Online Identification of IT Systems through Active Causal Learning

Kim Hammar; Rolf Stadler

REVIEW 3 major objections 5 minor 78 references

Online Identification of IT Systems through Active Causal Learning

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper presents the first principled method for online, data-driven identification of an IT system as a causal model, proving that the Gaussian-process estimator is Bayes-optimal and that rollout-chosen interventions improve on passive

desk verdict Solid engineering paper with correct but standard theory; the empirical validation has a load-bearing circularity when it compares its online GP to a 'ground truth' fitted with the same GP estimator. read the letter →

arxiv 2509.02130 v2 pith:XPXLA46R submitted 2025-09-02 cs.LG cs.DCcs.NI

Kim Hammar , Rolf Stadler This is my paper

classification cs.LGcs.DCcs.NI

keywords activecausallearningGaussianprocessregressionstructuralmodelsonlinesystemidentificationrolloutpolicyBayesianoptimalityITsystemsinterventioncost

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Operating a complex IT system automatically — scaling resources, diagnosing faults, stopping intrusions — requires a model of how changes in controllable variables (CPU allocation, routing, blocking, load) cause changes in service metrics (response times). The paper claims such a causal model can be learned online from data, without a human expert, by alternating measurement with targeted interventions that probe parts of the operating region the system never visits on its own. The learner is a set of independent Gaussian process regressors, one per causal function; the paper proves the posterior mean is the best possible estimate given the data (Bayes-optimal), that it converges to the true functions with enough data, and that the rollout-chosen intervention policy is guaranteed to be no worse than passive monitoring. On a live microservice testbed with a known causal graph, the active policy brings the estimation loss down from about 2.8 million to 84 thousand, where passive monitoring barely moves it, and the model re-adapts after the system changes mid-run. If the claims hold, model-based automation of network and service management becomes a data-gathering problem rather than an expert-consulting one.

What carries the argument

The structural causal model (SCM): a known directed acyclic causal graph G over exogenous and endogenous variables, with unknown causal functions F_t, one per endogenous variable. The estimator φ(D_t) = ∏ P[f_{V_i,t} | D_t], the product of independent Gaussian process posteriors; its mean is the Bayes-optimal point estimate (Prop. 1). The rollout policy: a dynamic program with belief state b_t = φ(D_t), step cost g(b,u) = expected surrogate-loss change plus intervention cost c(u), approximated by lookahead simulation (Eqs. 11–12) with the improvement guarantee of Prop. 3. The surrogate loss L(b) is the engine: it is zero exactly when the belief is a point mass on one set of causal functions,

What would settle it

Run the online learner against a ground-truth SCM whose causal functions include a discontinuity — outside the smooth kernel's RKHS — with the graph correct: Prop. 2 predicts per-function squared error tends to zero, while the violated RKHS assumption predicts a plateau; measuring which happens settles the estimator claim. In a second test, delete one edge from the causal graph; if the estimated functions still track the true ones, the method tolerates graph misspecification, contradicting the paper's stated assumption.

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Extended reading notes

Core claim

Identifying an IT system, on the paper's terms, reduces to estimating the causal functions of a known-graph structural causal model. Each causal function has an independent Gaussian process prior; posteriors update per intervention batch, and the estimate is their product distribution φ(D_t). Prop. 1: the posterior mean minimizes expected loss among all graph-compatible models (Bayes-optimal). Prop. 2: it converges to the true functions as data grows, under an RKHS condition. Interventions are chosen by a rollout policy that trades expected surrogate-loss reduction against intervention cost; Prop. 3 guarantees it improves on the base policy. Testbed: 30 active samples track ground truth clos

Load-bearing premise

The method assumes the causal graph — the list of which variables causally depend on which — and the distribution of external factors are fixed and known; if the dependency structure changes while the system runs, the guarantees and the loss weighting no longer apply.

