progress increments \(V_t\) by minimizing the contouring error \(e^c_{t+k|t}\) between the world-model rollout \(\hat{z}_{t+k|t}\) and \(\bar{z}_t(s_{t+k|t})\), maximizing progress \(\Delta s\) along the contour, and encouraging action smoothness (Sec. IV-C, Eq. (25)). The first \(T_{a}\) actions are executed and both the contour and the plan are recomputed from the next observation.

Learning a latent world model from play

Predict the next latent state from the current one and an action.

Visual observations are encoded into a compact latent state, and an action-conditioned latent dynamics model is trained on play transitions with a next-latent prediction objective[8][9]. Because the encoder observes both the robot and the manipulated scene, the learned dynamics capture task-relevant robot–object evolution.

Latent contour generation from expert demonstrations

Preserve the ordering of the generated task evolution and remove its timing.

The frozen world-model encoder encodes expert demonstrations into the same latent space, and a latent trajectory generator learns to predict the future latent sequence from the current latent state. A path reparameterization then removes the demonstrations' timing, turning this prediction into a contour that keeps the order of task progress and leaves its traversal speed to the controller.

Latent contouring control

Make maximal progress along the contour while limiting deviation from it.

Following model predictive contouring control[10][11], EPCC jointly optimizes the action sequence and progress along the contour with contouring, progress and action regularization costs. The contouring cost preserves the expert-derived task evolution, while the progress cost drives the predicted rollout forward as quickly as permitted by the world model. Replanning from every new observation, EPCC accelerates whenever faster execution stays consistent with the intended task evolution.

Deep diveContour, costs and optimization

World model. With \(z_t = h_\phi(o_t)\) and \(\hat z_{t+1} = f_\theta(z_t, a_t)\), play trains

\[ \mathcal{L}_{\mathrm{WM}}(\phi,\theta) = \mathbb{E}_{(o_t,a_t,o_{t+1})\sim\mathcal{D}_{\mathrm{p}}}\big\|f_\theta\big(h_\phi(o_t),a_t\big) - h_\phi(o_{t+1})\big\|_2^2 . \]

Contour. The generator predicts \(G_\psi(z_t) = (\tilde z_{t+1|t},\ldots,\tilde z_{t+L|t})\). Each state gets a normalized cumulative path coordinate

\[ s_{t,k} = \frac{\sum_{j=1}^{k} \|\tilde z_{t+j|t}-\tilde z_{t+j-1|t}\|_2}{\sum_{j=1}^{L} \|\tilde z_{t+j|t}-\tilde z_{t+j-1|t}\|_2}, \qquad \tilde z_{t|t}=z_t, \]

and the contour \(\bar z_t:[0,1]\to\mathcal{Z}\) interpolates linearly between consecutive states, so \(\bar z_t(0)=z_t\) and \(\bar z_t(1)=\tilde z_{t+L|t}\).

Costs. With progress \(s_{t+k+1|t} = s_{t+k|t} + \nu_{t+k|t}\) and \(s_{t|t}=0\):

\[ J_{\mathrm{cont}} = \sum_{k=1}^{H}\big\|\hat z_{t+k|t} - \bar z_t(s_{t+k|t})\big\|_{Q_c}^2,\qquad J_{\mathrm{prog}} = -w_p\sum_{k=0}^{H-1}\nu_{t+k|t},\qquad J_{\mathrm{act}} = \sum_{k=0}^{H-1}\big\|a_{t+k|t}-a_{t+k-1|t}\big\|_{R_\Delta}^2 . \]

Optimization. At each control step EPCC solves

\[ \min_{A_t,\,V_t}\; J_{\mathrm{cont}} + J_{\mathrm{prog}} + J_{\mathrm{act}} \quad\text{s.t.}\quad \hat z_{t|t}=h_\phi(o_t),\; \hat z_{t+k+1|t}=f_\theta(\hat z_{t+k|t},a_{t+k|t}),\; 0\le s_{t+k|t}\le 1,\; a_{t+k|t}\in\mathcal{A},\; 0\le\nu_{t+k|t}\le\nu_{\max}, \]

executes the first \(T_a\) actions and replans from the next observation.

