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Counterfactual Realizability
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Formalizes realizability of counterfactual (Layer 3) distributions via physical experiments, gives a complete graphical algorithm (CTF-REALIZE) for deciding it, and shows counterfactual randomization yields better fairness constraints and an optimal realizable bandit strategy.
Problem
Which Layer 3 (counterfactual) distributions can be sampled directly by physical experimentation given the constraint that a unit cannot undergo the same mechanism twice, beyond the known ETT case.
Approach
Defines counterfactual randomization (ctf-Rand) that fixes a variable as perceived by a subset of its children while leaving its natural value intact, and gives a complete topological-order algorithm that checks for conflicting necessary conditions to decide realizability of an L3 query.
Key results
- In the bandit example, the optimal L3 strategy achieves avg. reward 0.80, versus 0.75 for the ETT baseline, 0.70 for naive L2 randomization, and 0.65 for the behavioral policy.
- Classifiers trained on the L2 fairness proxy show mu_ctf > 0.05 for nearly half of 1000 simulations, while classifiers trained on the L3 counterfactual measure nearly always meet the fairness requirement.
- The paper proves CTF-REALIZE is correct and complete, with O(kn^2) time complexity, and proves the L3 strategy pi_opt is optimal among realizable strategies in the MAB template.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use naive randomization instead of following the behavioral policy | Multi-arm bandit strategy · Example 3 multi-arm bandit | Avg. Reward: 0.65 -> 0.7 | Helped |
| Use the ETT counterfactual strategy instead of naive randomization | Multi-arm bandit strategy · Example 3 multi-arm bandit | Avg. Reward: 0.7 -> 0.75 | Helped |
| Use the optimal L3 strategy instead of the ETT baseline strategy | Multi-arm bandit strategy · Example 3 multi-arm bandit | Avg. Reward: 0.75 -> 0.80 | Helped |
| Train classifiers using the interventional fairness measures rather than the counterfactual fairness measure | Causal fairness classifiers · Causal fairness simulation | Counterfactual fairness score (μ_ctf): > 5% | Hurt |
| Train classifiers directly using the counterfactual fairness measure | Causal fairness classifiers · Causal fairness simulation | Fairness requirement satisfaction | Helped |
| Use the optimal L3 strategy rather than the ETT baseline strategy | Thompson Sampling bandit algorithms · Example 3 online simulation | Cumulative regret | Helped |
| Use the optimal L3 strategy rather than naive L2 strategies | Thompson Sampling bandit algorithms · Example 3 online simulation | Optimal arm probability (OAP) | Helped |
Surprising findings
- Distributions such as P(Y_x, X, Y) (probability of sufficiency) are not realizable even with maximal experimental capabilities, contrary to the belief that counterfactuals are untestable.
- A fairness measure based only on interventional (L2) quantities can approve classifiers that still show counterfactual discrimination in about half of simulations.
Limitations
- Requires a correct causal graph as input to the algorithm.
- Counterfactual randomization may not be feasible in many real settings; the framework depends on the available physical actions.
- Optimality result is proven only for the MAB template, not sequential or Markov decision processes.
Experimental setup
Metrics: cumulative regret optimal arm probability average reward fairness measure mu_ctf distribution
Baselines: Behavioral policy (L1) Naive randomization (L2) ETT baseline strategy (L3) UCB EXP3 Thompson Sampling
Builds on: Bareinboim, Forney & Pearl (2015) counterfactual randomization Pearl Causal Hierarchy Thompson Sampling
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