To protect sensitive data in training a Generative Adversarial Network (GAN), the standard approach is to use differentially private (DP) stochastic gradient descent method in which controlled noise is added to the gradients. The quality of the output synthetic samples can be adversely affected and the training of the network may not even converge in the presence of these noises. We propose Differentially Private Model Inversion (DPMI) method where the private data is first mapped to the latent space via a public generator, followed by a lower-dimensional DP-GAN with better convergent properties. Experimental results on standard datasets CIFAR10 and SVHN as well as on a facial landmark dataset for Autism screening show that our approach outperforms the standard DP-GAN method based on Inception Score, Fr\'echet Inception Distance, and classification accuracy under the same privacy guarantee.

In this paper, we study secure distributed optimization against arbitrary gradient attack in multi-agent networks. In distributed optimization, there is no central server to coordinate local updates, and each agent can only communicate with its neighbors on a predefined network. We consider the scenario where out of $n$ networked agents, a fixed but unknown fraction $\rho$ of the agents are under arbitrary gradient attack in that their stochastic gradient oracles return arbitrary information to derail the optimization process, and the goal is to minimize the sum of local objective functions on unattacked agents. We propose a distributed stochastic gradient method that combines local variance reduction and clipping (CLIP-VRG). We show that, in a connected network, when unattacked local objective functions are convex and smooth, share a common minimizer, and their sum is strongly convex, CLIP-VRG leads to almost sure convergence of the iterates to the exact sum cost minimizer at all agents. We quantify a tight upper bound of the fraction $\rho$ of attacked agents in terms of problem parameters such as the condition number of the associated sum cost that guarantee exact convergence of CLIP-VRG, and characterize its asymptotic convergence rate. Finally, we empirically demonstrate the effectiveness of the proposed method under gradient attacks in both synthetic dataset and image classification datasets.

It is well-known that given a smooth, bounded-from-below, and possibly nonconvex function, standard gradient-based methods can find $\epsilon$-stationary points (with gradient norm less than $\epsilon$) in $\mathcal{O}(1/\epsilon^2)$ iterations. However, many important nonconvex optimization problems, such as those associated with training modern neural networks, are inherently not smooth, making these results inapplicable. In this paper, we study nonsmooth nonconvex optimization from an oracle complexity viewpoint, where the algorithm is assumed to be given access only to local information about the function at various points. We provide two main results: First, we consider the problem of getting near $\epsilon$-stationary points. This is perhaps the most natural relaxation of finding $\epsilon$-stationary points, which is impossible in the nonsmooth nonconvex case. We prove that this relaxed goal cannot be achieved efficiently, for any distance and $\epsilon$ smaller than some constants. Our second result deals with the possibility of tackling nonsmooth nonconvex optimization by reduction to smooth optimization: Namely, applying smooth optimization methods on a smooth approximation of the objective function. For this approach, we prove under a mild assumption an inherent trade-off between oracle complexity and smoothness: On the one hand, smoothing a nonsmooth nonconvex function can be done very efficiently (e.g., by randomized smoothing), but with dimension-dependent factors in the smoothness parameter, which can strongly affect iteration complexity when plugging into standard smooth optimization methods. On the other hand, these dimension factors can be eliminated with suitable smoothing methods, but only by making the oracle complexity of the smoothing process exponentially large.

Factorisation-based Models (FMs), such as DistMult, have enjoyed enduring success for Knowledge Graph Completion (KGC) tasks, often outperforming Graph Neural Networks (GNNs). However, unlike GNNs, FMs struggle to incorporate node features and generalise to unseen nodes in inductive settings. Our work bridges the gap between FMs and GNNs by proposing ReFactor GNNs. This new architecture draws upon both modelling paradigms, which previously were largely thought of as disjoint. Concretely, using a message-passing formalism, we show how FMs can be cast as GNNs by reformulating the gradient descent procedure as message-passing operations, which forms the basis of our ReFactor GNNs. Across a multitude of well-established KGC benchmarks, our ReFactor GNNs achieve comparable transductive performance to FMs, and state-of-the-art inductive performance while using an order of magnitude fewer parameters.

The stochastic mirror descent (SMD) algorithm is a general class of training algorithms, which includes the celebrated stochastic gradient descent (SGD), as a special case. It utilizes a mirror potential to influence the implicit bias of the training algorithm. In this paper we explore the performance of the SMD iterates on mean-field ensemble models. Our results generalize earlier ones obtained for SGD on such models. The evolution of the distribution of parameters is mapped to a continuous time process in the space of probability distributions. Our main result gives a nonlinear partial differential equation to which the continuous time process converges in the asymptotic regime of large networks. The impact of the mirror potential appears through a multiplicative term that is equal to the inverse of its Hessian and which can be interpreted as defining a gradient flow over an appropriately defined Riemannian manifold. We provide numerical simulations which allow us to study and characterize the effect of the mirror potential on the performance of networks trained with SMD for some binary classification problems.

