Learning Deployable Causal Action Geometry under Temporal Non-Stationarity

Changjian Liu; Tianyu Wang; Yuwei Xu; Xiaoxuan Deng; Zhilin Zhang; Yong Gao; Chuan Yu; Jian Xu

cs.LGOct 12, 2026

Learning Deployable Causal Action Geometry under Temporal Non-Stationarity

Authors: Changjian Liu, Tianyu Wang, Yuwei Xu, Xiaoxuan Deng, Zhilin Zhang, Yong Gao, Chuan Yu, Jian Xu,

Organizations: Institute of Remote Sensing and Geographic Information System, School of Earth and Space Sciences, Peking University, Beijing, China · Beijing Key Laboratory of Spatio-temporal Perception and Urban Resilience · Taobao & Tmall Group of Alibaba, Beijing, China · The Chinese University of Hong Kong, Shenzhen, China ·

Abstract

Learning a response law for continuous decisions from observational time series is central to many real-world decision systems, yet temporal non-stationarity poses a fundamental challenge: as outcomes drift over time, naively pooled models can conflate action effects with shifting baselines and even reverse action rankings. Even when the one-step response is identifiable, unrestricted cross-time generalization remains fundamentally ill-posed. We therefore seek the part of the response that remains stable for decisions even when outcome levels do not. We propose deployable causal action geometry: the action-response shape that remains after anchoring away action-independent level shifts on a selected link scale and profiling out positive amplitude variation. Building on this target, we develop a two-stage orthogonal estimator that first obtains cross-fitted pilot estimates of anchored responses and then performs honest profiled selection over link, representation, and shape classes. The resulting estimator admits oracle guarantees for the restricted target and, under approximate persistence, produces decision rules that remain near optimal in future periods. Experiments on synthetic data and Dominick's support the proposed target and its transfer behavior. In a randomized Taobao A/B test, the deployed system improves GMV and purchase counts by $1.16\%$ and $1.70\%$ .

Figures & tables

Figure 1: Target mismatch under drift. Pooled data under non-stationary environments compares confounded temporal mixtures, leading to action ranking reversal despite good historical fit.

Figure 2: From drifting responses to deployable action geometry.

Panel of Figure 3 — Figure 3: Synthetic evidence. Top: link recovery in the exact regimes. Bottom: future-period SIMSE and regret.

Regime	Conf.	Ours	Fixed-correct	Pooled
$R1$	1.0	$0.169{\pm}0.011$ / $0.065{\pm}0.005$	$0.164{\pm}0.004$ / $0.065{\pm}0.005$	$0.265{\pm}0.005$ / $0.388{\pm}0.080$
	1.5	$0.154{\pm}0.011$ / $0.094{\pm}0.007$	$0.149{\pm}0.004$ / $0.094{\pm}0.007$	$0.259{\pm}0.006$ / $0.422{\pm}0.083$
	2.0	$0.151{\pm}0.016$ / $0.102{\pm}0.006$	$0.140{\pm}0.003$ / $0.101{\pm}0.006$	$0.252{\pm}0.005$ / $0.330{\pm}0.035$
$R2$	1.0	$0.008{\pm}0.001$ / $0.011{\pm}0.004$	$0.009{\pm}0.001$ / $0.010{\pm}0.004$	$0.139{\pm}0.008$ / $0.189{\pm}0.018$
	1.5	$0.008{\pm}0.003$ / $0.083{\pm}0.029$	$0.007{\pm}0.001$ / $0.083{\pm}0.029$	$0.169{\pm}0.007$ / $0.220{\pm}0.009$
	2.0	$0.009{\pm}0.004$ / $0.131{\pm}0.033$	$0.006{\pm}0.000$ / $0.136{\pm}0.036$	$0.172{\pm}0.006$ / $0.220{\pm}0.014$

Table 1: Future-period deployment. Each cell reports SIMSE / regret. Fixed-correct denotes the regime-matched fixed link: raw in

R1

and log in

R2

Method	RMAE $\downarrow$	MAPE $\downarrow$	Stability $\downarrow$	DR Policy Value Index $\uparrow$
Logged / behavior	–	–	–	100.00
NPM	0.176	18.27	–	121.72
VCNet	0.385	48.85	0.452	116.09
Causal Transformer	0.174	17.35	0.566	107.18
Pooled predictive	0.337	44.69	0.503	89.43
Time-aware pooled	0.496	57.91	0.433	72.96

Table 2: Offline evaluation.

Figure 4: Real-world diagnostics and deployment. (a) temporal drift. (b) future profile favors the log link while revealing heterogeneity. (c) Online A/B testing shows positive lift.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Term	Standard interpretation	Role in our framework
Link function $\ell_{k}$	Monotone response scale	Defines the scale on which action-independent temporal variation can be removed. The main candidates are the identity and log links.
Anchored response $\Delta_{k,t}(h,a)$	Reference-action contrast	$\ell_{k}\{m_{t}(h,a)\}-\ell_{k}\{m_{t}(h,a_{0})\}$ . Anchoring removes an action-independent offset while preserving action rankings.
Positive amplitude $s_{t}(h)$	Nuisance scale factor	Captures period- and history-specific changes in the magnitude of the anchored response. It is profiled out when comparing candidate geometries.
Action geometry $\rho(u(h),a)$	Normalized conditional action-response shape	The decision-relevant shape remaining after anchoring and positive-scale profiling; it determines the action ranking through $\arg\max_{a}\rho(u(h),a)$ .
Deployable causal action geometry	Decision-sufficient response equivalence class	An anchored action-response shape considered modulo linked-scale offsets and positive rescaling, restricted to the chosen link, representation, and shape classes.
Profiled geometry loss	Nuisance-amplitude-profiled discrepancy	Measures how well one shared action geometry explains period-specific anchored responses after optimally rescaling their amplitudes.

