We propose an adaptive variance-reduction method, called AdaSpider, for minimization of $L$-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fairly distinct, adaptive step-size schedule with the recursive stochastic path integrated estimator proposed in [Fang et al., 2018]. To our knowledge, Adaspider is the first parameter-free non-convex variance-reduction method in the sense that it does not require the knowledge of problem-dependent parameters, such as smoothness constant $L$, target accuracy $\epsilon$ or any bound on gradient norms. In doing so, we are able to compute an $\epsilon$-stationary point with $\tilde{O}\left(n + \sqrt{n}/\epsilon^2\right)$ oracle-calls, which matches the respective lower bound up to logarithmic factors.

We introduce the notion of performative power, which measures the ability of a firm operating an algorithmic system, such as a digital content recommendation platform, to cause change in a population of participants. We relate performative power to the economic study of competition in digital economies. Traditional economic concepts struggle with identifying anti-competitive patterns in digital platforms not least due to the complexity of market definition. In contrast, performative power is a causal notion that is identifiable with minimal knowledge of the market, its internals, participants, products, or prices. Low performative power implies that a firm can do no better than to optimize their objective on current data. In contrast, firms of high performative power stand to benefit from steering the population towards more profitable behavior. We confirm in a simple theoretical model that monopolies maximize performative power. A firm's ability to personalize increases performative power, while competition and outside options decrease performative power. On the empirical side, we propose an observational causal design to identify performative power from discontinuities in how digital platforms display content. This allows to repurpose causal effects from various studies about digital platforms as lower bounds on performative power. Finally, we speculate about the role that performative power might play in competition policy and antitrust enforcement in digital marketplaces.

For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully uncovered by the gradient correction term and its equivalent implicit-velocity form. Furthermore, based on the high-resolution differential equation framework with the corresponding emerging techniques, phase-space representation and Lyapunov function, the squared gradient norm of Nesterov's accelerated gradient descent (\texttt{NAG}) method at an inverse cubic rate is discovered. However, this result cannot be directly generalized to composite optimization widely used in practice, e.g., the linear inverse problem with sparse representation. In this paper, we meticulously observe a pivotal inequality used in composite optimization about the step size $s$ and the Lipschitz constant $L$ and find that it can be improved tighter. We apply the tighter inequality discovered in the well-constructed Lyapunov function and then obtain the proximal subgradient norm minimization by the phase-space representation, regardless of gradient-correction or implicit-velocity. Furthermore, we demonstrate that the squared proximal subgradient norm for the class of iterative shrinkage-thresholding algorithms (ISTA) converges at an inverse square rate, and the squared proximal subgradient norm for the class of faster iterative shrinkage-thresholding algorithms (FISTA) is accelerated to convergence at an inverse cubic rate.

Distributing machine learning predictors enables the collection of large-scale datasets while leaving sensitive raw data at trustworthy sites. We show that locally training support vector machines (SVMs) and computing their averages leads to a learning technique that is scalable to a large number of users, satisfies differential privacy, and is applicable to non-trivial tasks, such as CIFAR-10. For a large number of participants, communication cost is one of the main challenges. We achieve a low communication cost by requiring only a single invocation of an efficient secure multiparty summation protocol. By relying on state-of-the-art feature extractors (SimCLR), we are able to utilize differentially private convex learners for non-trivial tasks such as CIFAR-10. Our experimental results illustrate that for $1{,}000$ users with $50$ data points each, our scheme outperforms state-of-the-art scalable distributed learning methods (differentially private federated learning, short DP-FL) while requiring around $500$ times fewer communication costs: For CIFAR-10, we achieve a classification accuracy of $79.7\,\%$ for an $\varepsilon = 0.59$ while DP-FL achieves $57.6\,\%$. More generally, we prove learnability properties for the average of such locally trained models: convergence and uniform stability. By only requiring strongly convex, smooth, and Lipschitz-continuous objective functions, locally trained via stochastic gradient descent (SGD), we achieve a strong utility-privacy tradeoff.

Today there exists no shortage of outlier detection algorithms in the literature, yet the complementary and critical problem of unsupervised outlier model selection (UOMS) is vastly understudied. In this work we propose ELECT, a new approach to select an effective candidate model, i.e. an outlier detection algorithm and its hyperparameter(s), to employ on a new dataset without any labels. At its core, ELECT is based on meta-learning; transferring prior knowledge (e.g. model performance) on historical datasets that are similar to the new one to facilitate UOMS. Uniquely, it employs a dataset similarity measure that is performance-based, which is more direct and goal-driven than other measures used in the past. ELECT adaptively searches for similar historical datasets, as such, it can serve an output on-demand, being able to accommodate varying time budgets. Extensive experiments show that ELECT significantly outperforms a wide range of basic UOMS baselines, including no model selection (always using the same popular model such as iForest) as well as more recent selection strategies based on meta-features.

Healthcare IoMT systems are becoming intelligent, miniaturized, and more integrated into daily life. As for the distributed devices in the IoMT, federated learning has become a topical area with cloud-based training procedures when meeting data security. However, the distribution of IoMT has the risk of protection from data poisoning attacks. Poisoned data can be fabricated by falsifying medical data, which urges a security defense to IoMT systems. Due to the lack of specific labels, the filtering of malicious data is a unique unsupervised scenario. One of the main challenges is finding robust data filtering methods for various poisoning attacks. This paper introduces a Federated Data Sanitization Defense, a novel approach to protect the system from data poisoning attacks. To solve this unsupervised problem, we first use federated learning to project all the data to the subspace domain, allowing unified feature mapping to be established since the data is stored locally. Then we adopt the federated clustering to re-group their features to clarify the poisoned data. The clustering is based on the consistent association of data and its semantics. After we get the clustering of the private data, we do the data sanitization with a simple yet efficient strategy. In the end, each device of distributed ImOT is enabled to filter malicious data according to federated data sanitization. Extensive experiments are conducted to evaluate the efficacy of the proposed defense method against data poisoning attacks. Further, we consider our approach in the different poisoning ratios and achieve a high Accuracy and a low attack success rate.

