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AI Research
arXiv CS.AI·May 25·8 min read
Robust Counterfactual Inference in Markov Decision Processes
TL;DR
Counterfactual inference in MDPs (Markov Decision Processes—sequential decision models) typically assumes one fixed causal model, but multiple causal models can match observed data while producing different predictions. Lally et al. developed a non-parametric method computing tight probability bounds across all compatible causal models using closed-form expressions instead of expensive optimization.
✦ Why It Matters
Engineers can now make safer sequential decisions under causal model uncertainty without prohibitive computational costs.
Key Takeaways
- Use interval bounds instead of fixed causal models to capture model uncertainty in decision problems.
- Closed-form solutions eliminate exponential optimization complexity, enabling scalability to realistic problem sizes.
- Worst-case reward optimization provides safety guarantees when true causal model is unknown.
- Method applies to any MDP where multiple causal models match observational data.
Full Summary
Markov Decision Processes (MDPs) are mathematical frameworks for modeling sequential decision-making under uncertainty. Counterfactual inference answers "what if" questions about alternative actions or outcomes.
Existing methods lock in a single causal model to make counterfactuals mathematically identifiable, but in practice many causal models align with observed data while predicting different counterfactual outcomes. This paper identifies that limitation and proposes a non-parametric approach computing interval bounds on counterfactual transition probabilities—the likelihood of moving between states—across all compatible causal models simultaneously.
Rather than solving exponentially-sized optimization problems, the method derives closed-form mathematical expressions for these bounds, enabling efficient computation on realistic MDPs. The authors then construct an interval counterfactual MDP and identify robust policies that optimize worst-case expected rewards given the uncertain probability ranges.
Empirical evaluation on case studies demonstrates improved robustness compared to existing single-model methods.