Learning Optimal Redistribution Mechanisms through Neural NetworksWe consider a setting where $p$ public resources are to be allocated among $n$ competing and strategic agents so as to maximize social welfare (the objects should be allocated to those who value them the most). This is called allocative efficiency (AE). We need the agents to report their valuations for obtaining these resources, truthfully referred to as dominant strategy incentive compatibility (DSIC). We use auction-based mechanisms to achieve AE and DSIC yet budget balance cannot be ensured, due to Green-Laffont Impossibility Theorem. That is, the net transfer of money cannot be zero. This problem has been addressed by designing a redistribution mechanism so as to ensure a minimum surplus of money as well as AE and DSIC. The objective could be to minimize surplus in expectation or in the worst case and these $p$ objects could be homogeneous or heterogeneous. Designing redistribution mechanisms which perform well in expectation becomes analytically challenging for heterogeneous settings. In this paper, we take a completely different, data-driven approach. We train a neural network to determine an optimal redistribution mechanism based on given settings with both the objectives, optimal in expectation and optimal in the worst case. We also propose a loss function to train a neural network to optimize worst case. We design neural networks with the underlying rebate functions being linear as well as nonlinear in terms of bids of the agents. Our networks' performances are same as the theoretical guarantees for the cases where it has been solved. We observe that a neural network based redistribution mechanism for homogeneous settings which uses nonlinear rebate functions outperforms linear rebate functions when the objective is optimal in expectation. Our approach also yields an optimal in expectation redistribution mechanism for heterogeneous settings.

Generative Adversarial Networks (GANs): What it can generate and What it cannot?Why are Generative Adversarial Networks (GANs) so popular? What is the purpose of designing GANs? Can we justify functioning of GANs theoretically? How are the theoretical guarantees? Are there any shortcomings? With the popularity of GANs, the researchers across the globe have been perplexed by these questions. In the last year (2017), a plethora of research papers attempted to answer the above questions. In this article, we put in our best efforts to compare and contrast different results and put forth a summary of theoretical contributions about GANs with focus on image/visual applications. Our main aim is to highlight the primary issues related to GANs that each of these papers examine. Besides we provide insight into how each of the discussed articles solve the concerned problems. We expect this summary paper to give a bird's eye view to a person wishing to understand the theory behind GANs.

A Neural Network Framework for Fair ClassifierMachine learning models are extensively being used in decision making, especially for prediction tasks. These models could be biased or unfair towards a specific sensitive group either of a specific race, gender or age. Researchers have put efforts into characterizing a particular definition of fairness and enforcing them into the models. In this work, mainly we are concerned with the following three definitions, Disparate Impact, Demographic Parity and Equalized Odds. Researchers have shown that Equalized Odds cannot be satisfied in calibrated classifiers unless the classifier is perfect. Hence the primary challenge is to ensure a degree of fairness while guaranteeing as much accuracy as possible. Fairness constraints are complex and need not be convex. Incorporating them into a machine learning algorithm is a significant challenge. Hence, many researchers have tried to come up with a surrogate loss which is convex in order to build fair classifiers. Besides, certain papers try to build fair representations by preprocessing the data, irrespective of the classifier used. Such methods, not only require a lot of unrealistic assumptions but also require human engineered analytical solutions to build a machine learning model. We instead propose an automated solution which is generalizable over any fairness constraint. We use a neural network which is trained on batches and directly enforces the fairness constraint as the loss function without modifying it further. We have also experimented with other complex performance measures such as H-mean loss, Q-mean-loss, F-measure; without the need for any surrogate loss functions. Our experiments prove that the network achieves similar performance as state of the art. Thus, one can just plug-in appropriate loss function as per required fairness constraint and performance measure of the classifier and train a neural network to achieve that.

poster.pdf

visual_comparison.pdf