Diffusion Learning with Partial Agent Participation and Local Updates

Diffusion learning is a framework that endows edge devices with advanced intelligence. By processing and analyzing data locally and allowing each agent to communicate with its immediate neighbors, diffusion effectively protects the privacy of edge devices, enables real-time response, and reduces reliance on central servers. However, traditional diffusion learning relies on communication at every iteration, leading to communication overhead, especially with large learning models. Furthermore, the inherent volatility of edge devices, stemming from power outages or signal loss, poses challenges to reliable communication between neighboring agents. To mitigate these issues, this paper investigates an enhanced diffusion learning approach incorporating local updates and partial agent participation. Local updates will curtail communication frequency, while partial agent participation will allow for the inclusion of agents based on their availability. We prove that the resulting algorithm is stable in the mean-square error sense and provide a tight analysis of its Mean-Square-Deviation (MSD) performance. Various numerical experiments are conducted to illustrate our theoretical findings.

Diffusion Stochastic Learning Over Adaptive Competing Networks

This paper studies a stochastic dynamic game between two competing teams, each consisting of a network of collaborating agents. Unlike fully cooperative settings, where all agents share a common objective, each team in this game aims to minimize its own distinct objective. In the adversarial setting, their objectives could be conflicting as in zero-sum games. Throughout the competition, agents share strategic information within their own team while simultaneously inferring and adapting to the strategies of the opposing team. We propose diffusion learning algorithms to address two important classes of this network game: i) a zero-sum game characterized by weak cross-team subgraph interactions, and ii) a general non-zero-sum game exhibiting strong cross-team subgraph interactions. We analyze the stability performance of the proposed algorithms under reasonable assumptions and illustrate the theoretical results through experiments on Cournot team competition and decentralized GAN training.

Doubly Adaptive Social Learning

In social learning, a network of agents assigns probability scores (beliefs) to some hypotheses of interest, which rule the generation of local streaming data observed by each agent. Belief formation takes place by means of an iterative two-step procedure where: i) the agents update locally their beliefs by using some likelihood model; and ii) the updated beliefs are combined with the beliefs of the neighboring agents, using a pooling rule. This procedure can fail to perform well in the presence of dynamic drifts, leading the agents to incorrect decision making. Here, we focus on the fully online setting where both the true hypothesis and the likelihood models can change over time. We propose the doubly adaptive social learning ($\text{A}^2\text{SL}$) strategy, which infuses social learning with the necessary adaptation capabilities. This goal is achieved by exploiting two adaptation stages: i) a stochastic gradient descent update to learn and track the drifts in the decision model; ii) and an adaptive belief update to track the true hypothesis changing over time. These stages are controlled by two adaptation parameters that govern the evolution of the error probability for each agent. We show that all agents learn consistently for sufficiently small adaptation parameters, in the sense that they ultimately place all their belief mass on the true hypothesis. In particular, the probability of choosing the wrong hypothesis converges to values on the order of the adaptation parameters. The theoretical analysis is illustrated both on synthetic data and by applying the $\text{A}^2\text{SL}$ strategy to a social learning problem in the online setting using real data.

Multi-agent Off-policy Actor-Critic Reinforcement Learning for Partially Observable Environments

This study proposes the use of a social learning method to estimate a global state within a multi-agent off-policy actor-critic algorithm for reinforcement learning (RL) operating in a partially observable environment. We assume that the network of agents operates in a fully-decentralized manner, possessing the capability to exchange variables with their immediate neighbors. The proposed design methodology is supported by an analysis demonstrating that the difference between final outcomes, obtained when the global state is fully observed versus estimated through the social learning method, is $\varepsilon$-bounded when an appropriate number of iterations of social learning updates are implemented. Unlike many existing dec-POMDP-based RL approaches, the proposed algorithm is suitable for model-free multi-agent reinforcement learning as it does not require knowledge of a transition model. Furthermore, experimental results illustrate the efficacy of the algorithm and demonstrate its superiority over the current state-of-the-art methods.

On the Trade-off between Flatness and Optimization in Distributed Learning

This paper proposes a theoretical framework to evaluate and compare the performance of gradient-descent algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have noticed that convergence toward flat local minima tend to enhance the generalization ability of learning algorithms. This work discovers two interesting results. First, it shows that decentralized learning strategies are able to escape faster away from local minimizers and favor convergence toward flatter minima relative to the centralized solution in the large-batch training regime. Second, and importantly, the ultimate classification accuracy is not solely dependent on the flatness of the local minimizer but also on how well a learning algorithm can approach that minimum. In other words, the classification accuracy is a function of both flatness and optimization performance. The paper examines the interplay between the two measures of flatness and optimization error closely. One important conclusion is that decentralized strategies of the diffusion type deliver enhanced classification accuracy because it strikes a more favorable balance between flatness and optimization performance.

