Differential Privacy (DP) [13] is an important privacy-enhancing technology for private machine learning systems. It allows to measure and bound the risk associated with an individual participation in a computation. However, it was recently observed that DP learning systems may exacerbate bias and unfairness for different groups of individuals [3, 27, 22]. This paper builds on these important observations and sheds light on the causes of the disparate impacts arising in the problem of differentially private empirical risk minimization. It focuses on the accuracy disparity arising among groups of individuals in two well-studied DP learning methods: output perturbation [10] and differentially private stochastic gradient descent [2]. The paper analyzes which data and model properties are responsible for the disproportionate impacts, why these aspects are affecting different groups disproportionately, and proposes guidelines to mitigate these effects. The proposed approach is evaluated on several datasets and settings.

The federated learning (FL) framework trains a machine learning model using decentralized data stored at edge client devices by periodically aggregating locally trained models. Popular optimization algorithms of FL use vanilla (stochastic) gradient descent for both local updates at clients and global updates at the aggregating server. Recently, adaptive optimization methods such as AdaGrad have been studied for server updates. However, the effect of using adaptive optimization methods for local updates at clients is not yet understood. We show in both theory and practice that while local adaptive methods can accelerate convergence, they can cause a non-vanishing solution bias, where the final converged solution may be different from the stationary point of the global objective function. We propose correction techniques to overcome this inconsistency and complement the local adaptive methods for FL. Extensive experiments on realistic federated training tasks show that the proposed algorithms can achieve faster convergence and higher test accuracy than the baselines without local adaptivity.

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same $L_2$-error for a wide range of matrix types. For example, it leads to 2 to 10 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

We theoretically study the fundamental problem of learning a single neuron with a bias term ($\mathbf{x} \mapsto \sigma(<\mathbf{w},\mathbf{x}> + b)$) in the realizable setting with the ReLU activation, using gradient descent. Perhaps surprisingly, we show that this is a significantly different and more challenging problem than the bias-less case (which was the focus of previous works on single neurons), both in terms of the optimization geometry as well as the ability of gradient methods to succeed in some scenarios. We provide a detailed study of this problem, characterizing the critical points of the objective, demonstrating failure cases, and providing positive convergence guarantees under different sets of assumptions. To prove our results, we develop some tools which may be of independent interest, and improve previous results on learning single neurons.

Gradient Descent algorithm is an iterative algorithm used for the optimization of parameters used in an equation and to decrease the Loss (often called a Cost function). But before diving deep, we first need to have a basic idea of what a gradient means? Why are we calculating the gradient of a function and what is our final goal to achieve by using this algorithm? The gradient of a function refers to the slope of the function at some point. We are calculating the gradient of a function to achieve the global minima of the function.

Federated learning aims at conducting inference when data are decentralised and locally stored on several clients, under two main constraints: data ownership and communication overhead. In this paper, we address these issues under the Bayesian paradigm. To this end, we propose a novel Markov chain Monte Carlo algorithm coined \texttt{QLSD} built upon quantised versions of stochastic gradient Langevin dynamics. To improve performance in a big data regime, we introduce variance-reduced alternatives of our methodology referred to as \texttt{QLSD}$^\star$ and \texttt{QLSD}$^{++}$. We provide both non-asymptotic and asymptotic convergence guarantees for the proposed algorithms and illustrate their benefits on several federated learning benchmarks.

Accelerated gradient-based methods are being extensively used for solving non-convex machine learning problems, especially when the data points are abundant or the available data is distributed across several agents. Two of the prominent accelerated gradient algorithms are AdaGrad and Adam. AdaGrad is the simplest accelerated gradient method, which is particularly effective for sparse data. Adam has been shown to perform favorably in deep learning problems compared to other methods. In this paper, we propose a new fast optimizer, Generalized AdaGrad (G-AdaGrad), for accelerating the solution of potentially non-convex machine learning problems. Specifically, we adopt a state-space perspective for analyzing the convergence of gradient acceleration algorithms, namely G-AdaGrad and Adam, in machine learning. Our proposed state-space models are governed by ordinary differential equations. We present simple convergence proofs of these two algorithms in the deterministic settings with minimal assumptions. Our analysis also provides intuition behind improving upon AdaGrad's convergence rate. We provide empirical results on MNIST dataset to reinforce our claims on the convergence and performance of G-AdaGrad and Adam.

