Think Fast, Plan Selectively: Adaptive Deliberation for Efficient Data-Driven MPC

Yi Xian Goh; Sze Jue Yang; Hao Luan

cs.ROSep 26, 2026

Think Fast, Plan Selectively: Adaptive Deliberation for Efficient Data-Driven MPC

Authors: Yi Xian Goh, Sze Jue Yang, Hao Luan

Organizations: Independent Researcher · Faculty of Computer Science and Information Technology, Universiti Malaya · School of Computing, National University of Singapore

Abstract

Data-driven model predictive control (MPC) combines learned world models with online trajectory optimization, achieving strong performance in continuous control. However, the per-step cost of sampling and evaluating hundreds of candidate trajectories restricts deployment to control frequencies well below what real-time robotics demands. Motivated by the dual-process theory of human cognition, which distinguishes between fast, intuitive processing (System 1) and slower, deliberative reasoning (System 2), we ask whether every decision requires the same degree of computational deliberation. We propose Fast-TD-MPC, a lightweight framework that adaptively routes between fast policy execution and test-time planning, reserving costly deliberation for states where it is most needed. Fast-TD-MPC delivers competitive task performance across 103 continuous control tasks while achieving up to ~4x faster inference. Under external disturbances, Fast-TD-MPC selectively falls back to planning, maintaining robustness comparable to the original planner.

Figures & tables

Figure 1: Overview of Fast-TD-MPC. Fast-TD-MPC uses TD-MPC2’s MPPI planner as System 2 (the slow, robust fallback), a compact amortized MLP trained via planner imitation as System 1 (the fast, reactive policy), and a lightweight OOD detector as the gating mechanism. At each decision step, the OOD detector evaluates the current state: in-distribution (ID) states are routed to the fast and compact System 1, while out-of-distribution (OOD) states fall back to System 2 (TD-MPC2’s MPPI planner). Since the detector itself costs negligible computation, the effective per-step latency scales linearly with the fraction of timesteps that require planning.

Figure 2: Pareto frontier. Return/success rate vs. per-step latency across 4 domains. Fast-TD-MPC (colored) traces the Pareto frontier across varying OOD thresholds, matching or surpassing baselines at comparable latency on DMControl, Meta-World, and ManiSkill2. Dashed line marks 90% of TD-MPC2’s performance. DreamerV3 and SAC performance referenced from Hansen et al. (2024) .

	DMControl		Meta-World		MyoSuite		ManiSkill2
Method	Return	Lat.	Succ.	Lat.	Succ.	Lat.	Succ.	Lat.
		(ms)	(%)	(ms)	(%)	(ms)	(%)	(ms)
DreamerV3 ${\dagger}$	$735_{\scriptscriptstyle\pm 93}$	$3.2_{\scriptscriptstyle\pm.1}$	$70_{\scriptscriptstyle\pm 8}$	$3.8_{\scriptscriptstyle\pm.1}$	$14_{\scriptscriptstyle\pm 17}$	$4.2_{\scriptscriptstyle\pm.1}$	$34_{\scriptscriptstyle\pm 56}$	$8.7_{\scriptscriptstyle\pm.7}$
SAC ${\dagger}$	$631_{\scriptscriptstyle\pm 108}$	$2.0_{\scriptscriptstyle\pm.4}$	$84_{\scriptscriptstyle\pm 7}$	$2.0_{\scriptscriptstyle\pm.2}$	$38_{\scriptscriptstyle\pm 20}$	$2.9_{\scriptscriptstyle\pm.5}$	$22_{\scriptscriptstyle\pm 54}$	$5.8_{\scriptscriptstyle\pm.7}$
S2-alone (TD-MPC2)	$820_{\scriptscriptstyle\pm 55}$	$27.3_{\scriptscriptstyle\pm 1.1}$	$84_{\scriptscriptstyle\pm 9}$	$26.9_{\scriptscriptstyle\pm.2}$	$40_{\scriptscriptstyle\pm 20}$	$35.5_{\scriptscriptstyle\pm.4}$	$65_{\scriptscriptstyle\pm 54}$	$45.9_{\scriptscriptstyle\pm 4.8}$
S2-alone ( $N{=}64$ )	$639_{\scriptscriptstyle\pm 100}$	$26.9_{\scriptscriptstyle\pm 1.1}$	$85_{\scriptscriptstyle\pm 7}$	$26.7_{\scriptscriptstyle\pm.2}$	$24_{\scriptscriptstyle\pm 16}$	$35.4_{\scriptscriptstyle\pm.4}$	$63_{\scriptscriptstyle\pm 53}$	$41.5_{\scriptscriptstyle\pm 3.4}$

Table 1: Benchmark results across 4 domains (103 tasks, 3 seeds each). Mean and 95% CI across all tasks in each domain.

{\dagger}

Return and success rate for DreamerV3 and SAC are referenced from Hansen et al. (2024) . all denotes the theoretical OOD mode; RG denotes the reward-gated mode. See Appendix F for full results including S2 invocation rate and peak GPU memory usage.

Figure 3: Per-step latency vs. S2 invocation rate (

\rho

). Each point is a task-seed configuration; red denotes the theoretical ( all ) OOD mode, purple denotes the reward-gated ( RG ) mode. The linear relationship (

R^{2}\geq 0.93

) confirms that per-step latency scales linearly with

\rho

H100 — DMControl + Meta-World + MyoSuite
	Policy components (ms)					Total	$\rho$	GPU
Method	$\mathcal{E}_{\theta}$	$g$	$\pi_{\text{S1}}$	$\pi_{\text{S2}}$	Env	(ms)	(%)	(MB)
S2-alone (TD-MPC2)	$0.31_{\scriptscriptstyle\pm.00}$	—	—	$26.2_{\scriptscriptstyle\pm.6}$	$1.4_{\scriptscriptstyle\pm.2}$	$27.9_{\scriptscriptstyle\pm.7}$	$100$	$95_{\scriptscriptstyle\pm 0}$
S1 alone	$0.38_{\scriptscriptstyle\pm.00}$	—	$0.49_{\scriptscriptstyle\pm.00}$	—	$1.4_{\scriptscriptstyle\pm.2}$	$2.3_{\scriptscriptstyle\pm.2}$	$0$	$68_{\scriptscriptstyle\pm 0}$
Fast-TD-MPC ( all , $\tau_{p50}$ )	$0.35_{\scriptscriptstyle\pm.00}$	$0.17_{\scriptscriptstyle\pm.00}$	$0.40_{\scriptscriptstyle\pm.01}$	$26.2_{\scriptscriptstyle\pm.5}$	$1.4_{\scriptscriptstyle\pm.2}$	$23.3_{\scriptscriptstyle\pm 1.4}$	$81_{\scriptscriptstyle\pm 4}$	$90_{\scriptscriptstyle\pm 2}$
Fast-TD-MPC ( all , $\tau_{p90}$ )	$0.35_{\scriptscriptstyle\pm.00}$	$0.17_{\scriptscriptstyle\pm.00}$	$0.38_{\scriptscriptstyle\pm.00}$	$26.3_{\scriptscriptstyle\pm.5}$	$1.4_{\scriptscriptstyle\pm.2}$	$10.9_{\scriptscriptstyle\pm 1.6}$	$33_{\scriptscriptstyle\pm 5}$	$76_{\scriptscriptstyle\pm 2}$

Table 2: Per-component latency breakdown by hardware group and peak GPU memory. Results are averaged within hardware groups: DMControl, Meta-World, and MyoSuite on H100; ManiSkill2 on A100.

