Information-Directed Sampling for Causal Bandits
Introduces a Bayesian framework for contextual causal bandits that incorporates non-manipulable variables observed before and after interventions. Develops causal variants of Thompson Sampling and Information-Directed Sampling (IDS) that leverage shared causal mechanisms to update reward estimates across different interventions. Establishes entropy-dependent sublinear Bayesian regret bounds for Thompson Sampling and derives a rigorous regret bound for IDS that accounts for Monte Carlo approximat
Analysis
TL;DR
- Introduces a Bayesian framework for contextual causal bandits that incorporates non-manipulable variables observed before and after interventions.
- Develops causal variants of Thompson Sampling and Information-Directed Sampling (IDS) that leverage shared causal mechanisms to update reward estimates across different interventions.
- Establishes entropy-dependent sublinear Bayesian regret bounds for Thompson Sampling and derives a rigorous regret bound for IDS that accounts for Monte Carlo approximation errors.
- Demonstrates through synthetic experiments that the proposed methods significantly outperform existing causal and non-causal baselines by more effectively exploiting information sharing.
Why It Matters
This research addresses a critical gap in causal reinforcement learning by handling scenarios where certain influential variables cannot be directly manipulated, which is common in real-world applications like healthcare and economics. By providing theoretical guarantees for Bayesian regret and practical algorithms that utilize observational data from non-manipulable variables, it enables more efficient decision-making in complex causal systems. This allows practitioners to accelerate the identification of optimal interventions while rigorously managing uncertainty.
Technical Details
- Problem Setting: Contextual causal bandits with non-manipulable variables, assuming a known causal graph without latent confounding. Context variables are observed pre-intervention, and additional variables are observed post-intervention.
- Bayesian Formulation: The unknown parameters are defined as the conditional probability tables of the observational distribution, allowing observations from one intervention to inform reward estimates for others via shared causal structures.
- Algorithmic Contributions: Implementation of causal Thompson Sampling and Information-Directed Sampling (IDS). The IDS variant includes high-probability confidence bounds for its Monte Carlo estimates of expected regret and information gain.
- Theoretical Guarantees: Proves an entropy-dependent sublinear Bayesian regret bound for Thompson Sampling. For IDS, derives a regret bound that explicitly quantifies the error introduced by Monte Carlo approximation, recovering standard sublinear rates when approximations are exact.
Industry Insight
- Organizations dealing with constrained intervention environments (e.g., clinical trials where certain treatments are unethical or impossible) can use these methods to maximize learning efficiency from observational data.
- The explicit handling of Monte Carlo approximation errors in the IDS regret bound provides a robust theoretical foundation for deploying these algorithms in safety-critical applications where performance guarantees are essential.
- Future work should focus on extending these techniques to settings with latent confounders or unknown causal graphs, which would broaden applicability to more realistic industrial scenarios.
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