An Identifiable Cost-Aware Causal Decision-Making Framework Using Counterfactual Reasoning

TL;DR

This work tackles decision-making under anomalies by introducing MiCCD, a framework that combines causal graphs with identifiable counterfactual reasoning and cost-aware optimization. A surrogate model—grounded in anomaly-pattern clustering and a variational autoencoder with embedded causal structure—facilitates counterfactual estimation, while a SLSQP-based optimizer finds the minimum-cost intervention under a PN feasibility constraint. The authors provide theoretical identifiability results for clustering and latent noises, and demonstrate robust improvements in cost efficiency, F1-score, and ranking (nDCG@k) on synthetic and real-world datasets. MiCCD supports personalized, cost-aware interventions across complex systems, highlighting its practical relevance to AI operations, maintenance, and beyond.

Abstract

Decision making under abnormal conditions is a critical process that involves evaluating the current state and determining the optimal action to restore the system to a normal state at an acceptable cost. However, in such scenarios, existing decision-making frameworks highly rely on reinforcement learning or root cause analysis, resulting in them frequently neglecting the cost of the actions or failing to incorporate causal mechanisms adequately. By relaxing the existing causal decision framework to solve the necessary cause, we propose a minimum-cost causal decision (MiCCD) framework via counterfactual reasoning to address the above challenges. Emphasis is placed on making counterfactual reasoning processes identifiable in the presence of a large amount of mixed anomaly data, as well as finding the optimal intervention state in a continuous decision space. Specifically, it formulates a surrogate model based on causal graphs, using abnormal pattern clustering labels as supervisory signals. This enables the approximation of the structural causal model among the variables and lays a foundation for identifiable counterfactual reasoning. With the causal structure approximated, we then established an optimization model based on counterfactual estimation. The Sequential Least Squares Programming (SLSQP) algorithm is further employed to optimize intervention strategies while taking costs into account. Experimental evaluations on both synthetic and real-world datasets reveal that MiCCD outperforms conventional methods across multiple metrics, including F1-score, cost efficiency, and ranking quality(nDCG@k values), thus validating its efficacy and broad applicability.

Figures (7)

• Figure 1: A toy decision-making example. If a data center ($Y$) loses power due to an earthquake ($Z_1$) and relies on backup power ($X_2$), RCA may recommend repairing the power station (the root cause ($X_1$)), but this is not feasible because the backup power ($X_2$) will be exhausted before the repair is complete. A feasible, lower-cost solution—such as increasing the backup generator’s fuel supply ($X_3$)—requires reasoning beyond root cause identification, incorporating cost and counterfactual evaluation. Here, solid nodes are the observed variables and dashed nodes are the potential noise. Grey fills in nodes represent anomalies, and green represents the optimal decision when anomalies occur.
• Figure 2: The MiCCD framework comprises two components: (a) a surrogate model that approximates the SCM by recovering noise variables and predicting outcomes to enable counterfactual reasoning, and (b) an optimization method to identify the minimum-cost intervention based on counterfactual reasoning. In the surrogate model, abnormal pattern labels are first obtained through clustering, and are subsequently incorporated into subgraph samples-- comprising the current variable and its parent variables—to recover the corresponding noise variables. These noise variables, along with the parent variables, are then fed into the decoder to reconstruct the current variable, or the counterfactual variable if a parent variable is subject to intervention. In the optimization phase, the encoder and decoder are employed to estimate counterfactual outcomes for candidate intervention vectors generated by the optimizer. Through iterative refinement, the framework determines the cost-minimizing intervention.
• Figure 3: An incomplete causal relationship diagram after removing hidden variables summarized by some field experts.
• Figure 4: Causes of PM2.5 in Beijing before APEC
• Figure 5: Comparison of Results under Varying Experimental Settings. The performance of different methods is evaluated under three varying settings: the number of nodes (left), the sparsity level of the causal graph (middle), and the strength of causal edge weights (right). In each subfigure, the top row reports the normalized decision cost, while the bottom row presents the corresponding F1-score. It can be observed that the proposed method consistently achieves the lowest intervention cost and yields superior F1-scores across all settings, indicating both higher decision efficiency and greater diagnostic accuracy compared to baseline approaches.

Theorems & Definitions (3)

• Definition 1: Structural Causal Models
• Lemma 1: Sufficient Condition for Identifiability Based on Weakly Separable Variables. tahmasebi2018identifiability
• Lemma 2: Identifiability of Latent Noise Variables khemakhem2020variational