ActTime: Action-Conditioned World Modeling for Time Series

Xinxing Zhou; Xiaojie Yuan; Yanlong Wen; Ming Jin

cs.AIOct 19, 2026

ActTime: Action-Conditioned World Modeling for Time Series

Authors: Xinxing Zhou, Xiaojie Yuan, Yanlong Wen, Ming Jin

Organizations: Nankai University · Griffith University

Abstract

Time-series models increasingly condition on known future inputs. In controlled systems, some of these inputs are actions that can be changed, compared, and optimized before execution. A model must therefore do more than predict the realized future: it must predict how outcomes change under different actions from the same observed history and support reliable comparison of candidate plans. We introduce ActTime, an action-conditioned world model for time series. Over the observed history, ActTime updates variable-specific latent states through an action-conditioned transition and corrects them using observations. It then rolls the same transition forward under candidate actions to generate future trajectories. Training uses only factual trajectories, without paired alternative-action outcomes or planning supervision. We construct a simulator-grounded evaluation suite across building energy, traffic, greenhouse climate, and inventory management, covering factual prediction, intervention-effect prediction, offline decision making, and closed-loop planning. ActTime ranks first in 12 of 16 domain-task settings. Across eight methods, the mean pairwise model-ranking reversal rate is 17.8% between factual prediction and intervention fidelity, and rises to 28.4% between intervention fidelity and decision ranking. These results show that factual accuracy, intervention fidelity, and decision quality are related but not interchangeable.

Figures & tables

Panel of Figure 1 — Figure 1: From factual prediction to decision making. Accurate prediction under observed actions (a) does not guarantee faithful responses under alternative actions (b) . Errors in these responses can further distort candidate-action rankings and lead to suboptimal decisions (c) .

Figure 2: Overview of ActTime . The model filters the observed history by alternating a shared action-conditioned transition with observation-based state correction. A frozen pretrained temporal backbone provides a history prior through a lightweight residual adapter, after which the same transition rolls the state forward under candidate future actions for prediction. The bottom panels detail the transition, correction, and prior modules.

Domain	$D/A/P$	Step	$T/H$	Action	Targets
CityLearn	28/1/2	1 h	24/12	Battery charge/discharge	SOC, net electricity consumption
SUMO	25/4/6	10 s	24/12	Traffic-signal phase	Queue, waiting time, traffic flow
GreenLight	36/6/3	15 min	96/16	Climate actuators	CO 2 , temperature, humidity
Inventory	15/3/4	1 period	24/12	Replenishment requests	Backlog, echelon inventories

Table 1: Simulation environments and task configurations.

D/A/P

denote the observation, action, and target dimensions, and

T/H

the history/prediction horizons in simulator steps.

Domain	Task / Metric	Ridge	DLinear	PatchTST	iTransformer	TFT	RSSM	MTS3	ActTime
CityLearn	Factual MAE	0.2875	0.3585	0.3410	0.3602	0.2583	0.2501	0.2512	0.2486
	Effect NMAE	0.1495	0.3493	0.2700	0.3972	0.0498	0.0790	0.0716	0.0725
	Macro Regret	0.4793	0.3869	0.4396	0.5050	0.2880	0.3739	0.3105	0.2798
	Online Objective	0.8310	0.8541	0.8481	0.9099	0.8250	0.8196	0.8414	0.8317
SUMO	Factual MAE	0.3873	0.4358	0.4150	0.3730	0.1226	0.1730	0.2134	0.1076
	Effect NMAE	1.0851	0.9201	0.9202	0.9060	0.4184	0.4914	0.5776	0.4825

Table 2: Main results across four controlled dynamical systems and four evaluation settings. Lower is better for all task metrics (

\downarrow

). Macro Regret denotes the average normalized regret over the three predefined offline objectives. Best and second-best results are shown in bold and underlined , respectively. Ridge denotes Ridge-VARX, while DLinear, PatchTST, iTransformer, and TFT denote their action-conditioned variants.