Differential error feedback for communication-efficient decentralized learning

Communication-constrained algorithms for decentralized learning and optimization rely on local updates coupled with the exchange of compressed signals. In this context, differential quantization is an effective technique to mitigate the negative impact of compression by leveraging correlations between successive iterates. In addition, the use of error feedback, which consists of incorporating the compression error into subsequent steps, is a powerful mechanism to compensate for the bias caused by the compression. Under error feedback, performance guarantees in the literature have so far focused on algorithms employing a fusion center or a special class of contractive compressors that cannot be implemented with a finite number of bits. In this work, we propose a new decentralized communication-efficient learning approach that blends differential quantization with error feedback. The approach is specifically tailored for decentralized learning problems where agents have individual risk functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This constrained formulation includes consensus or single-task optimization as special cases, and allows for more general task relatedness models such as multitask smoothness and coupled optimization. We show that, under some general conditions on the compression noise, and for sufficiently small step-sizes $\mu$, the resulting communication-efficient strategy is stable both in terms of mean-square error and average bit rate: by reducing $\mu$, it is possible to keep the estimation errors small (on the order of $\mu$) without increasing indefinitely the bit rate as $\mu\rightarrow 0$. The results establish that, in the small step-size regime and with a finite number of bits, it is possible to attain the performance achievable in the absence of compression.

Accelerated Stochastic Min-Max Optimization Based on Bias-corrected Momentum

Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ oracle complexity to find an $\varepsilon$-stationary point. Some works indicate that this complexity can be improved to $\mathcal{O}(\varepsilon^{-3})$ when the loss gradient is Lipschitz continuous. The question of achieving enhanced convergence rates under distinct conditions, remains unresolved. In this work, we address this question for optimization problems that are nonconvex in the minimization variable and strongly concave or Polyak-Lojasiewicz (PL) in the maximization variable. We introduce novel bias-corrected momentum algorithms utilizing efficient Hessian-vector products. We establish convergence conditions and demonstrate a lower iteration complexity of $\mathcal{O}(\varepsilon^{-3})$ for the proposed algorithms. The effectiveness of the method is validated through applications to robust logistic regression using real-world datasets.

Causal Influence in Federated Edge Inference

In this paper, we consider a setting where heterogeneous agents with connectivity are performing inference using unlabeled streaming data. Observed data are only partially informative about the target variable of interest. In order to overcome the uncertainty, agents cooperate with each other by exchanging their local inferences with and through a fusion center. To evaluate how each agent influences the overall decision, we adopt a causal framework in order to distinguish the actual influence of agents from mere correlations within the decision-making process. Various scenarios reflecting different agent participation patterns and fusion center policies are investigated. We derive expressions to quantify the causal impact of each agent on the joint decision, which could be beneficial for anticipating and addressing atypical scenarios, such as adversarial attacks or system malfunctions. We validate our theoretical results with numerical simulations and a real-world application of multi-camera crowd counting.

Detection of Malicious Agents in Social Learning

Social learning is a non-Bayesian framework for distributed hypothesis testing aimed at learning the true state of the environment. Traditionally, the agents are assumed to receive observations conditioned on the same true state, although it is also possible to examine the case of heterogeneous models across the graph. One important special case is when heterogeneity is caused by the presence of malicious agents whose goal is to move the agents towards a wrong hypothesis. In this work, we propose an algorithm that allows to discover the true state of every individual agent based on the sequence of their beliefs. In so doing, the methodology is also able to locate malicious behavior.

Asynchronous Diffusion Learning with Agent Subsampling and Local Updates

In this work, we examine a network of agents operating asynchronously, aiming to discover an ideal global model that suits individual local datasets. Our assumption is that each agent independently chooses when to participate throughout the algorithm and the specific subset of its neighbourhood with which it will cooperate at any given moment. When an agent chooses to take part, it undergoes multiple local updates before conveying its outcomes to the sub-sampled neighbourhood. Under this setup, we prove that the resulting asynchronous diffusion strategy is stable in the mean-square error sense and provide performance guarantees specifically for the federated learning setting. We illustrate the findings with numerical simulations.