This paper proposes a novel approach for constructing effective personalized policies when the observed data lacks counter-factual information, is biased and possesses many features. The approach is applicable in a wide variety of settings from healthcare to advertising to education to finance. These settings have in common that the decision maker can observe, for each previous instance, an array of features of the instance, the action taken in that instance, and the reward realized—but not the rewards of actions that were not taken: the counterfactual information. Learning in such settings is made even more difficult because the observed data is typically biased by the existing policy (that generated the data) and because the array of features that might affect the reward in a particular instance—and hence should be taken into account in deciding on an action in each particular instance—is often vast. The approach presented here estimates propensity scores for the observed data, infers counterfactuals, identifies a (relatively small) number of features that are (most) relevant for each possible action and instance, and prescribes a policy to be followed. Comparison of the proposed algorithm against state-of-art algorithms on actual datasets demonstrates that the proposed algorithm achieves a significant improvement in performance.
We should also note two papers that were written after the current paper was originally submitted. The work of @cite_28 extends the earlier work of @cite_4 @cite_5 to non-linear policies. Our own (preliminary) work @cite_9 propose a different approach for learning a representation function and a policy. Unlike the present paper, our more recent work uses a loss function that embodies both a policy loss (similar to, but slightly different than, the policy loss used in the present paper) and a domain loss (which quantifies the divergence between the logging policy and the uniform policy under the representation function). The advantage of these changes is that they make it possible to learn the representation function and the policy in an end-to-end fashion.
@cite_28 @cite_5 @cite_9 @cite_4
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Matching images and sentences demands a fine understanding of both modalities. In this paper, we propose a new system to discriminatively embed the image and text to a shared visual-textual space. In this field, most existing works apply the ranking loss to pull the positive image text pairs close and push the negative pairs apart from each other. However, directly deploying the ranking loss is hard for network learning, since it starts from the two heterogeneous features to build inter-modal relationship. To address this problem, we propose the instance loss which explicitly considers the intra-modal data distribution. It is based on an unsupervised assumption that each image text group can be viewed as a class. So the network can learn the fine granularity from every image text group. The experiment shows that the instance loss offers better weight initialization for the ranking loss, so that more discriminative embeddings can be learned. Besides, existing works usually apply the off-the-shelf features, i.e., word2vec and fixed visual feature. So in a minor contribution, this paper constructs an end-to-end dual-path convolutional network to learn the image and text representations. End-to-end learning allows the system to directly learn from the data and fully utilize the supervision. On two generic retrieval datasets (Flickr30k and MSCOCO), experiments demonstrate that our method yields competitive accuracy compared to state-of-the-art methods. Moreover, in language based person retrieval, we improve the state of the art by a large margin. The code has been made publicly available. We study losses for binary classification and class probability estimation and extend the understanding of them from margin losses to general composite losses which are the composition of a proper loss with a link function. We characterise when margin losses can be proper composite losses, explicitly show how to determine a symmetric loss in full from half of one of its partial losses, introduce an intrinsic parametrisation of composite binary losses and give a complete characterisation of the relationship between proper losses and "classification calibrated" losses. We also consider the question of the "best" surrogate binary loss. We introduce a precise notion of "best" and show there exist situations where two convex surrogate losses are incommensurable. We provide a complete explicit characterisation of the convexity of composite binary losses in terms of the link function and the weight function associated with the proper loss which make up the composite loss. This characterisation suggests new ways of "surrogate tuning" as well as providing an explicit characterisation of when Bregman divergences on the unit interval are convex in their second argument. Finally, in an appendix we present some new algorithm-independent results on the relationship between properness, convexity and robustness to misclassification noise for binary losses and show that all convex proper losses are non-robust to misclassification noise. Problems of data classification can be studied in the framework of regularization theory as ill-posed problems. In this framework, loss functions play an important role in the application of regularization theory to classification. In this paper, we review some important convex loss functions, including hinge loss, square loss, modified square loss, exponential loss, logistic regression loss, as well as some non-convex loss functions, such as sigmoid loss, @math -loss, ramp loss, normalized sigmoid loss, and the loss function of 2 layer neural network. Based on the analysis of these loss functions, we propose a new differentiable non-convex loss function, called smoothed 0-1 loss function, which is a natural approximation of the 0-1 loss function. To compare the performance of different loss functions, we propose two binary classification algorithms for binary classification, one for convex loss functions, the other for non-convex loss functions. A set of experiments are launched on several binary data sets from the UCI repository. The results show that the proposed smoothed 0-1 loss function is robust, especially for those noisy data sets with many outliers. We present @math -loss, @math , a tunable loss function for binary classification that bridges log-loss ( @math ) and @math - @math loss ( @math ). We prove that @math -loss has an equivalent margin-based form and is classification-calibrated, two desirable properties for a good surrogate loss function for the ideal yet intractable @math - @math loss. For logistic regression-based classification, we provide an upper bound on the difference between the empirical and expected risk for @math -loss by exploiting its Lipschitzianity along with recent results on the landscape features of empirical risk functions. Finally, we show that @math -loss with @math performs better than log-loss on MNIST for logistic regression.