\pi_{\text{S1}}

and

\pi_{\text{S2}}

report per-invocation cost (zero entries excluded),

\rho

is the S2 invocation rate, and

t_{\text{total}}\approx\mathcal{E}\theta+g+\rho\pi{\text{S2}}+(1{-}\rho)\pi_{\text{S1}}+t_{\text{env}}

Figure 4: Pareto frontier under disturbances. Return/success rate vs. per-step latency across 4 domains. Fast-TD-MPC (colored) matches or surpasses TD-MPC2 at lower latency on DMControl, Meta-World, and ManiSkill2, with a

{\sim}13\%

performance drop on MyoSuite for up to

{\sim}2\times

speedup.

	DMControl		Meta-World		MyoSuite		ManiSkill2
Method	Return	Lat.	Succ.	Lat.	Succ.	Lat.	Succ.	Lat.
		(ms)	(%)	(ms)	(%)	(ms)	(%)	(ms)
S2-alone (TD-MPC2)	$616_{\scriptscriptstyle\pm 104}$	$27.2_{\scriptscriptstyle\pm 1.1}$	$51_{\scriptscriptstyle\pm 10}$	$26.8_{\scriptscriptstyle\pm.2}$	$40_{\scriptscriptstyle\pm 22}$	$35.7_{\scriptscriptstyle\pm.5}$	$66_{\scriptscriptstyle\pm 75}$	$43.1_{\scriptscriptstyle\pm 4.7}$
S2 policy-only	$390_{\scriptscriptstyle\pm 102}$	$1.9_{\scriptscriptstyle\pm.3}$	$49_{\scriptscriptstyle\pm 10}$	$2.8_{\scriptscriptstyle\pm.2}$	$17_{\scriptscriptstyle\pm 15}$	$3.9_{\scriptscriptstyle\pm.4}$	$63_{\scriptscriptstyle\pm 66}$	$11.4_{\scriptscriptstyle\pm 5.7}$
S1 alone	$405_{\scriptscriptstyle\pm 98}$	$1.7_{\scriptscriptstyle\pm.3}$	$47_{\scriptscriptstyle\pm 10}$	$2.6_{\scriptscriptstyle\pm.2}$	$32_{\scriptscriptstyle\pm 15}$	$3.5_{\scriptscriptstyle\pm.3}$	$17_{\scriptscriptstyle\pm 52}$	$10.4_{\scriptscriptstyle\pm 4.2}$
Round-robin (S2 50%)	$577_{\scriptscriptstyle\pm 102}$	$14.5_{\scriptscriptstyle\pm.7}$	$49_{\scriptscriptstyle\pm 11}$	$14.7_{\scriptscriptstyle\pm.2}$	$37_{\scriptscriptstyle\pm 20}$	$19.4_{\scriptscriptstyle\pm.3}$	$58_{\scriptscriptstyle\pm 89}$	$27.1_{\scriptscriptstyle\pm 2.0}$

Table 3: Results of benchmarks with disturbances across 4 domains (102 tasks, 3 seeds each). Mean and 95% CI across all tasks in each domain. all denotes theoretical OOD mode; RG denotes reward-gated mode. See Appendix G for detailed results with all evaluation metrics.

Figure 5: OOD gating dynamics. Per-step OOD score and cumulative latency for a representative episode of walker-walk-backwards under combined disturbances (DMControl,

\tau_{p90}

). Top: Cumulative latency of Fast-TD-MPC (red) vs. TD-MPC2 (teal, dashed). Bottom: OOD score (purple, left axis) with

\tau_{p90}

threshold (red dotted). Shaded regions and grey dashed lines mark timesteps where

g(z_{t})>\tau

, indicating S2 invocation. Disturbance norm (pink, right axis) shows the total perturbation magnitude per step, with a spike at step 312 from the velocity kick.

Appendix figures & tables28 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 9 — Algorithm 1 Fast-TD-MPC inference

Figure 6: Task visualizations. Visualization of random states from all 103 diverse continuous control tasks used in our evaluation, spanning DMControl ( Tassa et al., 2018 ) , Meta-World ( Yu et al., 2019 ) , MyoSuite ( Caggiano et al., 2022 ) , and ManiSkill2 ( Gu et al., 2023 ) . Tasks vary greatly in objective, embodiment, and action space. See Appendix C for task details.

Task	Obs. dim	Action dim
Acrobot Swingup	6	1
Cartpole Balance	5	1
Cartpole Balance Sparse	5	1
Cartpole Swingup	5	1
Cartpole Swingup Sparse	5	1
Cheetah Jump	17	6

Appendix

Table 4: DMControl. We consider a total 39 tasks from the DMControl domain. Observation dimension ranges from 3 - 223, with action dimensions ranging from 1 - 38. Metric: Return. Physics engine: MuJoCo.

Task	Obs. dim	Action dim
Assembly	39	4
Basketball	39	4
Bin Picking	39	4
Box Close	39	4
Button Press	39	4
Button Press Topdown	39	4

Appendix

Table 5: Meta-World. We consider a total 50 tasks from the Meta-World domain. Observation dimensions are fixed at 39, with action dimensions fixed at 4. Metric: Success rate. Physics engine: MuJoCo.

Task	Obs. dim	Action dim
Myo Hand Key Turn	93	39
Myo Hand Key Turn Hard	93	39
Myo Hand Obj Hold	91	39
Myo Hand Obj Hold Hard	91	39
Myo Hand Pen Twirl	83	39
Myo Hand Pen Twirl Hard	83	39

Appendix

Table 6: MyoSuite. We consider a total 10 tasks from the MyoSuite domain. Observation dimensions ranges from 83 - 115, with action dimensions fixed at 39. Metric: Success rate. Physics engine: MuJoCo.

Task	Obs. dim	Action dim
Lift Cube	42	4
Pick Cube	51	4
Pick Ycb	51	7
Stack Cube	55	4

Appendix

Table 7: ManiSkill2. We consider a total 4 tasks from the ManiSkill2 domain. Observation dimensions ranges from 42 - 55, with action dimensions ranging from 4 - 7. Metric: Success rate. Physics engine: SAPIEN.

	DMControl	Meta-World	ManiSkill2	MyoSuite
Episode length	1,000	200	200	100
Action repeat	2	2	2	1
Effective length	500	100	100	100
Performance metric	Reward	Success	Success	Success

Appendix

Table 8: Environment details. We list the episode length and action repeat used for each task domain, as well as the total number of environment steps and performance metrics that we use for benchmarking methods. All methods use the same values for all tasks.

Disturbance	Cat.	$p$	Mechanism	Parameter
Obs. noise	Obs.	1.0	Relative $\sigma\!\cdot\!\text{std}(s)$ on $s_{t}$	$\sigma=.005$
Act. noise	Act.	1.0	Additive $\mathcal{N}(0,\sigma^{2})$ on $a_{t}$ , clamp $[-1,1]$	$\sigma=.005$
Vel. kick	Env.	1.0 †	Impulse on $q_{\text{vel}}$ at 1–2 random $t$	$m_{\max}=.3$
Grav. shift	Env.	1.0	Sustained $g\leftarrow g\cdot k$ per episode	$\delta=.05$
Sus. force	Env.	0.15	Per-step force injection when active	$f_{\max}=.3$
Combined	All	—	All five applied simultaneously	—

Appendix

Table 9: Environment disturbance configurations.

p

denotes the per-step activation probability. † 1–2 kicks per episode at random timesteps within 10–90% of episode length. Obs. noise and vel. kick magnitudes are relative (scaled by per-episode std). Tasks: 102 (39 DMControl

