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Training neural network classifiers on datasets with label noise poses a risk
of overfitting them to the noisy labels. To address this issue, researchers
have explored alternative loss functions that aim to be more robust. However,
many of these alternatives are heuristic in nature and still vulnerable to
overfitting or underfitting. In this work, we propose a more direct approach to
tackling overfitting caused by label noise. We observe that the presence of
label noise implies a lower bound on the noisy generalised risk. Building upon
this observation, we propose imposing a lower bound on the empirical risk
during training to mitigate overfitting. Our main contribution is providing
theoretical results that yield explicit, easily computable bounds on the
minimum achievable noisy risk for different loss functions. We empirically
demonstrate that using these bounds significantly enhances robustness in
various settings, with virtually no additional computational cost.
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