Sebastian U. Stich

• PhD
• PostDoc Position at Swiss Federal Institute of Technology in Lausanne

Reducing communication complexity is critical for efficient decentralized optimization. The proximal decentralized optimization (PDO) framework is particularly appealing, as methods within this framework can exploit functional similarity among nodes to reduce communication rounds. Specifically, when local functions at different nodes are similar, t...

Modern machine learning tasks often involve massive datasets and models, necessitating distributed optimization algorithms with reduced communication overhead. Communication compression, where clients transmit compressed updates to a central server, has emerged as a key technique to mitigate communication bottlenecks. However, the theoretical under...

We focus on reducing communication overhead in multiplayer games, where frequently exchanging strategies between players is not feasible and players have noisy or outdated strategies of the other players. We introduce Decoupled SGDA, a novel adaptation of Stochastic Gradient Descent Ascent (SGDA). In this approach, players independently update thei...

We present a novel universal gradient method for solving convex optimization problems. Our algorithm -- Dual Averaging with Distance Adaptation (DADA) -- is based on the classical scheme of dual averaging and dynamically adjusts its coefficients based on observed gradients and the distance between iterates and the starting point, eliminating the ne...

LocalSGD and SCAFFOLD are widely used methods in distributed stochastic optimization, with numerous applications in machine learning, large-scale data processing, and federated learning. However, rigorously establishing their theoretical advantages over simpler methods, such as minibatch SGD (MbSGD), has proven challenging, as existing analyses oft...

We study gradient methods for solving an optimization problem with an $(L_0, L_1)$-smooth objective function. This problem class generalizes that of Lipschitz-smooth problems and has gained interest recently, as it captures a broader range of machine learning applications. We provide novel insights on the properties of this function class and devel...

In developing efficient optimization algorithms, it is crucial to account for communication constraints -- a significant challenge in modern federated learning settings. The best-known communication complexity among non-accelerated algorithms is achieved by DANE, a distributed proximal-point algorithm that solves local subproblems in each iteration...

We present adaptive gradient methods (both basic and accelerated) for solving convex composite optimization problems in which the main part is approximately smooth (a.k.a. $(\delta, L)$-smooth) and can be accessed only via a (potentially biased) stochastic gradient oracle. This setting covers many interesting examples including H\"older smooth prob...

Communication efficiency has garnered significant attention as it is considered the main bottleneck for large-scale decentralized Machine Learning applications in distributed and federated settings. In this regime, clients are restricted to transmitting small amounts of quantized information to their neighbors over a communication graph. Numerous e...

Local SGD is a popular optimization method in distributed learning, often outperforming other algorithms in practice, including mini-batch SGD. Despite this success, theoretically proving the dominance of local SGD in settings with reasonable data heterogeneity has been difficult, creating a significant gap between theory and practice. In this pape...

The recently proposed stochastic Polyak stepsize (SPS) and stochastic line-search (SLS) for SGD have shown remarkable effectiveness when training over-parameterized models. However, in non-interpolation settings, both algorithms only guarantee convergence to a neighborhood of a solution which may result in a worse output than the initial guess. Whi...

State-of-the-art federated learning algorithms such as FedAvg require carefully tuned stepsizes to achieve their best performance. The improvements proposed by existing adaptive federated methods involve tuning of additional hyperparameters such as momentum parameters, and consider adaptivity only in the server aggregation round, but not locally. T...

In federated learning, data heterogeneity is a critical challenge. A straightforward solution is to shuffle the clients' data to homogenize the distribution. However, this may violate data access rights, and how and when shuffling can accelerate the convergence of a federated optimization algorithm is not theoretically well understood. In this pape...

Distributed and federated learning algorithms and techniques associated primarily with minimization problems. However, with the increase of minimax optimization and variational inequality problems in machine learning, the necessity of designing efficient distributed/federated learning approaches for these problems is becoming more apparent. In this...

Stochastic Gradient Descent (SGD) algorithms are widely used in optimizing neural networks, with Random Reshuffling (RR) and Single Shuffle (SS) being popular choices for cycling through random or single permutations of the training data. However, the convergence properties of these algorithms in the non-convex case are not fully understood. Existi...

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c >0$. It is widely used for example for stabilizing the training of deep learning models (Goodfellow et al., 2016), or for enforcing differential privacy (Abadi et al., 2016). Despite popularity a...

Gradient tracking (GT) is an algorithm designed for solving decentralized optimization problems over a network (such as training a machine learning model). A key feature of GT is a tracking mechanism that allows to overcome data heterogeneity between nodes. We develop a novel decentralized tracking mechanism, $K$-GT, that enables communication-effi...

