End-to-end Early Classification of Time Series in Non-Stationary Environments

Aurélien Renault; Alexis Bondu; Antoine Cornuéjols; Vincent Lemaire

cs.LGAug 20, 2026

End-to-end Early Classification of Time Series in Non-Stationary Environments

Authors: Aurélien Renault, Alexis Bondu, Antoine Cornuéjols, Vincent Lemaire

Organizations: Orange Research & AgroParisTech Paris, France · Orange Research Paris, France · AgroParisTech UMR MIA-Paris Palaiseau, France

Abstract

Early Classification of Time Series (ECTS) requires making accurate decisions as early as possible in inherently online and evolving environments. Yet, most existing methods assume stationarity and rely on separable designs, where classification and triggering are optimized independently, an assumption that fundamentally limits their adaptability under drift. In this work, we challenge this paradigm and study ECTS under non-stationary conditions. We provide the first systematic comparison between separable and end-to-end approaches across controlled drifting scenarios. Building on Reinforcement Learning, we introduce DQeND, a unified architecture that jointly learns representation, classification, and triggering decisions, while remaining directly comparable to state-of-the-art separable baselines. Across a wide range of drifts, DQeND demonstrates strong robustness across various non-stationary scenarios, consistently outperforming separable baselines. An ablation study further highlights that jointly updating representation and decision modules is critical to these gains. Overall, our results indicate that end-to-end learning can offer improved adaptation capabilities for ECTS in dynamic environments, and motivate further investigation of alternatives to separable designs.

Figures & tables

Encoder	kernel sizes	$\{3,6,9,12\}$
	nb. of kernels	$\{128,64,32,16\}$
	embedding dim.	64
	time embedding dim.	2
Decision	nb. hidden layers	1
	hidden dim.	64
	activation function	tanh

Table 1. DQeND hyperparameters

Figure 2. The I_loc scenario.

Figure 3. The I_noise scenario.

Figure 4. The A_loc scenario.

Figure 5. The A_class scenario.

Panel of Figure 6 — Figure 6. Incremental drifts, deployment’s metrics, averaged over five seeds. From top to bottom: the raw cumulative cost; the hold-out AvgCost , obtained on unseen drifted data; the hold-out AvgCost original, obtained using the fixed test set from training phase. UPPERCASE approaches refers to end-to-end methods while lowercase indicates separable ones.

Panel of Figure 7 — Figure 7. Hold-out AvgCost drift: detailed performances. The figures display decomposition of the hold-out AvgCost drift into both earliness, i.e. the average proportion of the time series used, and error rate, during the deployment phase.

Panel of Figure 8 — Figure 8. Abrupt drifts, deployment’s metrics, averaged over five seeds. From top to bottom: the raw cumulative cost; the hold-out AvgCost , obtained on unseen drifted data; the hold-out AvgCost original, obtained using the fixed test set from training phase. UPPERCASE approaches refers to end-to-end methods while lowercase indicates separable ones.

Panel of Figure 9 — Figure 9. Hold-out AvgCost drift: detailed performances. The figures display decomposition of the hold-out AvgCost drift into both earliness, i.e. the average proportion of the time series used, and error rate, during the deployment phase.

	freeze encoder		freeze decision
	( a )	( b )	( a )	( b )
I_loc	$-32.42$ %	$-36.44$ %	$-36.61$ %	$-31.87$ %
I_noise	$-11.29$ %	$-4.04$ %	$-19.28$ %	$-6.63$ %
A_loc	$1.38$ %	$-0.34$ %	$-43.52$ %	$-45.30$ %
A_class	$1.32$ %	$2.14$ %	$-18.18$ %	$-4.39$ %

Table 2. ( a ): The mean percentage difference between the cumulative cost of full updated DQeND and the partially frozen version, over five random seeds. ( b ): The mean of the median percentage difference of the hold-out AvgCost drift of the full updated DQeND and partially frozen version, over five random seeds. Negative figures indicate degraded performance compared to original DQeND.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

	I_loc	I_noise	A_loc	A_class
Alert( online / freeze )	$29.02\pm 4.08$	$46.14\pm 0.3$	$31.06\pm 11$	$32.15\pm 1.27$
Alert( online / online )	$31.87\pm 5.49$	$37.92\pm 0.83$	$23.32\pm 1.88$	$30.86\pm 0.2$
DQeND	$\textbf{16.18}\pm 3.40$	$\textbf{36.2}\pm 1.04$	$\textbf{18.86}\pm 0.55$	$32.98\pm 3.88$
EARLIEST	$20.53\pm 6.54$	$43\pm 3.37$	$19.90\pm 0.79$	$32.44\pm 5.88$
ELECTS	$17.33\pm 1.81$	$38.63\pm 1.98$	$29.98\pm 12.06$	$\textbf{25.79}\pm 3.52$

Appendix

Table 3. The mean cumulative cost and standard deviation, over five random seeds. Bold value indicates the best average performing method.