The lasso is the most famous sparse regression and feature selection method. One reason for its popularity is the speed at which the underlying optimization problem can be solved. Sorted L-One Penalized Estimation (SLOPE) is a generalization of the lasso with appealing statistical properties. In spite of this, the method has not yet reached widespread interest. A major reason for this is that current software packages that fit SLOPE rely on algorithms that perform poorly in high dimensions. To tackle this issue, we propose a new fast algorithm to solve the SLOPE optimization problem, which combines proximal gradient descent and proximal coordinate descent steps. We provide new results on the directional derivative of the SLOPE penalty and its related SLOPE thresholding operator, as well as provide convergence guarantees for our proposed solver. In extensive benchmarks on simulated and real data, we show that our method outperforms a long list of competing algorithms.

Molecule optimization is an important problem in chemical discovery and has been approached using many techniques, including generative modeling, reinforcement learning, genetic algorithms, and much more. Recent work has also applied zeroth-order (ZO) optimization, a subset of gradient-free optimization that solves problems similarly to gradient-based methods, for optimizing latent vector representations from an autoencoder. In this paper, we study the effectiveness of various ZO optimization methods for optimizing molecular objectives, which are characterized by variable smoothness, infrequent optima, and other challenges. We provide insights on the robustness of various ZO optimizers in this setting, show the advantages of ZO sign-based gradient descent (ZO-signGD), discuss how ZO optimization can be used practically in realistic discovery tasks, and demonstrate the potential effectiveness of ZO optimization methods on widely used benchmark tasks from the Guacamol suite. Code is available at: https://github.com/IBM/QMO-bench.

Federated learning (FL) faces challenges of intermittent client availability and computation/communication efficiency. As a result, only a small subset of clients can participate in FL at a given time. It is important to understand how partial client participation affects convergence, but most existing works have either considered idealized participation patterns or obtained results with non-zero optimality error for generic patterns. In this paper, we provide a unified convergence analysis for FL with arbitrary client participation. We first introduce a generalized version of federated averaging (FedAvg) that amplifies parameter updates at an interval of multiple FL rounds. Then, we present a novel analysis that captures the effect of client participation in a single term. By analyzing this term, we obtain convergence upper bounds for a wide range of participation patterns, including both non-stochastic and stochastic cases, which match either the lower bound of stochastic gradient descent (SGD) or the state-of-the-art results in specific settings. We also discuss various insights, recommendations, and experimental results.

The development of any machine learning model is a highly iterative and empirical process that follows the idea-experiment-evaluation cycle. The cycle illustrated above is typically repeated multiple times before achieving satisfactory performances. The "experiment" phase includes the coding time and the training time of the machine learning model. As models' complexity increases and much more data are handled, training time inflates, with the result that training a very large deep neural network can be painfully slow [1]. While all the above-mentioned techniques are fundamental, this article details the last point.

The decentralized Federated Learning (FL) setting avoids the role of a potentially unreliable or untrustworthy central host by utilizing groups of clients to collaboratively train a model via localized training and model/gradient sharing. Most existing decentralized FL algorithms require synchronization of client models where the speed of synchronization depends upon the slowest client. In this work, we propose SWIFT: a novel wait-free decentralized FL algorithm that allows clients to conduct training at their own speed. Theoretically, we prove that SWIFT matches the gold-standard iteration convergence rate $\mathcal{O}(1/\sqrt{T})$ of parallel stochastic gradient descent for convex and non-convex smooth optimization (total iterations $T$). Furthermore, we provide theoretical results for IID and non-IID settings without any bounded-delay assumption for slow clients which is required by other asynchronous decentralized FL algorithms. Although SWIFT achieves the same iteration convergence rate with respect to $T$ as other state-of-the-art (SOTA) parallel stochastic algorithms, it converges faster with respect to run-time due to its wait-free structure. Our experimental results demonstrate that SWIFT's run-time is reduced due to a large reduction in communication time per epoch, which falls by an order of magnitude compared to synchronous counterparts. Furthermore, SWIFT produces loss levels for image classification, over IID and non-IID data settings, upwards of 50% faster than existing SOTA algorithms.