The Minimal Search Space for Conditional Causal Bandits

2025-02-10

AI Summary

This paper addresses the identification of the minimal sufficient intervention set in conditional causal bandits: given a causal graph, how to determine the smallest subset of nodes such that conditioning interventions on their observed values achieve optimal expected reward. We first derive a graph-theoretic characterization of nodes necessarily included in any optimal conditional intervention. Based on this characterization, we design an exact linear-time algorithm with time complexity O(|V| + |E|). Our method integrates causal graph reasoning, conditional intervention modeling, and efficient graph traversal, circumventing exhaustive search and provably minimizing the bandit action space dimension. Experiments demonstrate that our algorithm significantly accelerates convergence of standard bandit policies, and its effectiveness and scalability are validated across multiple benchmark causal graphs.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Heuristic Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Causal knowledge can be used to support decision-making problems. This has been recognized in the causal bandits literature, where a causal (multi-armed) bandit is characterized by a causal graphical model and a target variable. The arms are then interventions on the causal model, and rewards are samples of the target variable. Causal bandits were originally studied with a focus on hard interventions. We focus instead on cases where the arms are conditional interventions, which more accurately model many real-world decision-making problems by allowing the value of the intervened variable to be chosen based on the observed values of other variables. This paper presents a graphical characterization of the minimal set of nodes guaranteed to contain the optimal conditional intervention, which maximizes the expected reward. We then propose an efficient algorithm with a time complexity of $O(|V| + |E|)$ to identify this minimal set of nodes. We prove that the graphical characterization and the proposed algorithm are correct. Finally, we empirically demonstrate that our algorithm significantly prunes the search space and substantially accelerates convergence rates when integrated into standard multi-armed bandit algorithms.

Problem

• Identifies minimal node set for optimal conditional interventions
• Proposes efficient algorithm for conditional causal bandits
• Accelerates convergence by pruning search space

Innovation

• Conditional interventions in causal bandits
• Graphical minimal node set identification
• Efficient algorithm with O(|V| + |E|) complexity