AdaGossip: Adaptive Consensus Step-size for Decentralized Deep Learning with Communication Compression

Decentralized learning is crucial in supporting on-device learning over large distributed datasets, eliminating the need for a central server. However, the communication overhead remains a major bottleneck for the practical realization of such decentralized setups. To tackle this issue, several algorithms for decentralized training with compressed communication have been proposed in the literature. Most of these algorithms introduce an additional hyper-parameter referred to as consensus step-size which is tuned based on the compression ratio at the beginning of the training. In this work, we propose AdaGossip, a novel technique that adaptively adjusts the consensus step-size based on the compressed model differences between neighboring agents. We demonstrate the effectiveness of the proposed method through an exhaustive set of experiments on various Computer Vision datasets (CIFAR-10, CIFAR-100, Fashion MNIST, Imagenette, and ImageNet), model architectures, and network topologies. Our experiments show that the proposed method achieves superior performance ($0-2\%$ improvement in test accuracy) compared to the current state-of-the-art method for decentralized learning with communication compression.

Randomized Greedy Methods for Weak Submodular Sensor Selection with Robustness Considerations

We study a pair of budget- and performance-constrained weak submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the standard greedy procedure which explores the entire feasible search space. We propose a pair of stochastic greedy algorithms, namely, Modified Randomized Greedy (MRG) and Dual Randomized Greedy (DRG) to approximately solve the budget- and performance-constrained problems, respectively. For both algorithms, we derive approximation guarantees that hold with high probability. We then examine the use of DRG in robust optimization problems wherein the objective is to maximize the worst-case of a number of weak submodular objectives and propose the Randomized Weak Submodular Saturation Algorithm (Random-WSSA). We further derive a high-probability guarantee for when Random-WSSA successfully constructs a robust solution. Finally, we showcase the effectiveness of these algorithms in a variety of relevant uses within the context of Earth-observing LEO constellations which estimate atmospheric weather conditions and provide Earth coverage.

Localized Distributional Robustness in Submodular Multi-Task Subset Selection

In this work, we approach the problem of multi-task submodular optimization with the perspective of local distributional robustness, within the neighborhood of a reference distribution which assigns an importance score to each task. We initially propose to introduce a regularization term which makes use of the relative entropy to the standard multi-task objective. We then demonstrate through duality that this novel formulation itself is equivalent to the maximization of a submodular function, which may be efficiently carried out through standard greedy selection methods. This approach bridges the existing gap in the optimization of performance-robustness trade-offs in multi-task subset selection. To numerically validate our theoretical results, we test the proposed method in two different setting, one involving the selection of satellites in low Earth orbit constellations in the context of a sensor selection problem, and the other involving an image summarization task using neural networks. Our method is compared with two other algorithms focused on optimizing the performance of the worst-case task, and on directly optimizing the performance on the reference distribution itself. We conclude that our novel formulation produces a solution that is locally distributional robust, and computationally inexpensive.

FedNMUT -- Federated Noisy Model Update Tracking Convergence Analysis

A novel Decentralized Noisy Model Update Tracking Federated Learning algorithm (FedNMUT) is proposed that is tailored to function efficiently in the presence of noisy communication channels that reflect imperfect information exchange. This algorithm uses gradient tracking to minimize the impact of data heterogeneity while minimizing communication overhead. The proposed algorithm incorporates noise into its parameters to mimic the conditions of noisy communication channels, thereby enabling consensus among clients through a communication graph topology in such challenging environments. FedNMUT prioritizes parameter sharing and noise incorporation to increase the resilience of decentralized learning systems against noisy communications. Theoretical results for the smooth non-convex objective function are provided by us, and it is shown that the $\epsilon-$stationary solution is achieved by our algorithm at the rate of $\mathcal{O}\left(\frac{1}{\sqrt{T}}\right)$, where $T$ is the total number of communication rounds. Additionally, via empirical validation, we demonstrated that the performance of FedNMUT is superior to the existing state-of-the-art methods and conventional parameter-mixing approaches in dealing with imperfect information sharing. This proves the capability of the proposed algorithm to counteract the negative effects of communication noise in a decentralized learning framework.

Unveiling Privacy, Memorization, and Input Curvature Links

Deep Neural Nets (DNNs) have become a pervasive tool for solving many emerging problems. However, they tend to overfit to and memorize the training set. Memorization is of keen interest since it is closely related to several concepts such as generalization, noisy learning, and privacy. To study memorization, Feldman (2019) proposed a formal score, however its computational requirements limit its practical use. Recent research has shown empirical evidence linking input loss curvature (measured by the trace of the loss Hessian w.r.t inputs) and memorization. It was shown to be ~3 orders of magnitude more efficient than calculating the memorization score. However, there is a lack of theoretical understanding linking memorization with input loss curvature. In this paper, we not only investigate this connection but also extend our analysis to establish theoretical links between differential privacy, memorization, and input loss curvature. First, we derive an upper bound on memorization characterized by both differential privacy and input loss curvature. Second, we present a novel insight showing that input loss curvature is upper-bounded by the differential privacy parameter. Our theoretical findings are further empirically validated using deep models on CIFAR and ImageNet datasets, showing a strong correlation between our theoretical predictions and results observed in practice.

