  Robust loss functions are essential for training deep neural networks with
better generalization power in the presence of noisy labels. Symmetric loss
functions are confirmed to be robust to label noise. However, the symmetric
condition is overly restrictive. In this work, we propose a new class of loss
functions, namely \textit{asymmetric loss functions}, which are robust to
learning with noisy labels for various types of noise. We investigate general
theoretical properties of asymmetric loss functions, including classification
calibration, excess risk bound, and noise tolerance. Meanwhile, we introduce
the asymmetry ratio to measure the asymmetry of a loss function. The empirical
results show that a higher ratio would provide better noise tolerance.
Moreover, we modify several commonly-used loss functions and establish the
necessary and sufficient conditions for them to be asymmetric. Experimental
results on benchmark datasets demonstrate that asymmetric loss functions can
outperform state-of-the-art methods. The code is available at
\href{https://github.com/hitcszx/ALFs}{https://github.com/hitcszx/ALFs}