We consider distributed optimization over several devices, each sending incremental model updates to a central server. This setting is considered, for instance, in federated learning. Various schemes have been designed to compress the model updates in order to reduce the overall communication cost. However, existing methods suffer from a significan...

We study the asynchronous stochastic gradient descent algorithm for distributed training over $n$ workers which have varying computation and communication frequency over time. In this algorithm, workers compute stochastic gradients in parallel at their own pace and return those to the server without any synchronization. Existing convergence rates o...

It has been widely observed in training of neural networks that when applying gradient descent (GD), a large step size is essential for obtaining superior models. However, the effect of large step sizes on the success of GD is not well understood theoretically. We argue that a complete understanding of the mechanics leading to GD's success may inde...

Decentralized learning provides an effective framework to train machine learning models with data distributed over arbitrary communication graphs. However, most existing approaches toward decentralized learning disregard the interaction between data heterogeneity and graph topology. In this paper, we characterize the dependence of convergence on th...

We introduce \algname{ProxSkip} -- a surprisingly simple and provably efficient method for minimizing the sum of a smooth ($f$) and an expensive nonsmooth proximable ($\psi$) function. The canonical approach to solving such problems is via the proximal gradient descent (\algname{ProxGD}) algorithm, which is based on the evaluation of the gradient o...

Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis cannot adequately explain this success. In particular, the standard analyses do not show global convergence of...

We consider decentralized machine learning over a network where the training data is distributed across $n$ agents, each of which can compute stochastic model updates on their local data. The agent's common goal is to find a model that minimizes the average of all local loss functions. While gradient tracking (GT) algorithms can overcome a key chal...

Collaborative training can improve the accuracy of a model for a user by trading off the model's bias (introduced by using data from other users who are potentially different) against its variance (due to the limited amount of data on any single user). In this work, we formalize the personalized collaborative learning problem as a stochastic optimi...

Uncertainty estimation (UE) techniques -- such as the Gaussian process (GP), Bayesian neural networks (BNN), Monte Carlo dropout (MCDropout) -- aim to improve the interpretability of machine learning models by assigning an estimated uncertainty value to each of their prediction outputs. However, since too high uncertainty estimates can have fatal c...

Federated learning is a powerful distributed learning scheme that allows numerous edge devices to collaboratively train a model without sharing their data. However, training is resource-intensive for edge devices, and limited network bandwidth is often the main bottleneck. Prior work often overcomes the constraints by condensing the models or messa...

In decentralized machine learning, workers compute model updates on their local data. Because the workers only communicate with few neighbors without central coordination, these updates propagate progressively over the network. This paradigm enables distributed training on networks without all-to-all connectivity, helping to protect data privacy as...

We consider federated learning (FL), where the training data is distributed across a large number of clients. The standard optimization method in this setting is Federated Averaging (FedAvg), which performs multiple local first-order optimization steps between communication rounds. In this work, we evaluate the performance of several second-order d...

Data augmentation is a widely adopted technique for avoiding overfitting when training deep neural networks. However, this approach requires domain-specific knowledge and is often limited to a fixed set of hard-coded transformations. Recently, several works proposed to use generative models for generating semantically meaningful perturbations to tr...

Federated learning and analytics are a distributed approach for collaboratively learning models (or statistics) from decentralized data, motivated by and designed for privacy protection. The distributed learning process can be formulated as solving federated optimization problems, which emphasize communication efficiency, data heterogeneity, compat...

For deploying deep learning models to lower end devices, it is necessary to train less resource-demanding variants of state-of-the-art architectures. This does not eliminate the need for more expensive models as they have a higher performance. In order to avoid training two separate models, we show that it is possible to train neural networks in su...

We consider decentralized stochastic variational inequalities where the problem data is distributed across many participating devices (heterogeneous, or non-IID data setting). We propose a novel method - based on stochastic extra-gradient - where participating devices can communicate over arbitrary, possibly time-varying network topologies. This co...

It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and -- in asynchronous implementations -- on the gradient staleness. Especially, it has been observed that the speedup saturates beyond a certain batch size and/or when the delays grow too large. We ide...

Decentralized training of deep learning models enables on-device learning over networks, as well as efficient scaling to large compute clusters. Experiments in earlier works reveal that, even in a data-center setup, decentralized training often suffers from the degradation in the quality of the model: the training and test performance of models tra...

Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks. In realistic learning scenarios, the presence of heterogeneity across different clients' local datasets poses an optimization challenge and may severely deteriorate the generalization performance. In this paper, we investi...

The term Federated Learning was coined as recently as 2016 to describe a machine learning setting where multiple entities collaborate in solving a machine learning problem, under the coordination of a central server or service provider. Each client’s raw data is stored locally and not exchanged or transferred; instead, focused updates intended for...

Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the entire system. We propose a new randomized first-order method which tackles the communication bottleneck by appl...

Lossy gradient compression, with either unbiased or biased compressors, has become a key tool to avoid the communication bottleneck in centrally coordinated distributed training of machine learning models. We analyze the performance of two standard and general types of methods: (i) distributed quantized SGD (D-QSGD) with arbitrary unbiased quantize...

Federated learning is a challenging optimization problem due to the heterogeneity of the data across different clients. Such heterogeneity has been observed to induce client drift and significantly degrade the performance of algorithms designed for this setting. In contrast, centralized learning with centrally collected data does not experience suc...

Generative Adversarial Networks are notoriously challenging to train. The underlying minmax optimization is highly susceptible to the variance of the stochastic gradient and the rotational component of the associated game vector field. To tackle these challenges, we propose the Lookahead algorithm for minmax optimization, originally developed for s...

Federated Learning (FL) is a machine learning setting where many devices collaboratively train a machine learning model while keeping the training data decentralized. In most of the current training schemes the central model is refined by averaging the parameters of the server model and the updated parameters from the client side. However, directly...

Deep neural networks often have millions of parameters. This can hinder their deployment to low-end devices, not only due to high memory requirements but also because of increased latency at inference. We propose a novel model compression method that generates a sparse trained model without additional overhead: by allowing (i) dynamic allocation of...

Deep learning networks are typically trained by Stochastic Gradient Descent (SGD) methods that iteratively improve the model parameters by estimating a gradient on a very small fraction of the training data. A major roadblock faced when increasing the batch size to a substantial fraction of the training data for improving training time is the persi...

Decentralized stochastic optimization methods have gained a lot of attention recently, mainly because of their cheap per iteration cost, data locality, and their communication-efficiency. In this paper we introduce a unified convergence analysis that covers a large variety of decentralized SGD methods which so far have required different intuitions...

We study local SGD (also known as parallel SGD and federated averaging), a natural and frequently used stochastic distributed optimization method. Its theoretical foundations are currently lacking and we highlight how all existing error guarantees in the convex setting are dominated by a simple baseline, minibatch SGD. (1) For quadratic objectives...

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitiga...

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitiga...

Federated learning is a key scenario in modern large-scale machine learning. In that scenario, the training data remains distributed over a large number of clients, which may be phones, other mobile devices, or network sensors and a centralized model is learned without ever transmitting client data over the network. The standard optimization algori...

We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two terms: (i) a stochastic term which is not affected by the delay, and (ii) a higher order deterministic term which...

Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks, as well as for efficient scaling to large compute clusters. As current approaches suffer from limited bandwidth of the network, we propose the use of communication compression in the decentralized training context. We show...

In this note we give a simple proof for the convergence of stochastic gradient (SGD) methods on $\mu$-strongly convex functions under a (milder than standard) $L$-smoothness assumption. We show that SGD converges after $T$ iterations as $O\left( L \|x_0-x^\star\|^2 \exp \bigl[-\frac{\mu}{4L}T \bigr] + \frac{\sigma^2}{\mu T} \right)$ where $\sigma^2...

We consider distributed optimization where the objective function is spread among different devices, each sending incremental model updates to a central server. To alleviate the communication bottleneck, recent work proposed various schemes to compress (e.g.\ quantize or sparsify) the gradients, thereby introducing additional variance $\omega \geq...

We consider decentralized stochastic optimization with the objective function (e.g. data samples for machine learning task) being distributed over $n$ machines that can only communicate to their neighbors on a fixed communication graph. To reduce the communication bottleneck, the nodes compress (e.g. quantize or sparsify) their model updates. We co...

Sign-based algorithms (e.g. signSGD) have been proposed as a biased gradient compression technique to alleviate the communication bottleneck in training large neural networks across multiple workers. We show simple convex counter-examples where signSGD does not converge to the optimum. Further, even when it does converge, signSGD may generalize poo...

Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension $n$, and requiring upto $n$ times fewer iterations. In this paper, we consider greedy updates...

Huge scale machine learning problems are nowadays tackled by distributed optimization algorithms, i.e. algorithms that leverage the compute power of many devices for training. The communication overhead is a key bottleneck that hinders perfect scalability. Various recent works proposed to use quantization or sparsification techniques to reduce the...

Mini-batch stochastic gradient methods are the current state of the art for large-scale distributed training of neural networks and other machine learning models. However, they fail to adapt to a changing communication vs computation trade-off in a system, such as when scaling to a large number of workers or devices. More so, the fixed requirement...