03 Experiments

When does dynamics-aware acceleration help?

Takeaway

EPCC gains most as interaction dynamics become more consequential and during contact-sensitive phases.

We compare against the imitation baseline DP[1] and three faster-than-demonstration methods, SkiP[2], SAIL[3] and SuP[4], on PushT, Cube[12] and the interaction-sensitive Slippery-PushT.

1Does richer dynamics awareness help?

On interaction-sensitive tasks, performance improves with richer dynamics awareness: from proxy-based SAIL and SkiP, to robot-state dynamics in SuP, to robot–object dynamics in EPCC.

		PushT			Cube			Slippery-PushT
	Dynamics	SR %	TTC s	TP 1/s	SR %	TTC s	TP 1/s	SR %	TTC s	TP 1/s
DP	–	88	24.3	.033	96	6.8	.137	68	28.8	.021
SkiP	proxy	60	20.8	.021	80	4.9	.146	24	23.6	−.003
SAIL	proxy	70	19.9	.037	96	3.8	.241	48	19.0	.018
SuP	robot state	88	13.4	.062	98	3.2	.318	56	29.3	.017
Play+Goal	robot–object	4	7.1	−.016	0	–	−.064	0	–	−.017
EPCC	robot–object	90	12.2	.068	96	3.3	.282	74	17.7	.039

Same 50 initial states per task; bold: best. Dynamics: what each method models to accelerate. Play+Goal: play-trained world model with a goal frame instead of the expert contour.

2What if robot–object interactions become more consequential?

EPCC and SuP perform similarly near the quasi-static regime; EPCC's advantage grows as coasting increases, with the same quasi-static PushT contour reused throughout.

SR, TTC and TP of EPCC, SuP and SAIL as the block's coasting time grows. — **Contact-dynamics sweep.** SR, TTC and TP vs. coasting time τ; the quasi-static PushT contour is reused at every τ.

3Which phases gain the most?

The additional speedup concentrates in contact phases, where faster execution changes robot–object evolution; free-motion speedups are comparable. This also explains the weaker Cube result: its interaction-sensitive grasp and release phases are a small part of an episode.

Speed-up during contact and free motion for EPCC, SuP, SAIL and SkiP on each task. — **Phase analysis.** Speed-up α in contact and free motion, on episodes every method solved.

04 Experiments

Does play data provide useful actions beyond temporal rescaling?

Takeaway

Restricting acceleration to retimed policy outputs becomes increasingly limiting when faster execution changes robot–object evolution. Temporal candidates can nevertheless provide a useful warm start.

Under the same objective, Select executes the best temporally rescaled candidate of SuP[4], EPCC-WS refines it beyond the candidate set, and EPCC optimizes without policy-derived candidates.

	PushT			Cube			Slippery-PushT
	SR %	TTC s	TP 1/s	SR %	TTC s	TP 1/s	SR %	TTC s	TP 1/s
Select	92	12.6	.069	96	3.5	.270	16	24.5	−.005
EPCC-WS	94	10.0	.092	78	2.6	.281	60	20.2	.030
EPCC	78	10.4	.073	84	2.5	.317	62	15.8	.033

Action search vs. temporal scaling; bold: best.

The benefit is largest on Slippery-PushT; policy-derived candidates can aid initialization but are not required.

05 Experiments

What play data is useful for acceleration?

Takeaway

Useful play should be fast enough to cover the accelerated interaction regime without moving too far from the task-relevant dynamics.

With the expert contour generator fixed, only the world model's training data varies: expert data alone (Expert-Only) is not sufficient, play without the expert contour (Play+Goal) rarely succeeds, and performance peaks at an intermediate play pace.

SR, TTC and TP of EPCC for play datasets of increasing pace on each task, with Expert-Only as a dashed line. — **Play pace.** EPCC with equal-budget play at different paces (× demo); dashed: Expert-Only. Throughput peaks at 2.6–3.5× the demonstration pace.

Try the combinations

06 What's next

Limitations and directions

World-model accuracy and coverageEPCC depends on the accuracy and coverage of its world model. More targeted play-data collection may improve reliability.
Planning costEPCC incurs additional planning cost. Faster world models may improve real-time performance.

References

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