	I_loc	I_noise	A_loc	A_class
Alert( online / freeze )	$0.3\pm 0.04$	$0.46\pm 0.003$	$0.31\pm 0.11$	$0.32\pm 0.01$
Alert( online / online )	$0.31\pm 0.07$	$0.38\pm 0.009$	$0.23\pm 0.02$	$0.31\pm 0.002$
DQeND	$\textbf{0.16}\pm 0.03$	$\textbf{0.36}\pm 0.01$	$\textbf{0.19}\pm 0.01$	$0.33\pm 0.04$
EARLIEST	$0.2\pm 0.06$	$0.43\pm 0.03$	$0.2\pm 0.01$	$0.32\pm 0.06$
ELECTS	$0.17\pm 0.02$	$0.39\pm 0.02$	$0.3\pm 0.12$	$\textbf{0.26}\pm 0.04$

Appendix

Table 4. The mean hold-out AvgCost drift and standard deviation, over all the deployment steps and five random seeds. Bold value indicates the best average performing method.

	I_loc	I_noise	A_loc	A_class
Alert( online / freeze )	$0.31\pm 0.02$	$0.31\pm 0.04$	$0.21\pm 0.04$	$\textbf{0.37}\pm 0.03$
Alert( online / online )	$0.33\pm 0.06$	$0.33\pm 0.02$	$0.18\pm 0.02$	$0.37\pm 0.003$
DQeND	$\textbf{0.09}\pm 0.04$	$\textbf{0.31}\pm 0.01$	$\textbf{0.11}\pm 0.02$	$0.4\pm 0.04$
EARLIEST	$0.27\pm 0.07$	$0.36\pm 0.01$	$0.11\pm 0.07$	$0.51\pm 0.01$
ELECTS	$0.14\pm 0.07$	$0.33\pm 0.01$	$0.19\pm 0.1$	$0.48\pm 0.02$

Appendix

Table 5. The mean hold-out AvgCost original and standard deviation, over all the deployment steps and five random seeds. Bold value indicates the best average performing method.

	Training	Deployment ( per batch )		Total $\downarrow$
	Fit	Inference	Update
ELECTS	31.89	0.026	0.05	39.22
EARLIEST	119.25	0.23	0.09	138.98
Alert ( online / online )	(78.02, 46.55)	2.39	2.45	612.75
Alert ( retrain / retrain )	(78.02, 46.55)	2.71	3.59	759.86
DQeND	248.74	2.90	5.75	1124.31

Appendix

Table 6. Computation times (in s. ). The deployment are displayed on a per batch basis. The total time accounts for the all 100 deployment steps. The fit time of the Alert-based methods are decomposed over ( classifier fit time, trigger fit time).

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TimEE: End-to-end Time Series Classification via In-Context Learning

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Time series classification (TSC) is dominated by a two-stage paradigm: train a feature encoder -- either from scratch on the target dataset or via pretraining on large corpora -- and then fit a task-specific classifier on top. While effective, this decoupling optimizes representation learning independently of the classification objective, requires per-dataset training, and prevents the model from exploiting label information during inference. We introduce TimEE, a 4.5M-parameter foundation model for end-to-end TSC via in-context learning. Given a labeled support set and a query time series, TimEE directly outputs a predicted class distribution in a single forward pass with no per-dataset training required. Following the prior-data fitted network (PFN) framework, TimEE is meta-trained exclusively on synthetic TSC tasks, where each task contains time series with distinct class identities arising from structured distributional shifts in the generative process. Despite seeing no real time series during pre-training, TimEE ranks first in ROC AUC (and third on accuracy) on the UCR benchmark among all compared methods, which include both foundation models and supervised deep learning baselines. To our knowledge, TimEE is the first purely synthetic-pretrained model to reach state-of-the-art performance on the UCR benchmark. These results establish end-to-end ICL with synthetic priors as a compelling, largely unexplored direction for TSC, with scaling, prior design, and richer generation mechanisms as natural avenues for improvement. Code is publicly available at http://github.com/automl/timee.

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