Mixability has been shown to be a powerful tool to obtain algorithms with optimal regret. However, the resulting methods often suffer from high computational complexity which has reduced their practical applicability. For example, in the case of multiclass logistic regression, the aggregating forecaster (Foster et al. (2018)) achieves a regret of O(log(Bn)) whereas Online Newton Step achieves O(eBlog(n)) obtaining a double exponential gain in B (a bound on the norm of comparative functions). However, this high statistical performance is at the price of a prohibitive computational complexity O(n37). In this paper, we use quadratic surrogates to make aggregating forecasters more efficient. We show that the resulting algorithm has still high statistical performance for a large class of losses. In particular, we derive an algorithm for multi-class logistic regression with a regret bounded by O(Blog(n)) and a computational complexity of only O(n4).

There is an increasing need for effective active learning algorithms that are compatible with deep neural networks. This paper motivates and revisits a classic, Fisher-based active selection objective, and proposes BAIT, a practical, tractable, and high-performing algorithm that makes it viable for use with neural models. BAIT draws inspiration from the theoretical analysis of maximum likelihood estimators (MLE) for parametric models. It selects batches of samples by optimizing a bound on the MLE error in terms of the Fisher information, which we show can be implemented efficiently at scale by exploiting linear-algebraic structure especially amenable to execution on modern hardware. Our experiments demonstrate that BAIT outperforms the previous state of the art on both classification and regression problems, and is flexible enough to be used with a variety of model architectures.

We consider the problem of variance reduction in randomized controlled trials, through the use of covariates correlated with the outcome but independent of the treatment. We propose a machine learning regression-adjusted treatment effect estimator, which we call MLRATE. MLRATE uses machine learning predictors of the outcome to reduce estimator variance. It employs cross-fitting to avoid overfitting biases, and we prove consistency and asymptotic normality under general conditions. MLRATE is robust to poor predictions from the machine learning step: if the predictions are uncorrelated with the outcomes, the estimator performs asymptotically no worse than the standard difference-in-means estimator, while if predictions are highly correlated with outcomes, the efficiency gains are large. In A/A tests, for a set of 48 outcome metrics commonly monitored in Facebook experiments the estimator has over 70% lower variance than the simple differencein-means estimator, and about 19% lower variance than the common univariate procedure which adjusts only for pre-experiment values of the outcome.

Modern machine learning systems such as deep neural networks are often highly over-parameterized so that they can fit the noisy training data exactly, yet they can still achieve small test errors in practice. In this paper, we study this "benign overfitting" phenomenon of the maximum margin classifier for linear classification problems. Specifically, we consider data generated from sub-Gaussian mixtures, and provide a tight risk bound for the maximum margin linear classifier in the over-parameterized setting. Our results precisely characterize the condition under which benign overfitting can occur in linear classification problems, and improve on previous work. They also have direct implications for over-parameterized logistic regression.

Though data augmentation has rapidly emerged as a key tool for optimization in modern machine learning, a clear picture of how augmentation schedules affect optimization and interact with optimization hyperparameters such as learning rate is nascent.

Bandit algorithms are increasingly used in real-world sequential decision-making problems. Associated with this is an increased desire to be able to use the resulting datasets to answer scientific questions like: Did one type of ad lead to more purchases? In which contexts is a mobile health intervention effective? However, classical statistical approaches fail to provide valid confidence intervals when used with data collected with bandit algorithms. Alternative methods have recently been developed for simple models (e.g., comparison of means). Yet there is a lack of general methods for conducting statistical inference using more complex models on data collected with (contextual) bandit algorithms; for example, current methods cannot be used for valid inference on parameters in a logistic regression model for a binary reward. In this work, we develop theory justifying the use of M-estimators--which includes estimators based on empirical risk minimization as well as maximum likelihood--on data collected with adaptive algorithms, including (contextual) bandit algorithms. Specifically, we show that M-estimators, modified with particular adaptive weights, can be used to construct asymptotically valid confidence regions for a variety of inferential targets.

Figure S1: Estimated Networks 1 & 3 from linear factor models of DS (Top) and Granger causality (Bottom) for simulated data experiment. Each panel shows a grid of DS or Granger causality (GC) features associated with the indicated network estimate. Within each grid, a plot corresponds to signal that is being transmitted from the channel listed on the left to the channel listed at the top. See Figure 1 for a description of the true networks. Each subplot represents the DS from the region listed on the left to the region listed on top. Power spectra are reasonable to model using a linear factor model because they satisfy Definition 1 under reasonable assumptions. We will use Scc(ω) to refer to the spectral power of the signal vc(t) at frequency ω, and vc(ω) to refer to the frequency domain representation of vc(t) at ω.