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Domain Generalisation via Imprecise Learning
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Proposes Imprecise Domain Generalisation, where learners train an augmented hypothesis over a continuum of CVaR risk levels via Imprecise Risk Optimisation so operators can pick their generalisation preference at deployment.
Problem
Out-of-distribution generalisation requires choosing a generalisation notion (average-case, worst-case, or interpolation), but this choice is made by model operators who are institutionally separated from learners and may not be known at training time.
Approach
Learners stay imprecise by optimising a scalarised objective over a distribution Q on CVaR risk levels, adaptively choosing Q via a multiple-gradient-descent-style C-Pareto improvement step; the learned augmented hypothesis takes the risk level lambda as input so the operator specifies lambda at deployment.
Key results
- On synthetic data, IL achieves maximum regret 0.867 versus 1.971 for the best fixed-lambda-free precise learner with uniform lambda_lr and 6.177 for lambda_lr=0.
- On CMNIST, IRO attains maximum regret 29.7, the lowest among compared methods, vs. 31.7 for Inf-Task and 46.9 for GrpDRO.
- On UCI Bike Rentals, IL achieves maximum regret 0.42, below PL-f with lambda_lr=1 (0.66) and INF-TASK-h (0.72).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use IRO instead of fixed-preference PL-f | Domain generalisation · Synthetic data | maximum regret: 1.971 -> 0.867; 6.177 -> 0.867; 2.010 -> 0.867 | Helped |
| Use IRO instead of prior-based PL-h | Domain generalisation · Synthetic data | maximum regret: 1.79 -> 0.56; 1.57 -> 0.56; 0.935 -> 0.56 | Helped |
| Use IRO instead of PL-f or Inf-Task-h | Domain generalisation · Bike Rentals | maximum regret: 4.81 -> 0.42; 0.66 -> 0.42; 0.72 -> 0.42 | Helped |
| Use IRO instead of Inf-Task | CMNIST · CMNIST test environments | regret: 31.7 -> 29.7 | Helped |
| Use IRO instead of Inf-Task | CMNIST · CMNIST e=0.0, e=0.5, e=1.0 | accuracy: 96.0 -> 95.8; 63.1 -> 69.5; 68.3 -> 70.3 | Mixed |
Surprising findings
- IL surpasses the ideal scenario at higher risk levels on the real-world Bike Rentals task, which the authors attribute to CVaR discarding data from lower-risk environments.
Limitations
- Assumes operators know their risk aversion level lambda, which may be hard to articulate.
- Imprecise learning is more computationally intensive than precise learning.
- Only CVaR is explored as the aggregation function.
Experimental setup
Datasets: CMNIST UCI Bike Sharing synthetic linear regression domains
Benchmarks: CMNIST UCI Bike Sharing synthetic linear regression
Metrics: maximum regret accuracy aggregated risk
Baselines: ERM GrpDRO SD IGA IRM VREx EQRM INF-TASK Oracle
Builds on: MGDA conditional value-at-risk invariant risk minimisation group DRO EQRM
Closest papers by meaning
- Rethinking the Evaluation Protocol of Domain Generalization (CVPR 2024 · similarity 0.86)
- Out-of-Variable Generalisation for Discriminative Models (ICLR 2024 · similarity 0.85)
- Lost Domain Generalization Is a Natural Consequence of Lack of Training Domains (AAAI 2024 · similarity 0.85)
- Towards Robust Out-of-Distribution Generalization Bounds via Sharpness (ICLR 2024 · similarity 0.85)
- In Search of Forgotten Domain Generalization (ICLR 2025 · similarity 0.84)
- OOD-Chameleon: Is Algorithm Selection for OOD Generalization Learnable? (ICML 2025 · similarity 0.84)
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