Editorial extensions

If this is right

Operators can keep a continuously updated causal model of their system from routine measurements plus a small number of targeted interventions, replacing expert-built, static models.
One identified model feeds forecasting, anomaly detection, root-cause analysis, automatic control, and digital-twin simulation, so the cost of learning it is amortized over many management tasks.
Bayes-optimality means that, within the model class defined by the known graph, no other estimator can achieve lower expected loss on the same data.
The rollout guarantee gives a safety property for deployment: the active policy is never worse than pure monitoring, so adopting it cannot degrade identification performance.
Consistency means the model converges to the true causal functions with sufficient data, making downstream predictions asymptotically exact under the stated regularity conditions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The paper fixes the causal graph, but its expected-loss machinery can be turned into a posterior over graphs: score each candidate graph by the same surrogate loss and let rollout pick interventions that discriminate between graph hypotheses, yielding joint structure-and-function identification — a direction the authors leave for future work.
Intervention costs are assigned per type (load emulation costs 3000, routing 1000, monitoring 1); making these costs state-dependent, e.g., higher during peak load, would change which interventions the policy selects and is directly testable on the same testbed.
Forgetting in the non-stationary scenario is handled by a fixed-size FIFO buffer of 10 samples; a Bayesian change-point detector on the GP posteriors could decide autonomously when a function has drifted, replacing the fixed forgetting schedule.
The surrogate loss weights every function by the exogenous distribution P[U]; reweighting it by a task-specific utility, such as prediction error on response time under the loads that actually occur, would tie identification directly to the operator's objective.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

What you should know: this paper does something real and useful, but its central empirical claim is weaker than the abstract suggests. The method—GP regression for causal functions, with a rollout-based intervention policy—is a sensible combination, and the proofs are fine (Prop. 1 is a textbook Bayes-optimality argument; Props. 2 and 3 are standard cited results). The testbed is a genuine microservice system, and the authors ship code and data, which counts for something. Active learning clearly beats passive monitoring at covering the operating region, and the visual difference in the illustrative example is convincing. The paper is honest about its assumptions: fixed known causal graph and known P[U], with relaxation left to future work.

The soft spot is exactly where the stress-test note lands, and I think the concern holds up. Section VII-D constructs the "true" causal functions by fitting the same GP estimator (with the same Matérn kernel, zero mean) to offline samples from the testbed. The loss curves in Fig. 17 are then one GP fit against another GP fit from the same model family. If the kernel is misspecified for the real system, both the offline "truth" and the online estimate share the same inductive bias, and the reported loss can be small while both are far from the actual behavior. There are no held-out measurements at unseen configurations, no non-GP ground truth, and no baseline like random or uniform-coverage interventions. So the quantitative claim of "accurate identification" is not actually established. The qualitative claim—that active exploration beats passive observation—is much better supported.

A few smaller issues: the "first principled method" framing overstates novelty given prior active causal learning work (e.g., Rubenstein et al. 2017), though the IT-systems application and rollout policy are new. The implementation in Scenario 2 uses a FIFO buffer, which diverges from the theory that assumes the full dataset; this is a mismatch between what is proven and what is evaluated. Hyperparameters are selected by random search, but no sensitivity analysis is reported.

Who is this for? Researchers in network/service management who want a practical tool for causal model identification, and readers interested in how rollout can be applied to active learning. It deserves a serious referee, not because the theory is deep, but because the engineering is solid and the empirical gap is fixable. The authors should add independent ground-truth measurements, compare against random or myopic intervention baselines, and report where the GP assumptions plausibly hold. My recommendation: send it to peer review, but require those changes before acceptance.

Referee Report

3 major / 5 minor

Summary. The paper proposes an online method, called active causal learning, for identifying the causal functions of a structural causal model (SCM) of an IT system, assuming the causal graph and the distribution of exogenous variables are known and fixed. The method iteratively estimates the causal functions via Gaussian process regression and selects interventions through a rollout-based policy that trades off expected reduction in surrogate loss against intervention cost. The authors prove Bayes-optimality of the posterior-mean estimator (Prop. 1), consistency of the GP estimator under RKHS assumptions (Prop. 2), and a cost-improvement guarantee for rollout under exact cost-to-go and compactness assumptions (Prop. 3). They validate the method on a synthetic SCM and on a Kubernetes/Istio testbed, reporting that the active policy achieves much lower loss than passive monitoring on both stationary and non-stationary scenarios.

