Fairness via Adversarial Attribute Neighbourhood Robust Learning

Improving fairness between privileged and less-privileged sensitive attribute groups (e.g, {race, gender}) has attracted lots of attention. To enhance the model performs uniformly well in different sensitive attributes, we propose a principled \underline{R}obust \underline{A}dversarial \underline{A}ttribute \underline{N}eighbourhood (RAAN) loss to debias the classification head and promote a fairer representation distribution across different sensitive attribute groups. The key idea of RAAN is to mitigate the differences of biased representations between different sensitive attribute groups by assigning each sample an adversarial robust weight, which is defined on the representations of adversarial attribute neighbors, i.e, the samples from different protected groups. To provide efficient optimization algorithms, we cast the RAAN into a sum of coupled compositional functions and propose a stochastic adaptive (Adam-style) and non-adaptive (SGD-style) algorithm framework SCRAAN with provable theoretical guarantee. Extensive empirical studies on fairness-related benchmark datasets verify the effectiveness of the proposed method.

Stochastic Constrained DRO with a Complexity Independent of Sample Size

Distributionally Robust Optimization (DRO), as a popular method to train robust models against distribution shift between training and test sets, has received tremendous attention in recent years. In this paper, we propose and analyze stochastic algorithms that apply to both non-convex and convex losses for solving Kullback Leibler divergence constrained DRO problem. Compared with existing methods solving this problem, our stochastic algorithms not only enjoy competitive if not better complexity independent of sample size but also just require a constant batch size at every iteration, which is more practical for broad applications. We establish a nearly optimal complexity bound for finding an $\epsilon$ stationary solution for non-convex losses and an optimal complexity for finding an $\epsilon$ optimal solution for convex losses. Empirical studies demonstrate the effectiveness of the proposed algorithms for solving non-convex and convex constrained DRO problems.

Multi-block-Single-probe Variance Reduced Estimator for Coupled Compositional Optimization

Variance reduction techniques such as SPIDER/SARAH/STORM have been extensively studied to improve the convergence rates of stochastic non-convex optimization, which usually maintain and update a sequence of estimators for a single function across iterations. {\it What if we need to track multiple functional mappings across iterations but only with access to stochastic samples of $\mathcal{O}(1)$ functional mappings at each iteration?} There is an important application in solving an emerging family of coupled compositional optimization problems in the form of $\sum_{i=1}^m f_i(g_i(\mathbf{w}))$, where $g_i$ is accessible through a stochastic oracle. The key issue is to track and estimate a sequence of $\mathbf g(\mathbf{w})=(g_1(\mathbf{w}), \ldots, g_m(\mathbf{w}))$ across iterations, where $\mathbf g(\mathbf{w})$ has $m$ blocks and it is only allowed to probe $\mathcal{O}(1)$ blocks to attain their stochastic values and Jacobians. To improve the complexity for solving these problems, we propose a novel stochastic method named Multi-block-Single-probe Variance Reduced (MSVR) estimator to track the sequence of $\mathbf g(\mathbf{w})$. It is inspired by STORM but introduces a customized error correction term to alleviate the noise not only in stochastic samples for the selected blocks but also in those blocks that are not sampled. With the help of the MSVR estimator, we develop several algorithms for solving the aforementioned compositional problems with improved complexities across a spectrum of settings with non-convex/convex/strongly convex objectives. Our results improve upon prior ones in several aspects, including the order of sample complexities and dependence on the strong convexity parameter. Empirical studies on multi-task deep AUC maximization demonstrate the better performance of using the new estimator.

GraphFM: Improving Large-Scale GNN Training via Feature Momentum

Training of graph neural networks (GNNs) for large-scale node classification is challenging. A key difficulty lies in obtaining accurate hidden node representations while avoiding the neighborhood explosion problem. Here, we propose a new technique, named feature momentum (FM), that uses a momentum step to incorporate historical embeddings when updating feature representations. We develop two specific algorithms, known as GraphFM-IB and GraphFM-OB, that consider in-batch and out-of-batch data, respectively. GraphFM-IB applies FM to in-batch sampled data, while GraphFM-OB applies FM to out-of-batch data that are 1-hop neighborhood of in-batch data. We provide a convergence analysis for GraphFM-IB and some theoretical insight for GraphFM-OB. Empirically, we observe that GraphFM-IB can effectively alleviate the neighborhood explosion problem of existing methods. In addition, GraphFM-OB achieves promising performance on multiple large-scale graph datasets.

