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Distributionally Robust Policy Learning under Concept Drifts
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Proposes a doubly-robust estimator and a KL-DRO policy learning algorithm for robust offline policy learning when only the conditional outcome distribution shifts (concept drift), with a Hamming-entropy-integral regret bound of order n^{-1/2} and a matching lower bound.
Problem
Offline policy learning that is robust to worst-case distribution shift in the conditional outcome distribution Y|X (concept drift) with covariate distribution fixed, avoiding the over-conservatism of joint-shift DRO methods and handling general covariate spaces.
Approach
Separate the distribution shift into a KL-bounded conditional outcome shift, derive a dual (ERM-form) representation of the worst-case value per covariate, and debias it with a doubly-robust estimator that stays root-n consistent even when nuisance optimizers converge slowly; policy learning maximizes the estimated value over a policy class, with per-action ERM to avoid per-policy nuisance fitting
Key results
- On simulated data with delta=0.05, the proposed policy has robust value about 0.227-0.231 versus 0.055-0.066 for SNLN across n=7500 to 19500 (50 seeds).
- At delta=0.2 the proposed policy achieves 0.078-0.083 versus 0.018-0.022 for SNLN.
- Worst-case reward on perturbed KL-sphere test sets at delta=0.1 is 0.207-0.217 for the proposed method versus 0.188-0.202 for SNLN.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use concept-drift robust policy learning rather than the SNLN joint-shift benchmark | Policy learning on the simulated dataset, δ=0.05 · Simulated dataset | robust policy value: 0.0664±0.003 -> 0.2310±0.001 | Helped |
| Use concept-drift robust policy learning rather than the SNLN joint-shift benchmark | Policy learning on the simulated dataset, δ=0.1 · Simulated dataset | robust policy value: 0.0616±0.004 -> 0.1678±0.002 | Helped |
| Use concept-drift robust policy learning rather than the SNLN joint-shift benchmark | Policy learning on the simulated dataset, δ=0.2 · Simulated dataset | robust policy value: 0.0219±0.003 -> 0.0831±0.002 | Helped |
| Use concept-drift robust policy learning rather than the SNLN joint-shift benchmark | Policy learning under concept drift, worst-case KL-sphere test · Simulated dataset, δ=0.1 | worst-case policy reward: 0.2020±0.004 -> 0.2167±0.003 | Helped |
| Increase the uncertainty radius δ | Algorithm LN and SNLN · Simulated dataset | robust policy value | Hurt |
Limitations
- Choice of the robustness radius delta strongly affects performance and has no data-driven selection in the paper.
- Extension to continuous action spaces is left open.
- Requires assumptions on smoothness and convergence rates of nuisance optimizers (slower-than-root-n rates for some nuisances).
Experimental setup
Datasets: simulated linear-boundary Gaussian reward data French unemployment assistance randomized experiment dataset
Benchmarks: simulated linear boundary dataset French unemployment assistance experiment
Metrics: empirical robust policy value worst-case policy reward on KL-sphere perturbed test sets
Baselines: SNLN
Builds on: SNLN (Si et al. distributionally robust policy learning) double machine learning policytree
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