On the Limitations of General Purpose Domain Generalisation Methods
Keywords: Domain Generalisation, Excess Risk, Empirical Risk Minimisation, Minimax, Rademacher Complexity
Abstract: The Domain Generalisation (DG) problem setting requires a model trained on a set of data distributions (domains) to generalise to new distributions. Despite a huge amount of empirical study, previous DG methods fail to substantially outperform empirical risk minimisation on rigorous DG benchmarks. Motivated by this, we analyse the DG problem from a learning theoretic perspective and *characterise in which situations DG will succeed or fail*. Specifically, we derive upper bounds on the excess risk of ERM and lower bounds on the minimax excess risk, for three settings with different restrictions on how the domains may differ. In the most unconstrained setting, we show that all learning algorithms converge slowly with respect to number of training domains, potentially explaining the lack of algorithmic progress in this area. We also consider constrained settings including limiting the pairwise domain distances as measured by a broad class of integral probability metrics, and constraining all domains to have the same underlying support. In these constrained cases, DG algorithms can converge more rapidly. Notably, for all three settings, the we demonstrate that ERM has an optimal rate of convergence towards the best possible model. Our analysis guides practitioners interested in knowing when cross-domain generalisation might be reliable, and suggests strategies for optimising the performance of ERM in each setting.
Primary Area: learning theory
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Submission Number: 7644
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