Algorithmic Foundation of Deep X-Risk Optimization

X-risk is a term introduced to represent a family of compositional measures or objectives, in which each data point is compared with a set of data points explicitly or implicitly for defining a risk function. It includes many widely used measures or objectives, e.g., AUROC, AUPRC, partial AUROC, NDCG, MAP, top-$K$ NDCG, top-$K$ MAP, listwise losses, p-norm push, top push, precision/recall at top $K$ positions, precision at a certain recall level, contrastive objectives, etc. While these measures/objectives and their optimization algorithms have been studied in the literature of machine learning, computer vision, information retrieval, and etc, optimizing these measures/objectives has encountered some unique challenges for deep learning. In this technical report, we survey our recent rigorous efforts for deep X-risk optimization (DXO) by focusing on its algorithmic foundation. We introduce a class of techniques for optimizing X-risk for deep learning. We formulate DXO into three special families of non-convex optimization problems belonging to non-convex min-max optimization, non-convex compositional optimization, and non-convex bilevel optimization, respectively. For each family of problems, we present some strong baseline algorithms and their complexities, which will motivate further research for improving the existing results. Discussions about the presented results and future studies are given at the end. Efficient algorithms for optimizing a variety of X-risks are implemented in the LibAUC library at www.libauc.org.

Multi-block Min-max Bilevel Optimization with Applications in Multi-task Deep AUC Maximization

In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual variables and lower level problems. Due to the intertwined multi-block min-max bilevel structure, the computational cost at each iteration could be prohibitively high, especially with a large number of blocks. To tackle this challenge, we present a single-loop randomized stochastic algorithm, which requires updates for only a constant number of blocks at each iteration. Under some mild assumptions on the problem, we establish its sample complexity of $\mathcal{O}(1/\epsilon^4)$ for finding an $\epsilon$-stationary point. This matches the optimal complexity for solving stochastic nonconvex optimization under a general unbiased stochastic oracle model. Moreover, we provide two applications of the proposed method in multi-task deep AUC (area under ROC curve) maximization and multi-task deep partial AUC maximization. Experimental results validate our theory and demonstrate the effectiveness of our method on problems with hundreds of tasks.

Smoothed Online Convex Optimization Based on Discounted-Normal-Predictor

In this paper, we investigate an online prediction strategy named as Discounted-Normal-Predictor (Kapralov and Panigrahy, 2010) for smoothed online convex optimization (SOCO), in which the learner needs to minimize not only the hitting cost but also the switching cost. In the setting of learning with expert advice, Daniely and Mansour (2019) demonstrate that Discounted-Normal-Predictor can be utilized to yield nearly optimal regret bounds over any interval, even in the presence of switching costs. Inspired by their results, we develop a simple algorithm for SOCO: Combining online gradient descent (OGD) with different step sizes sequentially by Discounted-Normal-Predictor. Despite its simplicity, we prove that it is able to minimize the adaptive regret with switching cost, i.e., attaining nearly optimal regret with switching cost on every interval. By exploiting the theoretical guarantee of OGD for dynamic regret, we further show that the proposed algorithm can minimize the dynamic regret with switching cost in every interval.

Large-scale Stochastic Optimization of NDCG Surrogates for Deep Learning with Provable Convergence

NDCG, namely Normalized Discounted Cumulative Gain, is a widely used ranking metric in information retrieval and machine learning. However, efficient and provable stochastic methods for maximizing NDCG are still lacking, especially for deep models. In this paper, we propose a principled approach to optimize NDCG and its top-$K$ variant. First, we formulate a novel compositional optimization problem for optimizing the NDCG surrogate, and a novel bilevel compositional optimization problem for optimizing the top-$K$ NDCG surrogate. Then, we develop efficient stochastic algorithms with provable convergence guarantees for the non-convex objectives. Different from existing NDCG optimization methods, the per-iteration complexity of our algorithms scales with the mini-batch size instead of the number of total items. To improve the effectiveness for deep learning, we further propose practical strategies by using initial warm-up and stop gradient operator. Experimental results on multiple datasets demonstrate that our methods outperform prior ranking approaches in terms of NDCG. To the best of our knowledge, this is the first time that stochastic algorithms are proposed to optimize NDCG with a provable convergence guarantee.

AUC Maximization in the Era of Big Data and AI: A Survey

Area under the ROC curve, a.k.a. AUC, is a measure of choice for assessing the performance of a classifier for imbalanced data. AUC maximization refers to a learning paradigm that learns a predictive model by directly maximizing its AUC score. It has been studied for more than two decades dating back to late 90s and a huge amount of work has been devoted to AUC maximization since then. Recently, stochastic AUC maximization for big data and deep AUC maximization for deep learning have received increasing attention and yielded dramatic impact for solving real-world problems. However, to the best our knowledge there is no comprehensive survey of related works for AUC maximization. This paper aims to address the gap by reviewing the literature in the past two decades. We not only give a holistic view of the literature but also present detailed explanations and comparisons of different papers from formulations to algorithms and theoretical guarantees. We also identify and discuss remaining and emerging issues for deep AUC maximization, and provide suggestions on topics for future work.