Appendix

Table 3: Terminology and standard interpretations.

\hat{\Delta}_{0,T_{i},i}^{(m)}(u)=\hat{m}(u,H_{i},a^{(m)})-\hat{m}(u,H_{i},a_{0}),

Appendix

Algorithm 1 Selection and optional honest refit for deployable action geometry

Experiment	Regimes	Purpose	Reported evidence
Link recovery	$R1,R2$	recover identity/log links	Figure 3 (a,b), Tab. 5
Future deployment	$R1,R2$	improve future decisions	Figure 3 (c,d), Tab. 1
Orthogonal ablation	$R1,R2$	nuisance robustness	Tab. 6
Approximate drift	$R3$	persistence violation	Fig. 6
No stable geometry	$R4$	structural failure	Fig. 6
Overlap stress	$R1,R2$	support degradation	Fig. 7

Appendix

Table 4: Synthetic experiment roadmap.

Regime	LinkAcc	ReprAcc	Ours SIMSE	Fixed-correct SIMSE	Fixed-wrong SIMSE
$R1$	$0.786\pm 0.178$	$0.352\pm 0.200$	$0.181\pm 0.019$	$0.160\pm 0.006$	$0.259\pm 0.003$
$R2$	$0.833\pm 0.148$	$0.195\pm 0.162$	$0.011\pm 0.002$	$0.012\pm 0.002$	$0.0140\pm 0.004$

Appendix

Table 5: Exact-regime recovery summary. Fixed-correct denotes raw in

R1

and log in

R2

; Fixed-wrong uses the other link.

Figure 5: Full exact-regime sweep. Heatmaps over sample size and confounding strength for $R1$ and $R2$ . Panels show link selection accuracy and future regret.

R1
Regime / Misspec.	Method	SIMSE $\downarrow$	Regret $\downarrow$	Action MAE $\downarrow$
none	Ours	$0.1732\pm 0.0173$	$\mathbf{0.0669\pm 0.0088}$	$\mathbf{0.1205\pm 0.0072}$
	Plug-in	$\mathbf{0.1697\pm 0.0163}$	$0.2438\pm 0.0492$	$0.2446\pm 0.0249$
outcome	Ours	$0.1737\pm 0.0173$	$\mathbf{0.0683\pm 0.0095}$	$\mathbf{0.1231\pm 0.0075}$
	Plug-in	$\mathbf{0.1689\pm 0.0174}$	$0.1583\pm 0.0196$	$0.1920\pm 0.0148$
treatment	Ours	$0.1779\pm 0.0165$	$\mathbf{0.0710\pm 0.0050}$	$\mathbf{0.1250\pm 0.0046}$

Appendix

Table 6: Post-selection estimator ablation under nuisance misspecification.

Selection $\to$ refit	$R1$ regret $\downarrow$	$R2$ regret $\downarrow$
$O\to O$	0.0754	0.1220
$P\to O$	0.0754	0.1220
$O\to P$	0.1292	0.1444
$P\to P$	0.1292	0.1445
$PP-OO$	0.0538 [0.0505, 0.0569]	0.0225 [0.0092, 0.0422]

Appendix

Table 7: End-to-end orthogonalization ablation. Mean dense-grid regret under outcome-model misspecification over 30 paired runs using the full representation library.

Figure 6: Boundary diagnostics. Left: approximate persistence violation in $R3$ as $\epsilon_{\rm drift}$ increases. Right: no-stable-geometry stress in $R4$ as shape drift increases.

$\epsilon_{\mathrm{drift}}$	$\operatorname{Rel}\xi_{\infty}$	Oracle-geometry regret
0.00	0.000	0.0000
0.05	0.027	0.0004
0.10	0.055	0.0018
0.20	0.114	0.0095
0.30	0.179	0.0242

Appendix

Table 8: Controlled persistence-violation sweep in

R3

. Relative persistence violation and the regret of the oracle-geometry policy as action-dependent drift increases.

Figure 8: Grid and anchor sensitivity. Top: sensitivity to the Stage-II action grid. Bottom: sensitivity to the anchor $a_{0}$ with the data-generating process and raw-response oracle fixed.

Method	NRegret	Difference	Paired 95% CI
Given-link reference	0.1384	$-0.00008$	[ $-0.00025$ , 0.00008]
Ours	0.1385	—	—
Plug-in selector	0.1412	0.00269	[0.00160, 0.00378]
Fixed identity	0.1416	0.00309	[0.00205, 0.00413]
Fixed log	0.1422	0.00368	[0.00291, 0.00445]

Appendix

Table 9: Link selection under transport shift. Lower NRegret is better. Paired differences are method minus Ours; a positive interval excluding zero favors Ours.

Method	A	M	V
Ours	$\mathbf{0.123}\;(0.007)$	$\mathbf{0.063}\;(0.003)$	$\mathbf{0.075}\;(0.003)$
Pooled	$0.259\;(0.008)$	$0.072\;(0.005)$	$0.089\;(0.004)$
Time-aware pooled	$0.248\;(0.008)$	$0.067\;(0.004)$	$0.091\;(0.005)$
VCNet	$0.761\;(0.015)$	$0.730\;(0.012)$	$0.697\;(0.009)$
Causal Transformer	$0.772\;(0.013)$	$0.731\;(0.012)$	$0.726\;(0.009)$

Appendix

Table 10: Semi-synthetic evaluation on Dominick’s. Each entry reports mean true future NRegret (reported uncertainty in parentheses); lower is better. A and M denote exact additive and log-linked persistence. V averages over four levels of action-dependent shape drift.

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