We show that Newton's method converges globally at a linear rate for objective functions whose Hessians are stable. This class of problems includes many functions which are not strongly convex, such as logistic regression. Our linear convergence result is (i) affine-invariant, and holds even if an (ii) approximate Hessian is used, and if the subpro...

Mini-batch stochastic gradient descent (SGD) is the state of the art in large scale parallel machine learning, but its scalability is limited by a communication bottleneck. Recent work proposed local SGD, i.e. running SGD independently in parallel on different workers and averaging only once in a while. This scheme shows promising results in practi...

In recent years, many variance reduced algorithms for empirical risk minimization have been introduced. In contrast to vanilla SGD, these methods converge linearly on strong convex problems. To obtain the variance reduction, current methods either require frequent passes over the full data to recompute gradients---without making any progress during...

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we p...

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices in such a way that all iterates (approximate solutions) generated by the algorithm are positive...

Importance sampling has become an indispensable strategy to speed up optimization algorithms for large-scale applications. Improved adaptive variants - using importance values defined by the complete gradient information which changes during optimization - enjoy favorable theoretical properties, but are typically computationally infeasible. In this...

We propose a new selection rule for the coordinate selection in coordinate descent methods for huge-scale optimization. The efficiency of this novel scheme is provably better than the efficiency of uniformly random selection, and can reach the efficiency of steepest coordinate descent (SCD), enabling an acceleration of a factor of up to $n$, the nu...

Let P be a finite point set in the plane. A c-ordinary triangle in P is a subset of P consisting of three non-collinear points such that each of the three lines determined by the three points contains at most c points of P. Motivated by a question of Erdős, and answering a question of de Zeeuw, we prove that there exists a constant c>0 such that P...

Let $P$ be a finite point set in the plane. A \emph{$c$-ordinary triangle} in $P$ is a subset of $P$ consisting of three non-collinear points such that each of the three lines determined by the three points contains at most $c$ points of $P$. Motivated by a question of Erd\H{o}s, and answering a question of de Zeeuw, we prove that there exists a co...

In this paper we prove a new complexity bound for a variant of Accelerated Coordinate Descent Method [7]. We show that this method often outperforms the standard Fast Gradient Methods (FGM, [3, 6]) on optimization problems with dense data. In many important situations, the computational expenses of oracle and method itself at each iteration of our...

Recently it was shown by Nesterov (2011) that techniques form convex optimization can be used to successfully accelerate simple derivative-free randomized optimization methods. The appeal of those schemes lies in their low complexity, which is only Θ(n) per iteration—compared to Θ(n 2) for algorithms storing second-order information or covariance m...

We consider the problem of continuum armed bandits where the arms are indexed by a compact subset of \(\mathbb {R}^{d}\). For large d, it is well known that mere smoothness assumptions on the reward functions lead to regret bounds that suffer from the curse of dimensionality. A typical way to tackle this in the literature has been to make further a...

Recently it was shown by Nesterov (2011) that techniques form convex optimization can be used to successfully accelerate simple derivative-free randomized optimization methods. The appeal of those schemes lies in their low complexity, which is only $\Theta(n)$ per iteration---compared to $\Theta(n^2)$ for algorithms storing second-order information...

We consider a stochastic continuum armed bandit problem where the arms are indexed by the $\ell_2$ ball $B_{d}(1+r)$ of radius $1+r$ in $\mathbb{R}^d$. The reward functions $r :B_{d}(1+r) \rightarrow \mathbb{R}$ are considered to intrinsically depend on $k \ll d$ unknown linear parameters so that $r(\mathbf{x}) = g(\mathbf{A} \mathbf{x})$ where $\m...

We consider unconstrained randomized optimization of smooth convex objective functions in the gradient-free setting. We analyze Random Pursuit (RP) algorithms with fixed (F-RP) and variable metric (V-RP). The algorithms only use zeroth-order information about the objective function and compute an approximate solution by repeated optimization over r...

We evaluate the performance of several gradient-free variable-metric continuous optimization schemes on a specific set of quadratic functions. We revisit a randomized Hessian approximation scheme (D. Leventhal and A. S. Lewis. Randomized Hessian estimation and directional search, 2011), discuss its theoretical underpinnings, and introduce a novel,...

We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a randomly chosen one-dimensional subspace. This randomized method only uses zeroth-order information about the objecti...

We consider the fair Hamiltonian cycle Maker-Breaker game, played on the edge set of the complete graph Kn on n vertices. It is known that Maker wins this game if n is sucien tly large. We are interested in the minimum number of moves needed for Maker in order to win the Hamiltonian cycle game, and in the smallest n for which Maker has a winning st...