In this work, we explore combining automatic hyperparameter tuning and optimization for federated learning (FL) in an online, one-shot procedure. We apply a principled approach on a method for adaptive client learning rate, number of local steps, and batch size. In our federated learning applications, our primary motivations are minimizing communication budget as well as local computational resources in the training pipeline. Conventionally, hyperparameter tuning methods involve at least some degree of trial-and-error, which is known to be sample inefficient. In order to address our motivations, we propose FATHOM (Federated AuTomatic Hyperparameter OptiMization) as a one-shot online procedure. We investigate the challenges and solutions of deriving analytical gradients with respect to the hyperparameters of interest. Our approach is inspired by the fact that, with the exception of local data, we have full knowledge of all components involved in our training process, and this fact can be exploited in our algorithm impactfully. We show that FATHOM is more communication efficient than Federated Averaging (FedAvg) with optimized, static valued hyperparameters, and is also more computationally efficient overall. As a communication efficient, one-shot online procedure, FATHOM solves the bottleneck of costly communication and limited local computation, by eliminating a potentially wasteful tuning process, and by optimizing the hyperparamters adaptively throughout the training procedure without trial-and-error. We show our numerical results through extensive empirical experiments with the Federated EMNIST-62 (FEMNIST) and Federated Stack Overflow (FSO) datasets, using FedJAX as our baseline framework.

Multi-armed bandit (MAB) algorithms are efficient approaches to reduce the opportunity cost of online experimentation and are used by companies to find the best product from periodically refreshed product catalogs. However, these algorithms face the so-called cold-start at the onset of the experiment due to a lack of knowledge of customer preferences for new products, requiring an initial data collection phase known as the burn-in period. During this period, MAB algorithms operate like randomized experiments, incurring large burn-in costs which scale with the large number of products. We attempt to reduce the burn-in by identifying that many products can be cast into two-sided products, and then naturally model the rewards of the products with a matrix, whose rows and columns represent the two sides respectively. Next, we design two-phase bandit algorithms that first use subsampling and low-rank matrix estimation to obtain a substantially smaller targeted set of products and then apply a UCB procedure on the target products to find the best one. We theoretically show that the proposed algorithms lower costs and expedite the experiment in cases when there is limited experimentation time along with a large product set. Our analysis also reveals three regimes of long, short, and ultra-short horizon experiments, depending on dimensions of the matrix. Empirical evidence from both synthetic data and a real-world dataset on music streaming services validates this superior performance.

Federated learning provides an effective paradigm to jointly optimize a model benefited from rich distributed data while protecting data privacy. Nonetheless, the heterogeneity nature of distributed data makes it challenging to define and ensure fairness among local agents. For instance, it is intuitively "unfair" for agents with data of high quality to sacrifice their performance due to other agents with low quality data. Currently popular egalitarian and weighted equity-based fairness measures suffer from the aforementioned pitfall. In this work, we aim to formally represent this problem and address these fairness issues using concepts from co-operative game theory and social choice theory. We model the task of learning a shared predictor in the federated setting as a fair public decision making problem, and then define the notion of core-stable fairness: Given $N$ agents, there is no subset of agents $S$ that can benefit significantly by forming a coalition among themselves based on their utilities $U_N$ and $U_S$ (i.e., $\frac{|S|}{N} U_S \geq U_N$). Core-stable predictors are robust to low quality local data from some agents, and additionally they satisfy Proportionality and Pareto-optimality, two well sought-after fairness and efficiency notions within social choice. We then propose an efficient federated learning protocol CoreFed to optimize a core stable predictor. CoreFed determines a core-stable predictor when the loss functions of the agents are convex. CoreFed also determines approximate core-stable predictors when the loss functions are not convex, like smooth neural networks. We further show the existence of core-stable predictors in more general settings using Kakutani's fixed point theorem. Finally, we empirically validate our analysis on two real-world datasets, and we show that CoreFed achieves higher core-stability fairness than FedAvg while having similar accuracy.

In offline reinforcement learning (RL), a learner leverages prior logged data to learn a good policy without interacting with the environment. A major challenge in applying such methods in practice is the lack of both theoretically principled and practical tools for model selection and evaluation. To address this, we study the problem of model selection in offline RL with value function approximation. The learner is given a nested sequence of model classes to minimize squared Bellman error and must select among these to achieve a balance between approximation and estimation error of the classes. We propose the first model selection algorithm for offline RL that achieves minimax rate-optimal oracle inequalities up to logarithmic factors. The algorithm, ModBE, takes as input a collection of candidate model classes and a generic base offline RL algorithm. By successively eliminating model classes using a novel one-sided generalization test, ModBE returns a policy with regret scaling with the complexity of the minimally complete model class. In addition to its theoretical guarantees, it is conceptually simple and computationally efficient, amounting to solving a series of square loss regression problems and then comparing relative square loss between classes. We conclude with several numerical simulations showing it is capable of reliably selecting a good model class.