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Optimistic Algorithms for Adaptive Estimation of the Average Treatment Effect
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Proposes OPTrack, an optimistic adaptive allocation algorithm for ATE estimation with AIPW that plays the feasible allocation closest to 1/2 under a confidence sequence for the Neyman allocation, achieving logarithmic Neyman regret.
Problem
Adaptive estimation of the average treatment effect with finite-sample guarantees, where prior adaptive methods either are asymptotic, use suboptimal IPW estimators, or incur linear Neyman regret.
Approach
Use the AIPW (A2IPW) estimator and an optimism principle: play the allocation closest to 1/2 among those consistent with a confidence sequence for the Neyman allocation, and define Neyman regret against the minimum variance over all estimator-allocation pairs, yielding logarithmic regret.
Key results
- OPTrack outperforms ClipSDT with roughly 10-15% lower normalized MSE for small T across six Bernoulli instances averaged over 500,000 simulations.
- OPTrack achieves Neyman regret of order tilde-O(Delta_sigma^-2 + (1/underline-pi*)^2 log T) with high probability, whereas ClipSMT and ClipOGD are shown to have linear Neyman regret under the stronger definition.
- OPTrack is competitive with and sometimes outperforms the sequential reward-estimation oracle.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use optimistic policy tracking: select the feasible Neyman allocation closest to 1/2, with adaptive AIPW reward estimates | Adaptive ATE estimation · Bernoulli ATE simulations, six problem instances; small T | normalized MSE (T · MSE): 10-15 percent improvement | Helped |
| Use optimistic policy tracking instead of clipping-based allocation tracking | Adaptive ATE estimation · Bernoulli ATE simulations, six problem instances | normalized MSE (T · MSE) | Helped |
| Use optimistic policy tracking instead of reward estimation oracle allocation | Adaptive ATE estimation · Some problem instances with moderate Neyman allocation | normalized MSE (T · MSE) | Mixed |
| Use optimistic policy tracking instead of clipping-based allocation tracking | Adaptive ATE estimation · Bernoulli ATE simulations, larger T | normalized MSE (T · MSE) | No clear effect |
| Use ClipSMT or ClipOGD rather than an estimator-and-allocation method that attains the minimum variance | Adaptive ATE estimation · Adaptive ATE estimation | Neyman regret: linear Neyman regret | Hurt |
Surprising findings
- Under the stronger Neyman regret definition, prior clipping-based methods (ClipSMT, ClipOGD) have linear regret, and the paper argues Neyman loss is asymmetric so under-exploration is costlier than over-exploration.
- OPTrack sometimes outperforms the reward-estimation oracle because its extra early exploration yields better reward estimates.
Limitations
- Analysis restricted to two arms and no covariates; reward estimation uses simple sample means.
- Multi-arm extension would add a factor K to the T-dependent term according to the authors.
- Experiments limited to simulated Bernoulli instances with a fixed treatment mean.
Experimental setup
Benchmarks: simulated Bernoulli bandit instances (6 problem instances, T from 100 to 2000)
Metrics: normalized MSE (T * MSE) Neyman regret
Baselines: ClipSDT Reward estimation oracle (Neyman allocation with sequentially estimated reward) Neyman allocation oracle with true reward
Builds on: A2IPW ClipSDT ClipSMT ClipOGD
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