We study the problem of fitting task-specific learning rate schedules from the perspective of hyperparameter optimization. This allows us to explicitly search for schedules that achieve good generalization. We describe the structure of the gradient of a validation error w.r.t. the learning rate, the hypergradient, and based on this we introduce a novel online algorithm. Research in this direction is vast (see Hutter et al. (2019) for an overview) and includes model-based (Snoek et al., 2012; Hutter et al., 2015), model-free (Bergstra & Bengio, 2012; Hansen, 2016), and gradient-based (Domke, 2012; Maclaurin et al., 2015) approaches. Problem (1) can be in principle solved by any HPO technique.

In many machine learning scenarios, looking for the best classifier that fits a particular dataset can be very costly in terms of time and resources. Moreover, it can require deep knowledge of the specific domain. We propose a new technique which does not require profound expertise in the domain and avoids the commonly used strategy of hyper-parameter tuning and model selection. Our method is an innovative ensemble technique that uses voting rules over a set of randomly-generated classifiers. Given a new input sample, we interpret the output of each classifier as a ranking over the set of possible classes. We then aggregate these output rankings using a voting rule, which treats them as preferences over the classes. We show that our approach obtains good results compared to the state-of-the-art, both providing a theoretical analysis and an empirical evaluation of the approach on several datasets.

Developing learning methods which do not discriminate subgroups in the population is a central goal of algorithmic fairness. One way to reach this goal is by modifying the data representation in order to meet certain fairness constraints. In this work we measure fairness according to demographic parity. This requires the probability of the possible model decisions to be independent of the sensitive information. We argue that the goal of imposing demographic parity can be substantially facilitated within a multitask learning setting. We leverage task similarities by encouraging a shared fair representation across the tasks via low rank matrix factorization. We derive learning bounds establishing that the learned representation transfers well to novel tasks both in terms of prediction performance and fairness metrics. We present experiments on three real world datasets, showing that the proposed method outperforms state-of-the-art approaches by a significant margin.

We tackle the problem of algorithmic fairness, where the goal is to avoid the unfairly influence of sensitive information, in the general context of regression with possible continuous sensitive attributes. We extend the framework of fair empirical risk minimization to this general scenario, covering in this way the whole standard supervised learning setting. Our generalized fairness measure reduces to well known notions of fairness available in literature. We derive learning guarantees for our method, that imply in particular its statistical consistency, both in terms of the risk and the fairness measure. We then specialize our approach to kernel methods and propose a convex fair estimator in that setting. We test the estimator on a commonly used benchmark dataset (Communities and Crime) and on a new dataset collected at the University of Genova, containing the information of the academic career of five thousand students. The latter dataset provides a challenging real case scenario of unfair behaviour of standard regression methods that benefits from our methodology. The experimental results show that our estimator is effective at mitigating the trade-off between accuracy and fairness requirements.

We address the problem of algorithmic fairness: ensuring that sensitive information does not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint into the learning problem. It encourages the conditional risk of the learned classifier to be approximately constant with respect to the sensitive variable. We derive both risk and fairness bounds that support the statistical consistency of our methodology. We specify our approach to kernel methods and observe that the fairness requirement implies an orthogonality constraint which can be easily added to these methods. We further observe that for linear models the constraint translates into a simple data preprocessing step. Experiments indicate that the method is empirically effective and performs favorably against state-of-the-art approaches.

We address the problem of algorithmic fairness: ensuring that sensitive information does not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint into the learning problem. It encourages the conditional risk of the learned classifier to be approximately constant with respect to the sensitive variable. We derive both risk and fairness bounds that support the statistical consistency of our methodology. We specify our approach to kernel methods and observe that the fairness requirement implies an orthogonality constraint which can be easily added to these methods. We further observe that for linear models the constraint translates into a simple data preprocessing step. Experiments indicate that the method is empirically effective and performs favorably against state-of-the-art approaches.

A central goal of algorithmic fairness is to reduce bias in automated decision making. An unavoidable tension exists between accuracy gains obtained by using sensitive information (e.g., gender or ethnic group) as part of a statistical model, and any commitment to protect these characteristics. Often, due to biases present in the data, using the sensitive information in the functional form of a classifier improves classification accuracy. In this paper we show how it is possible to get the best of both worlds: optimize model accuracy and fairness without explicitly using the sensitive feature in the functional form of the model, thereby treating different individuals equally. Our method is based on two key ideas. On the one hand, we propose to use Multitask Learning (MTL), enhanced with fairness constraints, to jointly learn group specific classifiers that leverage information between sensitive groups. On the other hand, since learning group specific models might not be permitted, we propose to first predict the sensitive features by any learning method and then to use the predicted sensitive feature to train MTL with fairness constraints. This enables us to tackle fairness with a three-pronged approach, that is, by increasing accuracy on each group, enforcing measures of fairness during training, and protecting sensitive information during testing. Experimental results on two real datasets support our proposal, showing substantial improvements in both accuracy and fairness.

We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint into the learning problem. It encourages the conditional risk of the learned classifier to be approximately constant with respect to the sensitive variable. We derive both risk and fairness bounds that support the statistical consistency of our approach. We specify our approach to kernel methods and observe that the fairness requirement implies an orthogonality constraint which can be easily added to these methods. We further observe that for linear models the constraint translates into a simple data preprocessing step. Experiments indicate that the method is empirically effective and performs favorably against state-of-the-art approaches.

We consider a class of a nested optimization problems involving inner and outer objectives. We observe that by taking into explicit account the optimization dynamics for the inner objective it is possible to derive a general framework that unifies gradient-based hyperparameter optimization and meta-learning (or learning-to-learn). Depending on the specific setting, the variables of the outer objective take either the meaning of hyperparameters in a supervised learning problem or parameters of a meta-learner. We show that some recently proposed methods in the latter setting can be instantiated in our framework and tackled with the same gradient-based algorithms. Finally, we discuss possible design patterns for learning-to-learn and present encouraging preliminary experiments for few-shot learning.

We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic gradient descent. These procedures mirror two methods of computing gradients for recurrent neural networks and have different trade-offs in terms of running time and space requirements. Our formulation of the reverse-mode procedure is linked to previous work by Maclaurin et al. [2015] but does not require reversible dynamics. The forward-mode procedure is suitable for real-time hyperparameter updates, which may significantly speed up hyperparameter optimization on large datasets. We present experiments on data cleaning and on learning task interactions. We also present one large-scale experiment where the use of previous gradient-based methods would be prohibitive.