+

50 MetaWorld

+

10 MyoSuite

+

3 ManiSkill2; pick-ycb excluded).

Method	Return	Lat. (ms)	$\rho$ (%)	GPU (MB)
DreamerV3 ${\dagger}$	$735_{\scriptscriptstyle\pm 93}$	$3.2_{\scriptscriptstyle\pm.1}$	—	—
SAC ${\dagger}$	$631_{\scriptscriptstyle\pm 108}$	$2.0_{\scriptscriptstyle\pm.4}$	—	—
S2-alone (TD-MPC2)	$820_{\scriptscriptstyle\pm 55}$	$27.3_{\scriptscriptstyle\pm 1.1}$	$100$	$95_{\scriptscriptstyle\pm 0}$
S2-alone ( $N{=}64$ )	$639_{\scriptscriptstyle\pm 100}$	$26.9_{\scriptscriptstyle\pm 1.1}$	$100$	$69_{\scriptscriptstyle\pm 0}$
S2 policy-only	$560_{\scriptscriptstyle\pm 105}$	$1.9_{\scriptscriptstyle\pm.3}$	$0$	$66_{\scriptscriptstyle\pm 0}$
S1 alone	$623_{\scriptscriptstyle\pm 91}$	$1.6_{\scriptscriptstyle\pm.2}$	$0$	$68_{\scriptscriptstyle\pm 0}$

Appendix

Table 10: DMControl full results. 39 tasks, 3 seeds each. Mean and 95% CI across all tasks. Return, per-step latency, S2 invocation rate (

\rho

), and peak GPU memory. † Referenced from Hansen et al. (2024) . all : theoretical OOD mode; RG : reward-gated mode.

Method	Succ.	Lat. (ms)	$\rho$ (%)	GPU (MB)
DreamerV3 ${\dagger}$	$70_{\scriptscriptstyle\pm 8}$	$3.8_{\scriptscriptstyle\pm.1}$	—	—
SAC ${\dagger}$	$84_{\scriptscriptstyle\pm 7}$	$2.0_{\scriptscriptstyle\pm.2}$	—	—
S2-alone (TD-MPC2)	$84_{\scriptscriptstyle\pm 9}$	$26.9_{\scriptscriptstyle\pm.2}$	$100$	$95_{\scriptscriptstyle\pm 0}$
S2-alone ( $N{=}64$ )	$85_{\scriptscriptstyle\pm 7}$	$26.7_{\scriptscriptstyle\pm.2}$	$100$	$69_{\scriptscriptstyle\pm 0}$
S2 policy-only	$82_{\scriptscriptstyle\pm 8}$	$2.7_{\scriptscriptstyle\pm.2}$	$0$	$66_{\scriptscriptstyle\pm 0}$
S1 alone	$87_{\scriptscriptstyle\pm 8}$	$2.5_{\scriptscriptstyle\pm.2}$	$0$	$67_{\scriptscriptstyle\pm 0}$

Appendix

Table 11: Meta-World full results. 50 tasks, 3 seeds each. Mean and 95% CI across all tasks. Success rate, per-step latency, S2 invocation rate (

\rho

), and peak GPU memory. † Referenced from Hansen et al. (2024) . all : theoretical OOD mode; RG : reward-gated mode.

Method	Succ.	Lat. (ms)	$\rho$ (%)	GPU (MB)
DreamerV3 ${\dagger}$	$14_{\scriptscriptstyle\pm 17}$	$4.2_{\scriptscriptstyle\pm.1}$	—	—
SAC ${\dagger}$	$38_{\scriptscriptstyle\pm 20}$	$2.9_{\scriptscriptstyle\pm.5}$	—	—
S2-alone (TD-MPC2)	$40_{\scriptscriptstyle\pm 20}$	$35.5_{\scriptscriptstyle\pm.4}$	$100$	$97_{\scriptscriptstyle\pm 0}$
S2-alone ( $N{=}64$ )	$24_{\scriptscriptstyle\pm 16}$	$35.4_{\scriptscriptstyle\pm.4}$	$100$	$70_{\scriptscriptstyle\pm 0}$
S2 policy-only	$18_{\scriptscriptstyle\pm 15}$	$3.8_{\scriptscriptstyle\pm.4}$	$0$	$67_{\scriptscriptstyle\pm 0}$
S1 alone	$35_{\scriptscriptstyle\pm 16}$	$3.6_{\scriptscriptstyle\pm.3}$	$0$	$69_{\scriptscriptstyle\pm 0}$

Appendix

Table 12: MyoSuite full results. 10 tasks, 3 seeds each. Mean and 95% CI across all tasks. Success rate, per-step latency, S2 invocation rate (

\rho

), and peak GPU memory. † Referenced from Hansen et al. (2024) . all : theoretical OOD mode; RG : reward-gated mode.

Method	Succ.	Lat. (ms)	$\rho$ (%)	GPU (MB)
DreamerV3 ${\dagger}$	$34_{\scriptscriptstyle\pm 56}$	$8.7_{\scriptscriptstyle\pm.7}$	—	—
SAC ${\dagger}$	$22_{\scriptscriptstyle\pm 54}$	$5.8_{\scriptscriptstyle\pm.7}$	—	—
S2-alone (TD-MPC2)	$65_{\scriptscriptstyle\pm 54}$	$45.9_{\scriptscriptstyle\pm 4.8}$	$100$	$70_{\scriptscriptstyle\pm 0}$
S2-alone ( $N{=}64$ )	$63_{\scriptscriptstyle\pm 53}$	$41.5_{\scriptscriptstyle\pm 3.4}$	$100$	$44_{\scriptscriptstyle\pm 0}$
S2 policy-only	$48_{\scriptscriptstyle\pm 56}$	$11.1_{\scriptscriptstyle\pm 2.5}$	$0$	$41_{\scriptscriptstyle\pm 0}$
S1 alone	$19_{\scriptscriptstyle\pm 39}$	$10.7_{\scriptscriptstyle\pm 3.9}$	$0$	$42_{\scriptscriptstyle\pm 0}$

Appendix

Table 13: ManiSkill2 full results. 4 tasks, 3 seeds each. Mean and 95% CI across all tasks. Success rate, per-step latency, S2 invocation rate (

\rho

), and peak GPU memory. † Referenced from Hansen et al. (2024) . all : theoretical OOD mode; RG : reward-gated mode.

Task	S2-alone (TD-MPC2)		S1 alone		Fast-TD-MPC (all, $\tau_{p50}$ )		Fast-TD-MPC (all, $\tau_{p90}$ )
	Return	Lat. (ms)	Return	Lat. (ms)	Return	Lat. (ms)	Return	Lat. (ms)
Acrobot Swingup	$642_{\scriptscriptstyle\pm 25}$	$26.2_{\scriptscriptstyle\pm.8}$	$523_{\scriptscriptstyle\pm 163}$	$1.2_{\scriptscriptstyle\pm.0}$	$638_{\scriptscriptstyle\pm 87}$	$9.8_{\scriptscriptstyle\pm 3.1}$	$582_{\scriptscriptstyle\pm 155}$	$2.6_{\scriptscriptstyle\pm.9}$
Cartpole Balance Sparse	$1000$	$26.0_{\scriptscriptstyle\pm 1.7}$	$1000$	$1.3_{\scriptscriptstyle\pm.0}$	$1000$	$14.8_{\scriptscriptstyle\pm 23.9}$	$1000$	$4.8_{\scriptscriptstyle\pm 5.0}$
Cartpole Balance	$999_{\scriptscriptstyle\pm 1}$	$25.8_{\scriptscriptstyle\pm 1.4}$	$1000_{\scriptscriptstyle\pm 1}$	$1.4_{\scriptscriptstyle\pm.0}$	$999_{\scriptscriptstyle\pm 1}$	$21.1_{\scriptscriptstyle\pm 11.7}$	$999_{\scriptscriptstyle\pm 1}$	$3.4_{\scriptscriptstyle\pm 1.2}$
Cartpole Swingup Sparse	$297_{\scriptscriptstyle\pm 1189}$	$25.6_{\scriptscriptstyle\pm 1.3}$	$284_{\scriptscriptstyle\pm 1216}$	$1.2_{\scriptscriptstyle\pm.0}$	$284_{\scriptscriptstyle\pm 1216}$	$17.3_{\scriptscriptstyle\pm 13.9}$	$303_{\scriptscriptstyle\pm 1177}$	$3.8_{\scriptscriptstyle\pm 1.1}$
Cartpole Swingup	$661_{\scriptscriptstyle\pm 954}$	$26.2_{\scriptscriptstyle\pm 1.1}$	$665_{\scriptscriptstyle\pm 938}$	$1.4_{\scriptscriptstyle\pm.1}$	$654_{\scriptscriptstyle\pm 987}$	$14.4_{\scriptscriptstyle\pm 4.1}$	$666_{\scriptscriptstyle\pm 934}$	$3.5_{\scriptscriptstyle\pm 1.5}$

Appendix

Table 14: DMControl per-task results. 39 tasks, 3 seeds each. Mean and 95% CI per task. Return and per-step latency (ms) for 4 key methods. all : theoretical OOD mode.

