Learning Energy Networks with Generalized Fenchel-Young Losses
This work addresses a key bottleneck in training energy networks for machine learning practitioners, offering a more efficient method, though it is incremental as it builds on existing conjugate function concepts.
The paper tackles the challenge of training energy-based models by proposing generalized Fenchel-Young losses, which avoid the need for argmin/argmax differentiation in gradient computation, and demonstrates their effectiveness on multilabel classification and imitation learning tasks with efficient performance.
Energy-based models, a.k.a. energy networks, perform inference by optimizing an energy function, typically parametrized by a neural network. This allows one to capture potentially complex relationships between inputs and outputs. To learn the parameters of the energy function, the solution to that optimization problem is typically fed into a loss function. The key challenge for training energy networks lies in computing loss gradients, as this typically requires argmin/argmax differentiation. In this paper, building upon a generalized notion of conjugate function, which replaces the usual bilinear pairing with a general energy function, we propose generalized Fenchel-Young losses, a natural loss construction for learning energy networks. Our losses enjoy many desirable properties and their gradients can be computed efficiently without argmin/argmax differentiation. We also prove the calibration of their excess risk in the case of linear-concave energies. We demonstrate our losses on multilabel classification and imitation learning tasks.