Significance. If the empirical claims held as stated, the paper would make a solid contribution to network/service management: it provides a clean formal formulation of the online causal identification problem, a transparent combination of GP regression and rollout, and standard but correctly applied theoretical guarantees. The authors also make code and traces available ([29]), which is a strength. The main value is the integration of existing tools—GP-based Bayesian learning and rollout—into a principled framework for causal model identification of IT systems, rather than a fundamentally new theoretical result. However, the central empirical claim that the method 'enables accurate identification of a causal system model' is currently not supported because the testbed 'ground truth' functions are themselves estimated with the same GP estimator and kernel used by the proposed method. This circularity substantially weakens the experimental evidence and needs to be fixed before the paper can be accepted.

major comments (3)

[§VII-D, Figs. 14–17] The testbed evaluation is circular. Section VII-D constructs the ground-truth functions F_t by collecting >30,000 offline samples and then 'use[s] this data and the estimator φ [cf. (6)] to learn the causal functions F_t'—the same GP estimator, with the same Matérn kernel (13) and zero mean, used by the online method. Consequently, the loss L(ˆF_t, F_t) reported in Fig. 17 measures the difference between an online GP posterior (30 active samples) and an offline GP posterior (30,000 samples) under the same prior family. If the kernel is misspecified for the actual IT system (e.g., non-smooth or discontinuous dependencies), both estimates share the same inductive bias and the loss can be small even when both are far from the true system. The paper provides no direct measurements at held-out configurations, no non-GP ground truth, and no baseline such as random or uniform-coverage intervent
[§V-B, Prop. 3 vs. Eq. (11)–(12), App. C] The theoretical guarantee for the intervention policy does not cover the implemented algorithm. Proposition 3 assumes an exact cost-to-go estimate (˜J_π = J_π), a compact discretized belief space, and a bounded cost function. The implementation uses Monte Carlo sampling with L=10, a terminal approximation ˜J = L(b), a FIFO buffer, and differential evolution for the minimization in (12). These approximations are not shown to satisfy the proposition's conditions, so the claim in the abstract that the method 'produces effective interventions' is only a conditional statement under idealized conditions. The experiments compare the rollout policy only to passive monitoring; they do not demonstrate that the rollout policy is competitive with random intervention selection or a myopic uncertainty-sampling baseline. Adding such baselines would also help validate that the rollout approximation beha
[§IV, Prop. 2, §XI] Several assumptions that are load-bearing for the guarantees are either unverified or acknowledged as future work but not discussed in terms of their impact. Prop. 2 requires the true causal functions to lie in the RKHS of the chosen GP kernel; this is not verifiable on the testbed, and no sensitivity analysis with respect to kernel choice is provided. In addition, Scenario 2 involves time-varying functions, so Prop. 2—stated for fixed functions—does not apply there; the FIFO buffer heuristic (Section VII-E) is not covered by any theoretical tracking guarantee. Since the abstract claims optimality and effectiveness without these caveats, the paper should either restrict the claims to the assumptions actually verified or provide an explicit discussion of how the time-varying and misspecification cases are handled.

minor comments (5)

[Eq. (11) vs. Eq. (5)] The symbol L is used both for the loss function (5) and for the number of Monte-Carlo rollouts in (11), which is confusing. Consider renaming the latter, e.g., N_rollout.
[§VI, App. C] The hardware is referred to as 'M4PRO'; use the vendor style 'M4 Pro' for consistency.
[Ref. [33]] Typo: 'Instistute' should be 'Institute'.
[§VII-D] The description '100 samples per system variable for each configuration' is ambiguous—please specify the number of configurations, the varied variables, and the total count per variable.
[Fig. 12] The caption says 'upper plots show the ground truth causal functions for Scenario 1 and the lower plots show the ground truth causal functions for Scenario 2,' but the figure also includes several panels that are not labeled 'Scenario 1' or 'Scenario 2' individually. Make the panel grouping explicit.

Circularity Check

1 steps flagged · score 6.0 of 10

Testbed 'ground truth' causal functions are learned with the same GP estimator and kernel used by the online method, so the empirical validation reduces to comparing one GP fit to another.

fitted input called prediction [Section VII-D 'Causal Functions' (after Eq. (14), before Fig. 12); compare Eq. (6) and Eq. (13)]
"To evaluate our method, we need access to the causal functions F_t [cf. (14)] to compute the loss function L; cf. (5). To obtain these functions, we explore the (complete) operating region [cf. Def. 1] and collect100samples per system variable for each configuration of control variables we consider. This (offline) process takes several days and yields a total dataset of over30,000 measurement samples per system variable. We then use this data and the estimator φ[cf. (6)] to learn the causal functions F_t."