Task	S2-alone (TD-MPC2)		S1 alone		Fast-TD-MPC (all, $\tau_{p50}$ )		Fast-TD-MPC (all, $\tau_{p90}$ )
	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)
Assembly	$100$	$26.4_{\scriptscriptstyle\pm 1.1}$	$67_{\scriptscriptstyle\pm 143}$	$2.2_{\scriptscriptstyle\pm.2}$	$90_{\scriptscriptstyle\pm 25}$	$27.1_{\scriptscriptstyle\pm 1.6}$	$87_{\scriptscriptstyle\pm 57}$	$19.7_{\scriptscriptstyle\pm 24.9}$
Basketball	$97_{\scriptscriptstyle\pm 14}$	$26.2_{\scriptscriptstyle\pm.9}$	$100$	$2.0_{\scriptscriptstyle\pm.1}$	$90_{\scriptscriptstyle\pm 43}$	$26.7_{\scriptscriptstyle\pm.1}$	$83_{\scriptscriptstyle\pm 72}$	$20.6_{\scriptscriptstyle\pm 12.0}$
Bin Picking	$100$	$26.8_{\scriptscriptstyle\pm 1.4}$	$100$	$2.1_{\scriptscriptstyle\pm.2}$	$97_{\scriptscriptstyle\pm 14}$	$27.1_{\scriptscriptstyle\pm 2.3}$	$100$	$14.5_{\scriptscriptstyle\pm 15.7}$
Box Close	$100$	$27.6_{\scriptscriptstyle\pm.5}$	$100$	$3.4_{\scriptscriptstyle\pm.6}$	$100$	$27.8_{\scriptscriptstyle\pm 1.2}$	$100$	$9.7_{\scriptscriptstyle\pm 7.4}$
Button Press Topdown Wall	$100$	$26.9_{\scriptscriptstyle\pm.7}$	$100$	$2.7_{\scriptscriptstyle\pm.2}$	$100$	$17.0_{\scriptscriptstyle\pm 9.5}$	$100$	$5.9_{\scriptscriptstyle\pm 2.0}$

Appendix

Table 15: Meta-World per-task results. 50 tasks, 3 seeds each. Mean and 95% CI per task. Success rate (%) and per-step latency (ms) for 4 key methods. all : theoretical OOD mode.

Task	S2-alone (TD-MPC2)		S1 alone		Fast-TD-MPC (all, $\tau_{p50}$ )		Fast-TD-MPC (all, $\tau_{p90}$ )
	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)
MyoHand Key Turn Hard	$30_{\scriptscriptstyle\pm 66}$	$36.6_{\scriptscriptstyle\pm 1.5}$	$20_{\scriptscriptstyle\pm 86}$	$4.1_{\scriptscriptstyle\pm.5}$	$27_{\scriptscriptstyle\pm 57}$	$16.6_{\scriptscriptstyle\pm 6.0}$	$17_{\scriptscriptstyle\pm 38}$	$10.3_{\scriptscriptstyle\pm 2.2}$
MyoHand Key Turn	$27_{\scriptscriptstyle\pm 76}$	$36.1_{\scriptscriptstyle\pm 1.6}$	$33_{\scriptscriptstyle\pm 143}$	$4.6_{\scriptscriptstyle\pm 1.3}$	$27_{\scriptscriptstyle\pm 76}$	$36.1_{\scriptscriptstyle\pm 2.3}$	$23_{\scriptscriptstyle\pm 63}$	$34.2_{\scriptscriptstyle\pm 7.0}$
MyoHand Obj Hold Hard	$50_{\scriptscriptstyle\pm 66}$	$36.0_{\scriptscriptstyle\pm 1.4}$	$70_{\scriptscriptstyle\pm 50}$	$4.2_{\scriptscriptstyle\pm.7}$	$43_{\scriptscriptstyle\pm 29}$	$29.7_{\scriptscriptstyle\pm 6.3}$	$53_{\scriptscriptstyle\pm 63}$	$16.5_{\scriptscriptstyle\pm 20.0}$
MyoHand Obj Hold	$0$	$35.2_{\scriptscriptstyle\pm.5}$	$0$	$3.6_{\scriptscriptstyle\pm.2}$	$0$	$34.6_{\scriptscriptstyle\pm.7}$	$0$	$31.4_{\scriptscriptstyle\pm 6.3}$
MyoHand Pen Twirl Hard	$47_{\scriptscriptstyle\pm 29}$	$35.9_{\scriptscriptstyle\pm.8}$	$23_{\scriptscriptstyle\pm 14}$	$3.3_{\scriptscriptstyle\pm.6}$	$50_{\scriptscriptstyle\pm 75}$	$32.5_{\scriptscriptstyle\pm 5.2}$	$27_{\scriptscriptstyle\pm 14}$	$12.0_{\scriptscriptstyle\pm 5.9}$

Appendix

Table 16: MyoSuite per-task results. 10 tasks, 3 seeds each. Mean and 95% CI per task. Success rate (%) and per-step latency (ms) for 4 key methods. all : theoretical OOD mode.

Task	S2-alone (TD-MPC2)		S1 alone		Fast-TD-MPC (all, $\tau_{p50}$ )		Fast-TD-MPC (all, $\tau_{p90}$ )
	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)
Lift Cube	$100$	$46.1_{\scriptscriptstyle\pm 2.1}$	$20_{\scriptscriptstyle\pm 50}$	$8.2_{\scriptscriptstyle\pm 5.7}$	$93_{\scriptscriptstyle\pm 29}$	$38.1_{\scriptscriptstyle\pm 21.6}$	$60_{\scriptscriptstyle\pm 25}$	$17.0_{\scriptscriptstyle\pm 6.5}$
Pick Cube	$87_{\scriptscriptstyle\pm 57}$	$46.2_{\scriptscriptstyle\pm 2.3}$	$53_{\scriptscriptstyle\pm 72}$	$10.7_{\scriptscriptstyle\pm 1.3}$	$73_{\scriptscriptstyle\pm 94}$	$25.0_{\scriptscriptstyle\pm 8.1}$	$50_{\scriptscriptstyle\pm 66}$	$16.0_{\scriptscriptstyle\pm 1.3}$
Pick Ycb	$27_{\scriptscriptstyle\pm 38}$	$49.3_{\scriptscriptstyle\pm 3.8}$	$3_{\scriptscriptstyle\pm 14}$	$14.0_{\scriptscriptstyle\pm 2.4}$	$27_{\scriptscriptstyle\pm 57}$	$41.9_{\scriptscriptstyle\pm 8.0}$	$13_{\scriptscriptstyle\pm 14}$	$19.3_{\scriptscriptstyle\pm 9.1}$
Stack Cube	$47_{\scriptscriptstyle\pm 115}$	$41.9_{\scriptscriptstyle\pm 2.0}$	$0$	$9.7_{\scriptscriptstyle\pm.6}$	$23_{\scriptscriptstyle\pm 80}$	$30.5_{\scriptscriptstyle\pm 11.9}$	$7_{\scriptscriptstyle\pm 29}$	$11.6_{\scriptscriptstyle\pm 2.0}$

Appendix

Table 17: ManiSkill2 per-task results. 4 tasks, 3 seeds each. Mean and 95% CI per task. Success rate (%) and per-step latency (ms) for 4 key methods. all : theoretical OOD mode.

