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Gradual Domain Adaptation via Manifold-Constrained Distributionally Robust Optimization
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Proposes DRODA, a manifold-constrained Wasserstein DRO method with adaptive radius for gradual domain adaptation, with theory showing error propagation can be eliminated for Gaussian mixtures and expandable distributions, plus a small rotating-MNIST experiment.
Problem
Gradual domain adaptation: adapting a classifier from a labeled source through a sequence of gradually shifting unlabeled distributions, where naive self-training errors can grow exponentially with sequence length T.
Approach
Run Wasserstein DRO on pseudo-labeled previous distribution with an adaptive radius, restricting the adversarial ball to a known manifold of distributions (e.g., Gaussian mixtures with margins or expandable distributions); introduces a "compatibility" function g_lambda that characterizes error propagation dynamics.
Key results
- On rotating MNIST (rotations 0 to 60 degrees), the proposed method outperforms GDA by about 8 percentage points on the last domain D4.
- Theory: for Gaussian mixtures with margin, the compatibility bound gives g(eta) <= exp(-L^2/(18 sigma^2)) with no error propagation over T steps.
- Theory: unconstrained DRO compatibility is lower bounded by Omega(exp(-L^2/(2sigma^2)) + sqrt(eta exp(-L^2/(2sigma^2)))), showing potential error propagation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use manifold-constrained DRO for gradual domain adaptation instead of GDA | Rotating MNIST · Rotating MNIST D4 | accuracy: 8 percent | Helped |
Surprising findings
- Without the manifold constraint on the Wasserstein ball, the error bound can grow with sequence length, so the manifold restriction is claimed to be essential.
Limitations
- Experiments are limited to a single rotating-MNIST setup; the expandable-distribution theory is not validated empirically beyond this.
- Theoretical results for the Gaussian case assume known manifold and linear classifiers; the 0-1 loss and label-swap issues require algorithmic modifications.
Experimental setup
Datasets: MNIST (rotating MNIST variant)
Benchmarks: Rotating MNIST
Metrics: accuracy
Baselines: GDA (gradual domain adaptation, Kumar et al.)
Builds on: gradual self-training (Kumar et al.) Wasserstein DRO strong duality
Closest papers by meaning
- Understanding Gradual Domain Adaptation: Improved Analysis, Optimal Path and Beyond (ICML 2022 · similarity 0.89)
- Understanding Self-Training for Gradual Domain Adaptation (ICML 2020 · similarity 0.88)
- Domain Adaptation with Adaptive $f$-Divergence: Tighter Variational Representation and Generalization Bounds (ICML 2026 · similarity 0.87)
- Minimax Statistical Learning with Wasserstein distances (NeurIPS 2018 · similarity 0.87)
- On $f$-Divergence Principled Domain Adaptation: An Improved Framework (NeurIPS 2024 · similarity 0.86)
- Robust Domain Generalization under Divergent Marginal and Conditional Distributions (NeurIPS 2026 · similarity 0.86)
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