We present a robust aggregation approach to make federated learning robust to settings when a fraction of the devices may be sending corrupted updates to the server. The proposed approach relies on a robust secure aggregation oracle based on the geometric median, which returns a robust aggregate using a constant number of calls to a regular non-robust secure average oracle. The robust aggregation oracle is privacy-preserving, similar to the secure average oracle it builds upon. We provide experimental results of the proposed approach with linear models and deep networks for two tasks in computer vision and natural language processing. The robust aggregation approach is agnostic to the level of corruption; it outperforms the classical aggregation approach in terms of robustness when the level of corruption is high, while being competitive in the regime of low corruption.

Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic optimization problems. In this paper, we investigate the stochastic compositional optimization in the general smooth non-convex setting. We employ a recently developed idea of \textit{Stochastic Recursive Gradient Descent} to design a novel algorithm named SARAH-Compositional, and prove a sharp Incremental First-order Oracle (IFO) complexity upper bound for stochastic compositional optimization: $\mathcal{O}((n+m)^{1/2} \varepsilon^{-2})$ in the finite-sum case and $\mathcal{O}(\varepsilon^{-3})$ in the online case. Such a complexity is known to be the best one among IFO complexity results for non-convex stochastic compositional optimization, and is believed to be optimal. Our experiments validate the theoretical performance of our algorithm.

In this work, we aim to solve data-driven optimization problems, where the goal is to find an input that maximizes an unknown score function given access to a dataset of inputs with corresponding scores. When the inputs are high-dimensional and valid inputs constitute a small subset of this space (e.g., valid protein sequences or valid natural images), such model-based optimization problems become exceptionally difficult, since the optimizer must avoid out-of-distribution and invalid inputs. We propose to address such problem with model inversion networks (MINs), which learn an inverse mapping from scores to inputs. MINs can scale to high-dimensional input spaces and leverage offline logged data for both contextual and non-contextual optimization problems. MINs can also handle both purely offline data sources and active data collection. We evaluate MINs on tasks from the Bayesian optimization literature, high-dimensional model-based optimization problems over images and protein designs, and contextual bandit optimization from logged data.

We propose a stochastic optimization method for minimizing loss functions, which can be expressed as an expected value, that adap-tively controls the batch size used in the computation of gradient approximations and the step size used to move along such directions, eliminating the need for the user to tune the learning rate. The proposed method exploits local curvature information and ensures that search directions are descent directions with high probability using an acute-angle test. The method is proved to have, under reasonable assumptions, a global linear rate of convergence on self-concordant functions with high probability. Numerical experiments show that this method is able to choose the best learning rates and compares favorably to fine-tuned SGD for training logistic regression and Deep Neural Networks (DNNs). We also propose an adaptive version of ADAM that eliminates the need to tune the base learning rate and compares favorably to fine-tuned ADAM for training DNNs.

This paper proposes Evolutionary Multi-objective Optimization (EMO)-based Adversarial Example (AE) design method that performs under black-box setting. Previous gradient-based methods produce AEs by changing all pixels of a target image, while previous EC-based method changes small number of pixels to produce AEs. Thanks to EMO's property of population based-search, the proposed method produces various types of AEs involving ones locating between AEs generated by the previous two approaches, which helps to know the characteristics of a target model or to know unknown attack patterns. Experimental results showed the potential of the proposed method, e.g., it can generate robust AEs and, with the aid of DCT-based perturbation pattern generation, AEs for high resolution images.

Highly non-linear machine learning algorithms have the capacity to handle large, complex datasets. However, the predictive performance of a model usually critically depends on the choice of multiple hyperparameters. Optimizing these (often) constitutes an expensive black-box problem. Model-based optimization is one state-of-the-art method to address this problem. Furthermore, resulting models often lack interpretability, as models usually contain many active features with non-linear effects and higher-order interactions. One model-agnostic way to enhance interpretability is to enforce sparse solutions through feature selection. It is in many applications desirable to forego a small drop in performance for a substantial gain in sparseness, leading to a natural treatment of feature selection as a multi-objective optimization task. Despite the practical relevance of both hyperparameter optimization and feature selection, they are often carried out separately from each other, which is neither efficient, nor does it take possible interactions between hyperparameters and selected features into account. We present, discuss and compare two algorithmically different approaches for joint and multi-objective hyperparameter optimization and feature selection: The first uses multi-objective model-based optimization to tune a feature filter ensemble. The second is an evolutionary NSGA-II-based wrapper-approach to feature selection which incorporates specialized sampling, mutation and recombination operators for the joint decision space of included features and hyperparameter settings. We compare and discuss the approaches on a variety of benchmark tasks. While model-based optimization needs fewer objective evaluations to achieve good performance, it incurs significant overhead compared to the NSGA-II-based approach. The preferred choice depends on the cost of training the ML model on the given data.

Multi-task learning is a powerful method for solving multiple correlated tasks simultaneously. However, it is often impossible to find one single solution to optimize all the tasks, since different tasks might conflict with each other. Recently, a novel method is proposed to find one single Pareto optimal solution with good trade-off among different tasks by casting multi-task learning as multiobjective optimization. In this paper, we generalize this idea and propose a novel Pareto multi-task learning algorithm (Pareto MTL) to find a set of well-distributed Pareto solutions which can represent different trade-offs among different tasks. The proposed algorithm first formulates a multi-task learning problem as a multiobjective optimization problem, and then decomposes the multiobjective optimization problem into a set of constrained subproblems with different trade-off preferences. By solving these subproblems in parallel, Pareto MTL can find a set of well-representative Pareto optimal solutions with different trade-off among all tasks. Practitioners can easily select their preferred solution from these Pareto solutions, or use different trade-off solutions for different situations. Experimental results confirm that the proposed algorithm can generate well-representative solutions and outperform some state-of-the-art algorithms on many multi-task learning applications.

Rajesh Kumar Arora is a senior engineer at the Indian Space Research Organization, where he has been working for more than two decades. He obtained his PhD in aerospace engineering from the Indian Institute of Science, Bangalore. His research interests include mission design, simulation of launch vehicle systems, and trajectory optimization.

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This paper introduces a new approach to learning from i.i.d. data under model miss-specification. This approach casts the problem of learning as minimizing the expected code-length of a Bayesian mixture code. To solve this problem, we build on PAC-Bayes bounds, information theory and a new family of second-order Jensen bounds. The key insight of this paper is that the use of the standard (first-order) Jensen bounds in learning is suboptimal when our model class is miss-specified (i.e. it does not contain the data generating distribution). As a consequence of this insight, this work provides strong theoretical arguments explaining why the Bayesian posterior is not optimal for making predictions that generalize under model miss-specification because the Bayesian posterior is directly related to the use of first-order Jensen bounds. We then argue for the use of second-order Jensen bounds, which leads to new families of learning algorithms. In this work, we introduce novel variational and ensemble learning methods based on the minimization of a novel family of second-order PAC-Bayes bounds over the expected code-length of a Bayesian mixture code. Using this new framework, we also provide novel hypotheses of why parameters in a flat minimum generalize better than parameters in a sharp minimum.