Method	Return	Lat. (ms)	$\rho$ (%)	GPU (MB)
S2-alone (TD-MPC2)	$616_{\scriptscriptstyle\pm 104}$	$27.2_{\scriptscriptstyle\pm 1.1}$	$100$	$95_{\scriptscriptstyle\pm 0}$
S2 policy-only	$390_{\scriptscriptstyle\pm 102}$	$1.9_{\scriptscriptstyle\pm.3}$	$0$	$66_{\scriptscriptstyle\pm 0}$
S1 alone	$405_{\scriptscriptstyle\pm 98}$	$1.7_{\scriptscriptstyle\pm.3}$	$0$	$68_{\scriptscriptstyle\pm 0}$
Round-robin (S2 50%)	$577_{\scriptscriptstyle\pm 102}$	$14.5_{\scriptscriptstyle\pm.7}$	$50$	$96_{\scriptscriptstyle\pm 0}$
Fast-TD-MPC ( all , $\tau_{p50}$ )	$617_{\scriptscriptstyle\pm 105}$	$24.5_{\scriptscriptstyle\pm 1.9}$	$88_{\scriptscriptstyle\pm 5}$	$91_{\scriptscriptstyle\pm 2}$
Fast-TD-MPC ( all , $\tau_{p75}$ )	$607_{\scriptscriptstyle\pm 103}$	$19.3_{\scriptscriptstyle\pm 2.9}$	$67_{\scriptscriptstyle\pm 10}$	$86_{\scriptscriptstyle\pm 3}$

Appendix

Table 18: DMControl full results under disturbances. 39 tasks, 3 seeds each. Mean and 95% CI across all tasks. Return, per-step latency, S2 invocation rate (

\rho

), and peak GPU memory. all : theoretical OOD mode; RG : reward-gated mode.

Method	Succ.	Lat. (ms)	$\rho$ (%)	GPU (MB)
S2-alone (TD-MPC2)	$51_{\scriptscriptstyle\pm 10}$	$26.8_{\scriptscriptstyle\pm.2}$	$100$	$95_{\scriptscriptstyle\pm 0}$
S2 policy-only	$49_{\scriptscriptstyle\pm 10}$	$2.8_{\scriptscriptstyle\pm.2}$	$0$	$66_{\scriptscriptstyle\pm 0}$
S1 alone	$47_{\scriptscriptstyle\pm 10}$	$2.6_{\scriptscriptstyle\pm.2}$	$0$	$67_{\scriptscriptstyle\pm 0}$
Round-robin (S2 50%)	$49_{\scriptscriptstyle\pm 11}$	$14.7_{\scriptscriptstyle\pm.2}$	$50$	$96_{\scriptscriptstyle\pm 0}$
Fast-TD-MPC ( all , $\tau_{p50}$ )	$51_{\scriptscriptstyle\pm 11}$	$27.2_{\scriptscriptstyle\pm.2}$	$99_{\scriptscriptstyle\pm 0}$	$97_{\scriptscriptstyle\pm 0}$
Fast-TD-MPC ( all , $\tau_{p75}$ )	$51_{\scriptscriptstyle\pm 11}$	$25.6_{\scriptscriptstyle\pm.9}$	$93_{\scriptscriptstyle\pm 3}$	$96_{\scriptscriptstyle\pm 1}$

Appendix

Table 19: Meta-World full results under disturbances. 50 tasks, 3 seeds each. Mean and 95% CI across all tasks. Success rate, per-step latency, S2 invocation rate (

\rho

), and peak GPU memory. all : theoretical OOD mode; RG : reward-gated mode.

Method	Succ.	Lat. (ms)	$\rho$ (%)	GPU (MB)
S2-alone (TD-MPC2)	$40_{\scriptscriptstyle\pm 22}$	$35.7_{\scriptscriptstyle\pm.5}$	$100$	$97_{\scriptscriptstyle\pm 0}$
S2 policy-only	$17_{\scriptscriptstyle\pm 15}$	$3.9_{\scriptscriptstyle\pm.4}$	$0$	$67_{\scriptscriptstyle\pm 0}$
S1 alone	$32_{\scriptscriptstyle\pm 15}$	$3.5_{\scriptscriptstyle\pm.3}$	$0$	$69_{\scriptscriptstyle\pm 0}$
Round-robin (S2 50%)	$37_{\scriptscriptstyle\pm 20}$	$19.4_{\scriptscriptstyle\pm.3}$	$50$	$98_{\scriptscriptstyle\pm 0}$
Fast-TD-MPC ( all , $\tau_{p50}$ )	$36_{\scriptscriptstyle\pm 20}$	$32.2_{\scriptscriptstyle\pm 3.9}$	$89_{\scriptscriptstyle\pm 13}$	$94_{\scriptscriptstyle\pm 4}$
Fast-TD-MPC ( all , $\tau_{p75}$ )	$38_{\scriptscriptstyle\pm 22}$	$27.2_{\scriptscriptstyle\pm 5.9}$	$74_{\scriptscriptstyle\pm 19}$	$89_{\scriptscriptstyle\pm 5}$

Appendix

Table 20: MyoSuite full results under disturbances. 10 tasks, 3 seeds each. Mean and 95% CI across all tasks. Success rate, per-step latency, S2 invocation rate (

\rho

), and peak GPU memory. all : theoretical OOD mode; RG : reward-gated mode.

Method	Succ.	Lat. (ms)	$\rho$ (%)	GPU (MB)
S2-alone (TD-MPC2)	$66_{\scriptscriptstyle\pm 75}$	$43.1_{\scriptscriptstyle\pm 4.7}$	$100$	$70_{\scriptscriptstyle\pm 0}$
S2 policy-only	$63_{\scriptscriptstyle\pm 66}$	$11.4_{\scriptscriptstyle\pm 5.7}$	$0$	$41_{\scriptscriptstyle\pm 0}$
S1 alone	$17_{\scriptscriptstyle\pm 52}$	$10.4_{\scriptscriptstyle\pm 4.2}$	$0$	$42_{\scriptscriptstyle\pm 0}$
Round-robin (S2 50%)	$58_{\scriptscriptstyle\pm 89}$	$27.1_{\scriptscriptstyle\pm 2.0}$	$50$	$72_{\scriptscriptstyle\pm 0}$
Fast-TD-MPC ( all , $\tau_{p50}$ )	$66_{\scriptscriptstyle\pm 80}$	$34.6_{\scriptscriptstyle\pm 18.0}$	$74_{\scriptscriptstyle\pm 52}$	$63_{\scriptscriptstyle\pm 10}$
Fast-TD-MPC ( all , $\tau_{p75}$ )	$49_{\scriptscriptstyle\pm 108}$	$25.5_{\scriptscriptstyle\pm 22.3}$	$44_{\scriptscriptstyle\pm 65}$	$56_{\scriptscriptstyle\pm 10}$

Appendix

Table 21: ManiSkill2 full results under disturbances. 3 tasks, 3 seeds each. Mean and 95% CI across all tasks. Success rate, per-step latency, S2 invocation rate (

\rho

), and peak GPU memory. all : theoretical OOD mode; RG : reward-gated mode.