Figure 3: Model-order reversals across evaluation levels. Bars report the fraction of method pairs whose ordering reverses between adjacent levels. Error bars denote 95% bootstrap confidence intervals over histories.

Domain	Ridge	DLinear	PatchTST	iTransformer	TFT	RSSM	MTS3	ActTime
CityLearn	0.8608	0.8213	0.8361	0.8053	0.8381	0.7627	0.8123	0.8810
SUMO	0.4745	0.4709	0.4639	0.4619	0.9008	0.8532	0.8451	0.9048
GreenLight	0.5164	0.2612	0.1970	0.2713	0.7527	0.7284	0.7334	0.8514
Inventory	0.7934	0.6064	0.5799	0.6026	0.7703	0.7757	0.8071	0.8271
Avg.	0.6613	0.5399	0.5192	0.5352	0.8154	0.7800	0.7995	0.8661

Table 3: Candidate-action ranking fidelity. Mean per-history Spearman correlation between predicted and simulator candidate costs under each domain’s predefined primary decision objective. Higher is better. Best and second-best results are shown in bold and underlined, respectively.

Variant	Factual MAE	Effect NMAE	Macro Regret	Online Objective
Full	1.000	1.000	1.000	1.000
Simple Action Concatenation	1.059	1.035	1.137	1.021
w/o State Correction	2.137	2.132	2.215	1.031
Shared State Across Variables	5.787	5.367	4.360	1.146
w/o Action Conditioning	4.290	6.393	16.349	2.999

Table 4: Ablation study averaged across the four domains. Each entry is the ratio to the matched full-model metric within each domain, so

1.0

denotes parity and larger values indicate degradation.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Domain	Train	Validation	Test	Split construction
CityLearn	163,920	26,520	23,320	Disjoint calendar ranges
SUMO	88,000	19,400	13,000	Disjoint simulator seeds
GreenLight	74,444	23,428	22,596	Disjoint weather years
Inventory	35,368	8,748	7,808	Disjoint simulator seeds

Appendix

Table 5: Factual data used for training and evaluation. Window counts refer to unique supervised windows.

Domain	Intervention histories $\times$ plans	Offline histories $\times$ plans	Online episodes	Online $K/H$
CityLearn	$100\times 16$	$512\times 64$	8	$64/12$
SUMO	$96\times 6$	$256\times 6$	20	$16/12$
GreenLight	$256\times 13$	$384\times 16$	24	$24/16$
Inventory	$256\times 9$	$480\times 24$	24	$24/12$

Appendix

Table 6: Evaluation scale across domains. Intervention and Offline report the number of histories and candidate plans per history. For online planning,

K

denotes the candidate population size per CEM round and

H

the planning horizon.

Domain	Offline objectives	Online objective
CityLearn	Electricity cost, grid peak, grid energy	Electricity cost
SUMO	Balanced congestion, queue, waiting	Balanced congestion
GreenLight	Mean climate violation, peak climate violation, balanced cost	Balanced cost
Inventory	Economic stock cost, service risk, recovery cost	Economic stock cost

Appendix

Table 7: Decision objectives used in offline and closed-loop evaluation.

Method	CityLearn		SUMO		GreenLight		Inventory
	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$	MAE $\downarrow$	MSE $\downarrow$
Ridge-VARX	0.2875	0.2003	0.3873	0.3059	0.3263	0.1873	0.2210	0.1169
DLinear-Action	0.3585	0.2667	0.4358	0.4540	0.3699	0.2575	0.3812	0.3169
PatchTST-Action	0.3410	0.2589	0.4150	0.4051	0.3647	0.2485	0.3938	0.3314
iTransformer-Action	0.3602	0.2749	0.3730	0.3287	0.3398	0.2173	0.3706	0.2995
TFT-Action	0.2583	0.2354	0.1226	0.0521	0.0666	0.0099	0.0992	0.0391

Appendix

Table 8: Factual prediction results across the four domains. MAE and MSE are computed in standardized target space.

