4,434 research outputs found
Deep Bilevel Learning
We present a novel regularization approach to train neural networks that
enjoys better generalization and test error than standard stochastic gradient
descent. Our approach is based on the principles of cross-validation, where a
validation set is used to limit the model overfitting. We formulate such
principles as a bilevel optimization problem. This formulation allows us to
define the optimization of a cost on the validation set subject to another
optimization on the training set. The overfitting is controlled by introducing
weights on each mini-batch in the training set and by choosing their values so
that they minimize the error on the validation set. In practice, these weights
define mini-batch learning rates in a gradient descent update equation that
favor gradients with better generalization capabilities. Because of its
simplicity, this approach can be integrated with other regularization methods
and training schemes. We evaluate extensively our proposed algorithm on several
neural network architectures and datasets, and find that it consistently
improves the generalization of the model, especially when labels are noisy.Comment: ECCV 201
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Using EPECs to model bilevel games in restructured electricity markets with locational prices
CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context
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