Task	S2-alone (TD-MPC2)		S1 alone		Fast-TD-MPC (all, $\tau_{p50}$ )		Fast-TD-MPC (all, $\tau_{p90}$ )
	Return	Lat. (ms)	Return	Lat. (ms)	Return	Lat. (ms)	Return	Lat. (ms)
Acrobot Swingup	$443_{\scriptscriptstyle\pm 44}$	$25.4_{\scriptscriptstyle\pm 1.4}$	$284_{\scriptscriptstyle\pm 171}$	$1.3_{\scriptscriptstyle\pm.0}$	$386_{\scriptscriptstyle\pm 31}$	$20.6_{\scriptscriptstyle\pm 13.7}$	$368_{\scriptscriptstyle\pm 207}$	$3.8_{\scriptscriptstyle\pm 1.5}$
Cartpole Balance Sparse	$122_{\scriptscriptstyle\pm 132}$	$25.6_{\scriptscriptstyle\pm.4}$	$118_{\scriptscriptstyle\pm 128}$	$1.3_{\scriptscriptstyle\pm.1}$	$124_{\scriptscriptstyle\pm 135}$	$25.6_{\scriptscriptstyle\pm.5}$	$123_{\scriptscriptstyle\pm 132}$	$25.5_{\scriptscriptstyle\pm 1.2}$
Cartpole Balance	$324_{\scriptscriptstyle\pm 245}$	$25.8_{\scriptscriptstyle\pm 1.3}$	$323_{\scriptscriptstyle\pm 117}$	$1.5_{\scriptscriptstyle\pm.0}$	$322_{\scriptscriptstyle\pm 237}$	$25.6_{\scriptscriptstyle\pm.9}$	$325_{\scriptscriptstyle\pm 242}$	$26.1_{\scriptscriptstyle\pm 3.7}$
Cartpole Swingup Sparse	$9_{\scriptscriptstyle\pm 19}$	$25.3_{\scriptscriptstyle\pm.5}$	$4_{\scriptscriptstyle\pm 15}$	$1.3_{\scriptscriptstyle\pm.1}$	$2_{\scriptscriptstyle\pm 4}$	$21.4_{\scriptscriptstyle\pm 11.2}$	$3_{\scriptscriptstyle\pm 3}$	$11.9_{\scriptscriptstyle\pm 28.4}$
Cartpole Swingup	$244_{\scriptscriptstyle\pm 151}$	$25.8_{\scriptscriptstyle\pm.4}$	$213_{\scriptscriptstyle\pm 105}$	$1.5_{\scriptscriptstyle\pm.0}$	$241_{\scriptscriptstyle\pm 168}$	$24.5_{\scriptscriptstyle\pm 8.0}$	$246_{\scriptscriptstyle\pm 155}$	$18.6_{\scriptscriptstyle\pm 28.0}$

Appendix

Table 22: DMControl per-task results under disturbances. 39 tasks, 3 seeds each. Mean and 95% CI per task. Return and per-step latency (ms) for 4 key methods. all : theoretical OOD mode.

Task	S2-alone (TD-MPC2)		S1 alone		Fast-TD-MPC (all, $\tau_{p50}$ )		Fast-TD-MPC (all, $\tau_{p90}$ )
	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)
Assembly	$37_{\scriptscriptstyle\pm 29}$	$26.6_{\scriptscriptstyle\pm.3}$	$23_{\scriptscriptstyle\pm 63}$	$2.3_{\scriptscriptstyle\pm.3}$	$47_{\scriptscriptstyle\pm 52}$	$27.9_{\scriptscriptstyle\pm 3.7}$	$33_{\scriptscriptstyle\pm 38}$	$26.2_{\scriptscriptstyle\pm 1.5}$
Basketball	$13_{\scriptscriptstyle\pm 14}$	$26.2_{\scriptscriptstyle\pm 1.2}$	$20_{\scriptscriptstyle\pm 25}$	$2.0_{\scriptscriptstyle\pm.1}$	$10_{\scriptscriptstyle\pm 25}$	$27.4_{\scriptscriptstyle\pm 1.3}$	$10_{\scriptscriptstyle\pm 25}$	$26.9_{\scriptscriptstyle\pm 1.1}$
Bin Picking	$7_{\scriptscriptstyle\pm 29}$	$25.9_{\scriptscriptstyle\pm.3}$	$10_{\scriptscriptstyle\pm 25}$	$2.1_{\scriptscriptstyle\pm.1}$	$7_{\scriptscriptstyle\pm 29}$	$26.6_{\scriptscriptstyle\pm 1.1}$	$3_{\scriptscriptstyle\pm 14}$	$26.5_{\scriptscriptstyle\pm 1.0}$
Box Close	$77_{\scriptscriptstyle\pm 14}$	$27.4_{\scriptscriptstyle\pm.6}$	$53_{\scriptscriptstyle\pm 63}$	$2.9_{\scriptscriptstyle\pm.6}$	$77_{\scriptscriptstyle\pm 29}$	$28.5_{\scriptscriptstyle\pm.9}$	$77_{\scriptscriptstyle\pm 29}$	$26.8_{\scriptscriptstyle\pm 2.6}$
Button Press Topdown Wall	$97_{\scriptscriptstyle\pm 14}$	$27.0_{\scriptscriptstyle\pm.9}$	$100$	$2.8_{\scriptscriptstyle\pm.2}$	$100$	$26.6_{\scriptscriptstyle\pm 1.5}$	$93_{\scriptscriptstyle\pm 14}$	$15.3_{\scriptscriptstyle\pm 5.6}$

Appendix

Table 23: Meta-World per-task results under disturbances. 50 tasks, 3 seeds each. Mean and 95% CI per task. Success rate (%) and per-step latency (ms) for 4 key methods. all : theoretical OOD mode.

Task	S2-alone (TD-MPC2)		S1 alone		Fast-TD-MPC (all, $\tau_{p50}$ )		Fast-TD-MPC (all, $\tau_{p90}$ )
	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)
MyoHand Key Turn Hard	$30_{\scriptscriptstyle\pm 43}$	$36.9_{\scriptscriptstyle\pm 1.4}$	$17_{\scriptscriptstyle\pm 38}$	$4.1_{\scriptscriptstyle\pm.6}$	$30_{\scriptscriptstyle\pm 75}$	$15.2_{\scriptscriptstyle\pm 7.9}$	$7_{\scriptscriptstyle\pm 29}$	$10.5_{\scriptscriptstyle\pm 12.4}$
MyoHand Key Turn	$40_{\scriptscriptstyle\pm 90}$	$36.4_{\scriptscriptstyle\pm 1.6}$	$47_{\scriptscriptstyle\pm 125}$	$4.3_{\scriptscriptstyle\pm.7}$	$40_{\scriptscriptstyle\pm 90}$	$37.0_{\scriptscriptstyle\pm 1.5}$	$43_{\scriptscriptstyle\pm 103}$	$34.8_{\scriptscriptstyle\pm 8.3}$
MyoHand Obj Hold Hard	$70_{\scriptscriptstyle\pm 25}$	$36.9_{\scriptscriptstyle\pm 2.5}$	$50_{\scriptscriptstyle\pm 66}$	$4.2_{\scriptscriptstyle\pm.8}$	$60_{\scriptscriptstyle\pm 25}$	$33.8_{\scriptscriptstyle\pm 4.8}$	$43_{\scriptscriptstyle\pm 29}$	$16.7_{\scriptscriptstyle\pm 7.6}$
MyoHand Obj Hold	$0$	$36.0_{\scriptscriptstyle\pm 1.3}$	$0$	$3.5_{\scriptscriptstyle\pm.3}$	$0$	$35.4_{\scriptscriptstyle\pm 1.5}$	$0$	$32.3_{\scriptscriptstyle\pm 12.0}$
MyoHand Pen Twirl Hard	$30$	$35.4_{\scriptscriptstyle\pm 1.9}$	$27_{\scriptscriptstyle\pm 38}$	$3.2_{\scriptscriptstyle\pm.6}$	$30_{\scriptscriptstyle\pm 50}$	$32.7_{\scriptscriptstyle\pm 5.0}$	$33_{\scriptscriptstyle\pm 38}$	$13.9_{\scriptscriptstyle\pm 9.2}$

Appendix

Table 24: MyoSuite per-task results under disturbances. 10 tasks, 3 seeds each. Mean and 95% CI per task. Success rate (%) and per-step latency (ms) for 4 key methods. all : theoretical OOD mode.