Method	CityLearn		SUMO		GreenLight		Inventory
	Effect NMAE $\downarrow$	Macro NMAE $\downarrow$	Effect NMAE $\downarrow$	Macro NMAE $\downarrow$	Effect NMAE $\downarrow$	Macro NMAE $\downarrow$	Effect NMAE $\downarrow$	Macro NMAE $\downarrow$
Ridge-VARX	0.1495	0.1646	1.0851	1.1003	0.8622	0.8624	0.6538	1.0046
DLinear-Action	0.3493	0.3656	0.9201	0.9259	0.9384	0.9479	0.9711	1.1413
PatchTST-Action	0.2700	0.2730	0.9202	0.9266	0.9221	0.9368	0.9774	1.1116
iTransformer-Action	0.3972	0.3943	0.9060	0.9118	0.8860	0.8835	0.9567	1.0885
TFT-Action	0.0498	0.0718	0.4184	0.4213	0.2811	0.3059	0.3077	0.6023

Appendix

Table 9: Intervention-effect prediction results across the four domains. Effect NMAE pools normalized intervention-effect errors across targets, while Macro NMAE averages target-wise normalized effect errors.

Method	CityLearn	SUMO	GreenLight	Inventory
	Macro Regret $\downarrow$	Macro Regret $\downarrow$	Macro Regret $\downarrow$	Macro Regret $\downarrow$
Ridge-VARX	0.4793	0.5255	0.4352	0.1169
DLinear-Action	0.3869	0.5661	0.7962	0.2929
PatchTST-Action	0.4396	0.5662	0.8965	0.3221
iTransformer-Action	0.5050	0.5620	0.7096	0.3133
TFT-Action	0.2880	0.0296	0.2367	0.1585

Appendix

Table 10: Offline decision results on fixed candidate-action banks. Macro Regret is the equal-weight average of normalized regret over the three decision objectives defined in Appendix A.2 .

Method	CityLearn			SUMO			GreenLight			Inventory
	Electricity Cost $\downarrow$	Grid Energy $\downarrow$	Grid Peak $\downarrow$	Balanced Congestion $\downarrow$	Queue $\downarrow$	Stopped Waiting $\downarrow$	Balanced Cost $\downarrow$	Mean Climate Violation $\downarrow$	Peak Climate Violation $\downarrow$	Economic Cost $\downarrow$	Service-risk Cost $\downarrow$	Recovery Cost $\downarrow$
Ridge-VARX	0.8310	0.8053	1.0737	0.3940	0.2689	0.1105	0.3105	0.0363	0.3818	4.108	4.402	3.669
DLinear-Action	0.8541	0.8313	1.2742	0.3834	0.2601	0.8416	0.3201	0.0376	0.3995	4.295	6.196	4.107
PatchTST-Action	0.8481	0.8250	1.2708	0.3836	0.2451	0.8384	0.3232	0.0401	0.4444	4.376	6.461	4.390
iTransformer-Action	0.9099	0.8722	1.3994	0.3843	0.2518	0.8329	0.3258	0.0380	0.3829	4.288	5.821	4.046
TFT-Action	0.8250	0.8019	1.1022	0.3147	0.2657	0.0824	0.2946	0.0250	0.2674	3.892	4.247	3.868

Appendix

Table 11: Closed-loop planning results across the four domains. The first metric for each domain is the primary objective reported in the main paper, followed by two complementary operating metrics. Scores are comparable across methods within a domain but not across domains.

Transition	Spearman $\rho$	Kendall $\tau_{b}$	Reversals $\downarrow$
Prediction $\rightarrow$ Effect	0.763	0.643	17.8%
Effect $\rightarrow$ Decision	0.514	0.412	28.4%

Appendix

Table 12: Alignment between adjacent evaluation levels, macro-averaged across the four domains. Higher rank correlation and lower reversal rate indicate stronger agreement in model ordering.

Panel of Figure 4 — Figure 4: Downstream penalty from selecting the best method at the preceding evaluation level. For each test history, panel (a) compares the Effect NMAE of the prediction-best method with that of the effect-best method, while panel (b) compares the normalized regret of the effect-best method with that of the regret-best method. Method selection in this analysis uses the realized test outcome and is therefore intended only as a diagnostic of cross-level alignment.