Improved Convergence Analysis and SNR Control Strategies for Federated Learning in the Presence of Noise

We propose an improved convergence analysis technique that characterizes the distributed learning paradigm of federated learning (FL) with imperfect/noisy uplink and downlink communications. Such imperfect communication scenarios arise in the practical deployment of FL in emerging communication systems and protocols. The analysis developed in this paper demonstrates, for the first time, that there is an asymmetry in the detrimental effects of uplink and downlink communications in FL. In particular, the adverse effect of the downlink noise is more severe on the convergence of FL algorithms. Using this insight, we propose improved Signal-to-Noise (SNR) control strategies that, discarding the negligible higher-order terms, lead to a similar convergence rate for FL as in the case of a perfect, noise-free communication channel while incurring significantly less power resources compared to existing solutions. In particular, we establish that to maintain the $O(\frac{1}{\sqrt{K}})$ rate of convergence like in the case of noise-free FL, we need to scale down the uplink and downlink noise by $\Omega({\sqrt{k}})$ and $\Omega({k})$ respectively, where $k$ denotes the communication round, $k=1,\dots, K$. Our theoretical result is further characterized by two major benefits: firstly, it does not assume the somewhat unrealistic assumption of bounded client dissimilarity, and secondly, it only requires smooth non-convex loss functions, a function class better suited for modern machine learning and deep learning models. We also perform extensive empirical analysis to verify the validity of our theoretical findings.

Communication-Efficient Zeroth-Order Distributed Online Optimization: Algorithm, Theory, and Applications

This paper focuses on a multi-agent zeroth-order online optimization problem in a federated learning setting for target tracking. The agents only sense their current distances to their targets and aim to maintain a minimum safe distance from each other to prevent collisions. The coordination among the agents and dissemination of collision-prevention information is managed by a central server using the federated learning paradigm. The proposed formulation leads to an instance of distributed online nonconvex optimization problem that is solved via a group of communication-constrained agents. To deal with the communication limitations of the agents, an error feedback-based compression scheme is utilized for agent-to-server communication. The proposed algorithm is analyzed theoretically for the general class of distributed online nonconvex optimization problems. We provide non-asymptotic convergence rates that show the dominant term is independent of the characteristics of the compression scheme. Our theoretical results feature a new approach that employs significantly more relaxed assumptions in comparison to standard literature. The performance of the proposed solution is further analyzed numerically in terms of tracking errors and collisions between agents in two relevant applications.

Global Update Tracking: A Decentralized Learning Algorithm for Heterogeneous Data

Decentralized learning enables the training of deep learning models over large distributed datasets generated at different locations, without the need for a central server. However, in practical scenarios, the data distribution across these devices can be significantly different, leading to a degradation in model performance. In this paper, we focus on designing a decentralized learning algorithm that is less susceptible to variations in data distribution across devices. We propose Global Update Tracking (GUT), a novel tracking-based method that aims to mitigate the impact of heterogeneous data in decentralized learning without introducing any communication overhead. We demonstrate the effectiveness of the proposed technique through an exhaustive set of experiments on various Computer Vision datasets (CIFAR-10, CIFAR-100, Fashion MNIST, and ImageNette), model architectures, and network topologies. Our experiments show that the proposed method achieves state-of-the-art performance for decentralized learning on heterogeneous data via a $1-6\%$ improvement in test accuracy compared to other existing techniques.

On the Convergence of Decentralized Federated Learning Under Imperfect Information Sharing

Decentralized learning and optimization is a central problem in control that encompasses several existing and emerging applications, such as federated learning. While there exists a vast literature on this topic and most methods centered around the celebrated average-consensus paradigm, less attention has been devoted to scenarios where the communication between the agents may be imperfect. To this end, this paper presents three different algorithms of Decentralized Federated Learning (DFL) in the presence of imperfect information sharing modeled as noisy communication channels. The first algorithm, Federated Noisy Decentralized Learning (FedNDL1), comes from the literature, where the noise is added to their parameters to simulate the scenario of the presence of noisy communication channels. This algorithm shares parameters to form a consensus with the clients based on a communication graph topology through a noisy communication channel. The proposed second algorithm (FedNDL2) is similar to the first algorithm but with added noise to the parameters, and it performs the gossip averaging before the gradient optimization. The proposed third algorithm (FedNDL3), on the other hand, shares the gradients through noisy communication channels instead of the parameters. Theoretical and experimental results demonstrate that under imperfect information sharing, the third scheme that mixes gradients is more robust in the presence of a noisy channel compared with the algorithms from the literature that mix the parameters.

No-Regret Learning in Dynamic Stackelberg Games

In a Stackelberg game, a leader commits to a randomized strategy, and a follower chooses their best strategy in response. We consider an extension of a standard Stackelberg game, called a discrete-time dynamic Stackelberg game, that has an underlying state space that affects the leader's rewards and available strategies and evolves in a Markovian manner depending on both the leader and follower's selected strategies. Although standard Stackelberg games have been utilized to improve scheduling in security domains, their deployment is often limited by requiring complete information of the follower's utility function. In contrast, we consider scenarios where the follower's utility function is unknown to the leader; however, it can be linearly parameterized. Our objective then is to provide an algorithm that prescribes a randomized strategy to the leader at each step of the game based on observations of how the follower responded in previous steps. We design a no-regret learning algorithm that, with high probability, achieves a regret bound (when compared to the best policy in hindsight) which is sublinear in the number of time steps; the degree of sublinearity depends on the number of features representing the follower's utility function. The regret of the proposed learning algorithm is independent of the size of the state space and polynomial in the rest of the parameters of the game. We show that the proposed learning algorithm outperforms existing model-free reinforcement learning approaches.