Task	S2-alone (TD-MPC2)		S1 alone		Fast-TD-MPC (all, $\tau_{p50}$ )		Fast-TD-MPC (all, $\tau_{p90}$ )
	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)	Succ.	Lat. (ms)
Lift Cube	$93_{\scriptscriptstyle\pm 14}$	$44.3_{\scriptscriptstyle\pm 1.2}$	$10_{\scriptscriptstyle\pm 25}$	$8.5_{\scriptscriptstyle\pm 2.1}$	$93_{\scriptscriptstyle\pm 14}$	$42.7_{\scriptscriptstyle\pm 6.5}$	$73_{\scriptscriptstyle\pm 29}$	$21.8_{\scriptscriptstyle\pm 3.0}$
Pick Cube	$70_{\scriptscriptstyle\pm 90}$	$44.1_{\scriptscriptstyle\pm 1.5}$	$40_{\scriptscriptstyle\pm 50}$	$11.6_{\scriptscriptstyle\pm 2.5}$	$73_{\scriptscriptstyle\pm 94}$	$28.7_{\scriptscriptstyle\pm 9.3}$	$57_{\scriptscriptstyle\pm 80}$	$14.6_{\scriptscriptstyle\pm 2.9}$
Stack Cube	$33_{\scriptscriptstyle\pm 100}$	$40.9_{\scriptscriptstyle\pm 2.1}$	$0$	$11.2_{\scriptscriptstyle\pm.7}$	$30_{\scriptscriptstyle\pm 75}$	$32.4_{\scriptscriptstyle\pm 10.4}$	$7_{\scriptscriptstyle\pm 29}$	$14.4_{\scriptscriptstyle\pm 6.5}$

Appendix

Table 25: ManiSkill2 per-task results under disturbances. 3 tasks, 3 seeds each. Mean and 95% CI per task. Success rate (%) and per-step latency (ms) for 4 key methods. all : theoretical OOD mode.

		DMControl		Meta-World		MyoSuite		ManiSkill2
Config	Warm-Start	Return	Lat. (ms)	Succ. (%)	Lat. (ms)	Succ. (%)	Lat. (ms)	Succ. (%)	Lat. (ms)
( all , $\tau_{p50}$ )	Cold start	$829_{\scriptscriptstyle\pm 55}$	$19.4_{\scriptscriptstyle\pm 2.4}$	$85_{\scriptscriptstyle\pm 8}$	$24.8_{\scriptscriptstyle\pm 1.1}$	$39_{\scriptscriptstyle\pm 21}$	$31.4_{\scriptscriptstyle\pm 3.6}$	$54_{\scriptscriptstyle\pm 55}$	$33.9_{\scriptscriptstyle\pm 12.1}$
( all , $\tau_{p50}$ )	K-shifted	$829_{\scriptscriptstyle\pm 54}$	$19.1_{\scriptscriptstyle\pm 2.5}$	$85_{\scriptscriptstyle\pm 8}$	$24.6_{\scriptscriptstyle\pm 1.1}$	$38_{\scriptscriptstyle\pm 22}$	$31.6_{\scriptscriptstyle\pm 3.5}$	$55_{\scriptscriptstyle\pm 59}$	$33.9_{\scriptscriptstyle\pm 13.9}$
( all , $\tau_{p75}$ )	Cold start	$823_{\scriptscriptstyle\pm 55}$	$12.2_{\scriptscriptstyle\pm 2.7}$	$85_{\scriptscriptstyle\pm 8}$	$18.7_{\scriptscriptstyle\pm 1.5}$	$37_{\scriptscriptstyle\pm 21}$	$26.6_{\scriptscriptstyle\pm 5.8}$	$47_{\scriptscriptstyle\pm 54}$	$23.3_{\scriptscriptstyle\pm 10.7}$
( all , $\tau_{p75}$ )	K-shifted	$821_{\scriptscriptstyle\pm 54}$	$12.3_{\scriptscriptstyle\pm 2.7}$	$85_{\scriptscriptstyle\pm 8}$	$18.8_{\scriptscriptstyle\pm 1.5}$	$39_{\scriptscriptstyle\pm 22}$	$26.9_{\scriptscriptstyle\pm 5.8}$	$48_{\scriptscriptstyle\pm 51}$	$23.5_{\scriptscriptstyle\pm 11.6}$
( all , $\tau_{p90}$ )	Cold start	$785_{\scriptscriptstyle\pm 58}$	$6.5_{\scriptscriptstyle\pm 2.0}$	$85_{\scriptscriptstyle\pm 8}$	$12.2_{\scriptscriptstyle\pm 1.6}$	$37_{\scriptscriptstyle\pm 21}$	$22.6_{\scriptscriptstyle\pm 7.6}$	$32_{\scriptscriptstyle\pm 42}$	$16.0_{\scriptscriptstyle\pm 5.2}$

Appendix

Table 26: MPPI planner warm-start ablation across 4 domains (103 tasks, 3 seeds each). Mean and 95% CI across all tasks in each domain. all denotes the theoretical OOD mode; RG denotes the reward-gated mode. Cold start and

K

-shifted warm start yield equivalent results across all configurations.

		DMControl		Meta-World		MyoSuite		ManiSkill2
Config	Warm-Start	Return	Lat. (ms)	Succ. (%)	Lat. (ms)	Succ. (%)	Lat. (ms)	Succ. (%)	Lat. (ms)
( all , $\tau_{p50}$ )	Cold start	$617_{\scriptscriptstyle\pm 105}$	$24.5_{\scriptscriptstyle\pm 1.9}$	$51_{\scriptscriptstyle\pm 11}$	$27.2_{\scriptscriptstyle\pm.2}$	$36_{\scriptscriptstyle\pm 20}$	$32.2_{\scriptscriptstyle\pm 3.9}$	$66_{\scriptscriptstyle\pm 80}$	$34.6_{\scriptscriptstyle\pm 18.0}$
( all , $\tau_{p50}$ )	K-shifted	$618_{\scriptscriptstyle\pm 105}$	$24.5_{\scriptscriptstyle\pm 1.9}$	$51_{\scriptscriptstyle\pm 11}$	$27.1_{\scriptscriptstyle\pm.2}$	$38_{\scriptscriptstyle\pm 22}$	$32.0_{\scriptscriptstyle\pm 3.2}$	$69_{\scriptscriptstyle\pm 75}$	$35.4_{\scriptscriptstyle\pm 17.7}$
( all , $\tau_{p75}$ )	Cold start	$607_{\scriptscriptstyle\pm 103}$	$19.3_{\scriptscriptstyle\pm 2.9}$	$51_{\scriptscriptstyle\pm 11}$	$25.6_{\scriptscriptstyle\pm.9}$	$38_{\scriptscriptstyle\pm 22}$	$27.2_{\scriptscriptstyle\pm 5.9}$	$49_{\scriptscriptstyle\pm 108}$	$25.5_{\scriptscriptstyle\pm 22.3}$
( all , $\tau_{p75}$ )	K-shifted	$609_{\scriptscriptstyle\pm 103}$	$19.4_{\scriptscriptstyle\pm 2.9}$	$50_{\scriptscriptstyle\pm 10}$	$25.4_{\scriptscriptstyle\pm.9}$	$40_{\scriptscriptstyle\pm 22}$	$27.1_{\scriptscriptstyle\pm 6.1}$	$54_{\scriptscriptstyle\pm 108}$	$25.9_{\scriptscriptstyle\pm 21.4}$
( all , $\tau_{p90}$ )	Cold start	$586_{\scriptscriptstyle\pm 101}$	$13.6_{\scriptscriptstyle\pm 3.0}$	$49_{\scriptscriptstyle\pm 10}$	$22.8_{\scriptscriptstyle\pm 1.6}$	$34_{\scriptscriptstyle\pm 22}$	$22.9_{\scriptscriptstyle\pm 7.8}$	$46_{\scriptscriptstyle\pm 86}$	$16.9_{\scriptscriptstyle\pm 10.5}$

