The minimization of loss functions is the heart and soul of Machine Learning. In this paper, we propose an off-the-shelf optimization approach that can minimize virtually any non-differentiable and non-decomposable loss function (e.g. Miss-classification Rate, AUC, F1, Jaccard Index, Mathew Correlation Coefficient, etc.) seamlessly. Our strategy learns smooth relaxation versions of the true losses by approximating them through a surrogate neural network. The proposed loss networks are set-wise models which are invariant to the order of mini-batch instances. Ultimately, the surrogate losses are learned jointly with the prediction model via bilevel optimization. Empirical results on multiple datasets with diverse real-life loss functions compared with state-of-the-art baselines demonstrate the efficiency of learning surrogate losses.
Instead of relying on explicit surrogates, another research direction handles non-convex losses by means of the method @cite_5 , which minimizes a surrogate loss by embedding the true loss as a correction term. This method was recently extended to optimize neural networks @cite_0 . It assumes the loss can be decomposed into per-instance sub-losses and the authors derived an explicit decomposition of the average precision @cite_0 . Unfortunately, per-instance dis-aggregations are not trivially feasible in other cases (e.g. F1), making the direct loss optimization technique an impractical off-the-shelf option.
@cite_0 @cite_5
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Supervised training of deep neural nets typically relies on minimizing cross-entropy. However, in many domains, we are interested in performing well on metrics specific to the application. In this paper we propose a direct loss minimization approach to train deep neural networks, which provably minimizes the application-specific loss function. This is often non-trivial, since these functions are neither smooth nor decomposable and thus are not amenable to optimization with standard gradient-based methods. We demonstrate the effectiveness of our approach in the context of maximizing average precision for ranking problems. Towards this goal, we develop a novel dynamic programming algorithm that can efficiently compute the weight updates. Our approach proves superior to a variety of baselines in the context of action classification and object detection, especially in the presence of label noise. In discriminative machine learning one is interested in training a system to optimize a certain desired measure of performance, or loss. In binary classification one typically tries to minimizes the error rate. But in structured prediction each task often has its own measure of performance such as the BLEU score in machine translation or the intersection-over-union score in PASCAL segmentation. The most common approaches to structured prediction, structural SVMs and CRFs, do not minimize the task loss: the former minimizes a surrogate loss with no guarantees for task loss and the latter minimizes log loss independent of task loss. The main contribution of this paper is a theorem stating that a certain perceptron-like learning rule, involving features vectors derived from loss-adjusted inference, directly corresponds to the gradient of task loss. We give empirical results on phonetic alignment of a standard test set from the TIMIT corpus, which surpasses all previously reported results on this problem.