In this paper, we propose an energy-efficient federated meta-learning framework. The objective is to enable learning a meta-model that can be fine-tuned to a new task with a few number of samples in a distributed setting and at low computation and communication energy consumption. We assume that each task is owned by a separate agent, so a limited number of tasks is used to train a meta-model. Assuming each task was trained offline on the agent's local data, we propose a lightweight algorithm that starts from the local models of all agents, and in a backward manner using projected stochastic gradient ascent (P-SGA) finds a meta-model. The proposed method avoids complex computations such as computing hessian, double looping, and matrix inversion, while achieving high performance at significantly less energy consumption compared to the state-of-the-art methods such as MAML and iMAML on conducted experiments for sinusoid regression and image classification tasks.

A Spiking Neural Network (SNN) (Maass, 1997; Gerstner and Kistler, 2002b; Pfeiffer and Pfeil, 2018) is a neuro-inspired machine learning (ML) model that mimics the spike-based operation of the human brain (Bi and Poo, 1998). The Spike Time Dependent Plasticity (STDP) is a policy for unsupervised learning in rate-encoded SNNs (Bell et al., 1997; Magee and Johnston, 1997; Gerstner and Kistler, 2002a). The STDP relates the expected change in synaptic weights to the timing difference between postsynaptic spikes and presynaptic spikes (Feldman, 2012). Recent works using STDP trained SNNs have demonstrated promising results as an unsupervised learning paradigm for various tasks such as object classification and recognition (She et al., 2021; Diehl and Cook, 2015; Kheradpisheh et al., 2018). The generalizability is a measure of how well an ML model performs on test data that lies outside of the distribution of the training samples (Kawaguchi et al., 2017; Neyshabur et al., 2017). The generalization properties of Stochastic Gradient Descent (SGD) based training for deep neural network (DNN) have received significant attention in recent years (Poggio et al., 2019; Allen-Zhu et al., 2018; Allen-Zhu and Li, 2019). The dynamics of SGD have been studied via models of stochastic gradient Langevin dynamics with an assumption that gradient noise is Gaussian (Simsekli et al., 2020b). Here SGD is considered to be driven by a Brownian motion. Chen et al. showed that SGD dynamics commonly exhibit highly anisotropic and dynamic-changing properties (Chen et al., 2020), suggesting the presence of

We posit a new mechanism for cooperation in multi-agent reinforcement learning (MARL) based upon any nonlinear function of the team's long-term state-action occupancy measure, i.e., a \emph{general utility}. This subsumes the cumulative return but also allows one to incorporate risk-sensitivity, exploration, and priors. % We derive the {\bf D}ecentralized {\bf S}hadow Reward {\bf A}ctor-{\bf C}ritic (DSAC) in which agents alternate between policy evaluation (critic), weighted averaging with neighbors (information mixing), and local gradient updates for their policy parameters (actor). DSAC augments the classic critic step by requiring agents to (i) estimate their local occupancy measure in order to (ii) estimate the derivative of the local utility with respect to their occupancy measure, i.e., the "shadow reward". DSAC converges to $\epsilon$-stationarity in $\mathcal{O}(1/\epsilon^{2.5})$ (Theorem \ref{theorem:final}) or faster $\mathcal{O}(1/\epsilon^{2})$ (Corollary \ref{corollary:communication}) steps with high probability, depending on the amount of communications. We further establish the non-existence of spurious stationary points for this problem, that is, DSAC finds the globally optimal policy (Corollary \ref{corollary:global}). Experiments demonstrate the merits of goals beyond the cumulative return in cooperative MARL.