Metric	Ridge	DLinear	PatchTST	iTransformer	TFT	RSSM	MTS3	ActTime
Spearman $\rho$	0.6103	0.4985	0.4838	0.5117	0.7857	0.7581	0.7620	0.8270
Kendall $\tau_{b}$	0.5105	0.4025	0.3890	0.4129	0.6817	0.6486	0.6522	0.7272
Pairwise accuracy	0.7472	0.6881	0.6807	0.6913	0.8361	0.8213	0.8233	0.8624

Appendix

Table 13: Candidate-action ranking fidelity across decision objectives. Results are macro-averaged over the 12 domain-objective combinations. Higher is better. Best and second-best results are shown in bold and underlined, respectively.

Domain	Variant	Factual MAE $\downarrow$	Effect NMAE $\downarrow$	Macro Regret $\downarrow$	Online Cost $\downarrow$
CityLearn	Full	0.2510	0.0688	0.2931	0.8323
	Simple Action Concatenation	0.2518	0.0856	0.2808	0.8394
	w/o State Correction	0.3260	0.1516	0.3547	0.8565
	Shared State Across Variables	0.6957	0.6521	0.4984	0.8730
	w/o Action Conditioning	0.4457	1.0000	1.9871	0.8667
SUMO	Full	0.1107	0.5154	0.0247	0.3024

Appendix

Table 14: Per-domain absolute results for the controlled-dynamics ablations summarized in Table 4 . Full denotes the matched reference from the same controlled-ablation suite. Offline results report Macro Regret. Online objectives are domain-specific and are therefore comparable only across variants within the same domain. All metrics are lower-is-better.

Domain	Factual MAE $\downarrow$	Effect NMAE $\downarrow$	Macro Regret $\downarrow$	Online Cost $\downarrow$
CityLearn	0.2486 / 0.2476	0.0725 / 0.0703	0.2798 / 0.2784	0.8317 / 0.8335
SUMO	0.1076 / 0.1100	0.4825 / 0.4355	0.0221 / 0.0207	0.3036 / 0.3097
GreenLight	0.0498 / 0.0544	0.2091 / 0.2158	0.1397 / 0.1440	0.2944 / 0.2955
Inventory	0.0790 / 0.0811	0.2244 / 0.2248	0.1563 / 0.1523	3.8739 / 3.8945

Appendix

Table 15: Paired analysis of the pretrained temporal prior. Each entry reports Full / w/o EIDOS Prior. The two variants share the same Stage-A controlled core and differ only in the Stage-B prior adapter. Lower is better.

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A time series world model (TSWM) predicts a controlled system's state from its observed history and planned actions and exogenous inputs. Current approaches build forecasters with actions as covariates, trained and evaluated on prediction error under the executed plan. Yet world models compare unexecuted plans, but their responses to changed plans remain untested. We ask which design choices matter and whether accurate forecasters respond to changed plans as real systems do. We address both with a formalization and benchmark. The formalization separates state, actions and exogenous inputs, distinguishes continuous, mode and event actions, and introduces mechanism consistency, a metric built on declared action-state relations with known directions, such as a vasopressor raising blood pressure: it checks whether shifting an action moves the forecast in the declared direction. The benchmark consolidates eight public datasets with real actions from engineered infrastructure and clinical care, varying prediction space, plan fusion and plan encoding across seven backbones and five seeds. First, a frozen latent prediction space lowers MAE by 9.9% over observation space and gated output fusion lowers it by 12.7% over input concatenation on average, with both improving all eight datasets; temporal plan encoding changes average MAE by at most 2.2%. Second, prediction error and mechanism consistency diverge: the lowest-error configuration is at or below chance in consistency on four of five datasets with declared mechanisms, and no design choice avoids this. Finally, directional supervision, a loss penalizing the wrong-signed part of the response to a shifted action, significantly raises consistency on penalized mechanisms with no change in MAE. Together they give TSWMs a recipe: a frozen latent space and output-side fusion for accuracy, and a training objective for mechanism consistency.

Abstract

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