The 'true' causal functions F_t used as ground truth for the loss L (Eq. 5) are not measured independently; they are produced by the paper's own estimator φ (Eq. 6), instantiated with the same zero-mean Matérn kernel (Eq. 13) that the online active-learning method uses. Consequently, the loss curves in Fig. 17 and the visual comparisons in Figs. 14/15 measure distance between two posterior means from the same GP family: the offline φ-learned 'truth' and the online φ(D_t) estimate. Any misspecification of the GP prior/kernel relative to the real IT system is shared by both, so a small loss only shows that the online GP can approximate the offline GP, not that either accurately represents the actual system. No held-out direct measurements or non-GP ground truth are provided, so the abstract'

full rationale

The mathematical derivation is not circular. The estimator φ(D_t) is defined independently in Eq. (6) as a product of independent GP posteriors; Proposition 1 is a standard posterior-mean optimality argument proved in Appendix B; Proposition 2 cites an external GP-consistency theorem [14]; Proposition 3 cites Bertsekas's rollout results [16],[21],[22]. Author self-citations ([11],[18]-[20],[29]-[33]) are contextual or implementation-related and are not load-bearing for the proofs. The substantive circularity is confined to the testbed validation: Section VII-D constructs the 'ground truth' causal functions by applying the same estimator φ, with the same kernel (13), to offline data. The reported loss therefore compares two outputs of the same GP model family rather than the learned model to an independently characterized system. This makes the central empirical claim partially circular, while leaving the theoretical claims intact. Score 6 reflects one empirically load-bearing circular construction, not a circular derivation of the method itself.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The method rests on strong domain assumptions (known graph, known exogenous distribution, steady-state sampling) and several unstated hyperparameters. No new physical entities are postulated.

free parameters (7)

GP noise variance sigma_epsilon^2 = not reported
Appears in Appendix D posterior update; value is not stated, yet it controls the GP posterior and the loss.
GP covariance hyperparameters = unit variance, Matern 5/2 with unit length scale (13)
The kernel m(x)=0, k(x,x') as in (13) is chosen to encode smoothness; no length-scale or variance fitting is reported.
Discount factor gamma = not specified
Appears in objective (4) and cost-to-go (10); its value is never given.
Intervention costs c = Table 3: load 3000, routing 1000, blocking 2000, CPU 3000, passive 1
Chosen by hand to reflect relative disruption; results depend on these.
Horizons l, m and MC samples L = l=1, m=5, L=10 (Tables 1,5)
Rollout lookahead and rollout horizons set to small values; Table 1 shows substantial sensitivity.
FIFO buffer size = 10
Used in Scenario 2 to forget old data; changes the estimator from the Bayes-optimal one in Prop 1.
DE minimizer parameters = population 10, iterations 30 (Table 5)
Differential evolution settings used to approximate the minimization in (12).

assumptions (6)

domain assumption The causal graph G is known, fixed, and encodes all causal dependencies among system variables.
Stated in Section III and IV; the entire method estimates functions on this graph and does not update it.
domain assumption The distribution P[U] of exogenous variables is known and fixed.
Used to define the operating region and the weighting measure P[dx] in the loss (5); the paper says this is 'purely for ease of exposition' (Section XI) but none of the experiments relax it.
ad hoc to paper The true causal functions lie in the RKHS of the chosen GP kernel (or are well approximated by the GP prior).
Prop. 2 consistency requires the error between each f_Vi and the prior mean to be in the RKHS of k_i; this is assumed without verification for the testbed functions.
domain assumption Measurement samples are collected after the system reaches steady state under each intervention.
Section IV states samples are collected after transient effects settle; this is a practical requirement that is not validated.
ad hoc to paper Independent GP priors are placed on each causal function.
Section V-A; the product-form posterior (6) and Prop. 1 rely on independence across functions.
ad hoc to paper Rollout improvement conditions: exact cost-to-go estimation, compact operating region, bounded cost, discretized belief space.
Prop. 3 conditions are not verified in the implementation; MC estimation with L=10 and DE approximation means J~pi != J_pi in practice.

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Cite this review

Pith. "Pith review of Online Identification of IT Systems through Active Causal Learning." pith.science (2026). https://pith.science/paper/XPXLA46R

@misc{pith2026250902130,
  author       = {Pith},
  title        = {Pith review of: Online Identification of IT Systems through Active Causal Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XPXLA46R}},
  note         = {Machine review of arXiv:2509.02130}
}

read the original abstract

Identifying a causal model of an IT system is fundamental to many branches of systems engineering and operation. Such a model can be used to predict the effects of control actions, optimize operations, diagnose failures, detect intrusions, etc., which is central to achieving the longstanding goal of automating network and system management tasks. Traditionally, causal models have been designed and maintained by domain experts. This, however, proves increasingly challenging with the growing complexity and dynamism of modern IT systems. In this paper, we present the first principled method for online, data-driven identification of an IT system in the form of a causal model. The method, which we call active causal learning, estimates causal functions that capture the dependencies among system variables in an iterative fashion using Gaussian process regression based on system measurements, which are collected through a rollout-based intervention policy. We prove that this method is optimal in the Bayesian sense and that it produces effective interventions. Experimental validation on a testbed shows that our method enables accurate identification of a causal system model while inducing low interference with system operations.