Appendix

Table 27: MPPI planner warm-start ablation under disturbances across 4 domains (102 tasks, 3 seeds each). Mean and 95% CI across all tasks in each domain. all denotes the theoretical OOD mode; RG denotes the reward-gated mode. Cold start and

K

-shifted warm start yield equivalent results under perturbation.

		DMControl		Meta-World		MyoSuite		ManiSkill2
Config	Metric	Return	Lat. (ms)	Succ. (%)	Lat. (ms)	Succ. (%)	Lat. (ms)	Succ. (%)	Lat. (ms)
( all , $\tau_{p50}$ )	Maha.	$829_{\scriptscriptstyle\pm 55}$	$19.4_{\scriptscriptstyle\pm 2.4}$	$85_{\scriptscriptstyle\pm 8}$	$24.8_{\scriptscriptstyle\pm 1.1}$	$39_{\scriptscriptstyle\pm 21}$	$31.4_{\scriptscriptstyle\pm 3.6}$	$54_{\scriptscriptstyle\pm 55}$	$33.9_{\scriptscriptstyle\pm 12.1}$
( all , $\tau_{p50}$ )	Tan.	$819.9_{\scriptscriptstyle\pm 53.5}$	$15.4_{\scriptscriptstyle\pm 2.4}$	$69.9_{\scriptscriptstyle\pm 6.3}$	$21.5_{\scriptscriptstyle\pm 1.2}$	$40.2_{\scriptscriptstyle\pm 21}$	$27.8_{\scriptscriptstyle\pm 4.5}$	$48.0_{\scriptscriptstyle\pm 33.3}$	$24.7_{\scriptscriptstyle\pm 6.7}$
( all , $\tau_{p75}$ )	Maha.	$823_{\scriptscriptstyle\pm 55}$	$12.2_{\scriptscriptstyle\pm 2.7}$	$85_{\scriptscriptstyle\pm 8}$	$18.7_{\scriptscriptstyle\pm 1.5}$	$37_{\scriptscriptstyle\pm 21}$	$26.6_{\scriptscriptstyle\pm 5.8}$	$47_{\scriptscriptstyle\pm 54}$	$23.3_{\scriptscriptstyle\pm 10.7}$
( all , $\tau_{p75}$ )	Tan.	$796.9_{\scriptscriptstyle\pm 56.1}$	$9.9_{\scriptscriptstyle\pm 2.5}$	$69.4_{\scriptscriptstyle\pm 6.3}$	$13.6_{\scriptscriptstyle\pm 1.2}$	$38.4_{\scriptscriptstyle\pm 21.2}$	$19.1_{\scriptscriptstyle\pm 5.5}$	$41.1_{\scriptscriptstyle\pm 34.8}$	$18.8_{\scriptscriptstyle\pm 7.3}$
( all , $\tau_{p90}$ )	Maha.	$785_{\scriptscriptstyle\pm 58}$	$6.5_{\scriptscriptstyle\pm 2.0}$	$85_{\scriptscriptstyle\pm 8}$	$12.2_{\scriptscriptstyle\pm 1.6}$	$37_{\scriptscriptstyle\pm 21}$	$22.6_{\scriptscriptstyle\pm 7.6}$	$32_{\scriptscriptstyle\pm 42}$	$16.0_{\scriptscriptstyle\pm 5.2}$

Appendix

Table 28: OOD metric ablation across 4 domains (103 tasks, 3 seeds each). Mean and 95% CI across all tasks in each domain. all denotes the theoretical OOD mode; RG denotes the reward-gated mode.

		DMControl		Meta-World		MyoSuite		ManiSkill2
Config	Metric	Return	Lat. (ms)	Succ. (%)	Lat. (ms)	Succ. (%)	Lat. (ms)	Succ. (%)	Lat. (ms)
( all , $\tau_{p50}$ )	Maha.	$617_{\scriptscriptstyle\pm 105}$	$24.5_{\scriptscriptstyle\pm 1.9}$	$51_{\scriptscriptstyle\pm 11}$	$27.2_{\scriptscriptstyle\pm.2}$	$36_{\scriptscriptstyle\pm 20}$	$32.2_{\scriptscriptstyle\pm 3.9}$	$66_{\scriptscriptstyle\pm 80}$	$34.6_{\scriptscriptstyle\pm 18.0}$
( all , $\tau_{p50}$ )	Tan.	$606.0_{\scriptscriptstyle\pm 103.5}$	$20.5_{\scriptscriptstyle\pm 2.2}$	$42.7_{\scriptscriptstyle\pm 8.4}$	$25.9_{\scriptscriptstyle\pm 0.8}$	$34.8_{\scriptscriptstyle\pm 20.8}$	$27.3_{\scriptscriptstyle\pm 5.2}$	$57.9_{\scriptscriptstyle\pm 32.6}$	$26.7_{\scriptscriptstyle\pm 8.1}$
( all , $\tau_{p75}$ )	Maha.	$607_{\scriptscriptstyle\pm 103}$	$19.3_{\scriptscriptstyle\pm 2.9}$	$51_{\scriptscriptstyle\pm 11}$	$25.6_{\scriptscriptstyle\pm.9}$	$38_{\scriptscriptstyle\pm 22}$	$27.2_{\scriptscriptstyle\pm 5.9}$	$49_{\scriptscriptstyle\pm 108}$	$25.5_{\scriptscriptstyle\pm 22.3}$
( all , $\tau_{p75}$ )	Tan.	$571.4_{\scriptscriptstyle\pm 99.5}$	$14.8_{\scriptscriptstyle\pm 2.7}$	$43.0_{\scriptscriptstyle\pm 8.4}$	$22.0_{\scriptscriptstyle\pm 1.7}$	$35.0_{\scriptscriptstyle\pm 20.4}$	$19.6_{\scriptscriptstyle\pm 6}$	$45_{\scriptscriptstyle\pm 38.6}$	$19.3_{\scriptscriptstyle\pm 10.8}$
( all , $\tau_{p90}$ )	Maha.	$586_{\scriptscriptstyle\pm 101}$	$13.6_{\scriptscriptstyle\pm 3.0}$	$49_{\scriptscriptstyle\pm 10}$	$22.8_{\scriptscriptstyle\pm 1.6}$	$34_{\scriptscriptstyle\pm 22}$	$22.9_{\scriptscriptstyle\pm 7.8}$	$46_{\scriptscriptstyle\pm 86}$	$16.9_{\scriptscriptstyle\pm 10.5}$

Appendix

Table 29: OOD metric ablation under disturbances across 4 domains (102 tasks, 3 seeds each). Mean and 95% CI across all tasks in each domain. all denotes the theoretical OOD mode; RG denotes the reward-gated mode.

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