Figures

Figures reproduced from arXiv: 2509.02130 by the authors.

**Figure 1.** Online identification of IT systems through active causal learning. infrastructure (e.g., the available memory), its services (e.g., the response time of a service request), and external factors (e.g., the load generated by users of the services). Knowing the causal model of an IT system allows to predict how the system will react to a control action, such as scaling the CPU allocation, or to a change in an external… view at source ↗

**Figure 2.** Comparison between data collection with and without interventions. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Specifically, each endogenous variable Vi is determined by a causal function fVi,t , which maps its parent variables in the graph to its output value. For example, a causal function may take the form R = fR,t(L), where R represents response time and L represents system load. The collection of all such functions at time t is denoted by Ft ≜ {fVi,t}Vi∈V. We consider that these functions may evolve over time and that t… view at source ↗

Figures from the paper (15 more)

**Figure 4.** Figure 4: Our iterative method for online identification of a causal model of an [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: Learned causal functions using the GP estimator φ(Dt) [cf. (6)] for the example SCM in §VI. The functions are learned based on 30 samples, i.e., |Dt| = 30; cf. (3). The lower plots show the causal functions estimated through passive learning, i.e., the functions estima…

**Figure 6.** Figure 6: The causal graph and functions of the SCM in the illustrative example. Summary of our identification method ( [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: shows the value of the loss function L [cf. (5)], which we approximate through discretization. We observe that as the number of samples |Dt| increases, the loss of the model estimated through our method (red curve) decreases rapidly. In contrast, the loss of the model …

**Figure 8.** Figure 8: Architecture of the IT system for the experimental evaluation: a cloudbased web application with a service mesh backend. System configuration. The service mesh consists of 4 physical nodes (labeled 1-4 in [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

**Figure 10.** Figure 10: Causal graph of the IT system in [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]

**Figure 11.** Figure 11: Correlation matrix for the variables in the causal model [cf. [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]

**Figure 13.** Figure 13: Causal graph for Scenario 2. D. Causal Functions To evaluate our method, we need access to the causal functions Ft [cf. (14)] to compute the loss function L ; cf. (5). To obtain these functions, we explore the (complete) operating region [cf. Def. 1] and collect 100 s…

**Figure 12.** Figure 12: Some of the causal functions in the structural causal model ( [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]

**Figure 17.** Figure 17: Loss [cf. (5)] of the functions Fˆt estimated through passive learning (blue curve) and our active learning method (red curve) when applied to Scenario 1. Curves show the mean value from evaluations with 5 random seeds; shaded areas indicate standard deviations. Passi…

**Figure 14.** Figure 14: Scenario 1: the system is stationary and the causal functions do not change. The figure shows some of the causal functions for the IT system described in §VII-A estimated using the GP estimator φ(Dt) [cf. (6)] based on 30 samples (i.e., |Dt| = 30) collected through pa…

**Figure 15.** Figure 15: Scenario 1: the system is stationary and the causal functions do not change. The figure shows learned causal functions for the IT system described in §VII-A. The functions are learned using the GP estimator φ(Dt) [cf. (6)] based on 30 samples (i.e., |Dt| = 30) collect…

**Figure 16.** Figure 16: Scenario 1: the system is stationary and the causal functions do not change. The figure shows the evolution of the causal effect E{R2 | do(B2 = b2)} based on the functions Fˆt estimated through (6) as the dataset Dt [cf. (3)] is updated using our active learning metho…

**Figure 19.** Figure 19: Loss [cf. (5)] of the functions Fˆt estimated through passive learning (blue curve) and our active learning method (red curve) when applied to Scenario 2. Curves show the mean value from evaluations with 5 random seeds; shaded areas indicate standard deviations. At ti…

**Figure 18.** Figure 18: Scenario 2: a change in the IT system occurs between time steps t = 10 and t = 11, which causes the function fR2,t to change. The dataset Dt [cf. (3)] is defined as a first-in-first-out buffer of size 10 and is updated using our active learning method with the rollout…

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