In this paper, we consider the Byzantine-robust stochastic optimization problem defined over decentralized static and time-varying networks, where the agents collaboratively minimize the summation of expectations of stochastic local cost functions, but some of the agents are unreliable due to data corruptions, equipment failures or cyber-attacks. The unreliable agents, which are called as Byzantine agents thereafter, can send faulty values to their neighbors and bias the optimization process. Our key idea to handle the Byzantine attacks is to formulate a total variation (TV) norm-penalized approximation of the Byzantine-free problem, where the penalty term forces the local models of regular agents to be close, but also allows the existence of outliers from the Byzantine agents. A stochastic subgradient method is applied to solve the penalized problem. We prove that the proposed method reaches a neighborhood of the Byzantine-free optimal solution, and the size of neighborhood is determined by the number of Byzantine agents and the network topology. Numerical experiments corroborate the theoretical analysis, as well as demonstrate the robustness of the proposed method to Byzantine attacks and its superior performance comparing to existing methods.
Distributed machine learning algorithms enable learning of models from datasets that are distributed over a network without gathering the data at a centralized location. While efficient distributed algorithms have been developed under the assumption of faultless networks, failures that can render these algorithms nonfunctional occur frequently in the real world. This paper focuses on the problem of Byzantine failures, which are the hardest to safeguard against in distributed algorithms. While Byzantine fault tolerance has a rich history, existing work does not translate into efficient and prac…
This paper considers the policy evaluation problem in a multi-agent reinforcement learning (MARL) environment over decentralized and directed networks. The focus is on decentralized temporal difference (TD) learning with linear function approximation in the presence of unreliable or even malicious agents, termed as Byzantine agents. In order to evaluate the quality of a fixed policy in a common environment, agents usually run decentralized TD($λ$) collaboratively. However, when some Byzantine agents behave adversarially, decentralized TD($λ$) is unable to learn an accurate linear approximation…
Resilient Decentralized Preconditioned Stochastic Proximal Optimization with Gradient Sketching over Time-Varying Networks
Hubei Normal University（湖北师范大学）；City University of Hong Kong（香港城市大学）；University of New South Wales（新南威尔士大学）；Southwest University（西南大学）；Shenzhen University of Advanced Technology（深圳先进技术研究院）
Prox-DBRO-VR: A Unified Analysis on Byzantine-Resilient Decentralized Stochastic Composite Optimization with Variance Reduction and Non-Asymptotic Convergence Rates
Central South University（中南大学）；City University of Hong Kong（香港城市大学）；University of New South Wales（新南威尔士大学）；Southwest University（西南大学）
The Ohio State University（俄亥俄州立大学）；Iowa State University（爱荷华州立大学）；University of Minnesota（明尼苏达大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
In recent years, decentralized bilevel optimization problems have received increasing attention in the networking and machine learning communities thanks to their versatility in modeling decentralized learning problems over peer-to-peer networks (e.g., multi-agent meta-learning, multi-agent reinforcement learning, personalized training, and Byzantine-resilient learning). However, for decentralized bilevel optimization over peer-to-peer networks with limited computation and communication capabilities, how to achieve low sample and communication complexities are two fundamental challenges that r…
This paper investigates the design of decentralized output-feedback controllers for a class of a large scale switched nonlinear systems under arbitrary switching laws. A global large scale switched system can be split into a set of smaller interconnected switched Takagi Sugeno fuzzy subsystems. Then, in order to stabilize the overall closed-loop system, a set of switched non-PDC static output controllers is employed. The latter is designed based on Linear Matrix Inequality (LMI) conditions obtained from a multiple switched non quadratic-like Lyapunov candidate function. The controllers propose…
In this paper we generalized static team theory to dynamic team theory, in the context of stochastic differential decision system with decentralized noiseless feedback information structures. We apply Girsanov's theorem to transformed the initial stochastic dynamic team problem to an equivalent team problem, under a reference probability space, with state process and information structures independent of any of the team decisions. Subsequently, we show, under certain conditions, that continuous-time and discrete-time stochastic dynamic team problems, can be transformed to equivalent static tea…
In important applications involving multi-task networks with multiple objectives, agents in the network need to decide between these multiple objectives and reach an agreement about which single objective to follow for the network. In this work we propose a distributed decision-making algorithm. The agents are assumed to observe data that may be generated by different models. Through localized interactions, the agents reach agreement about which model to track and interact with each other in order to enhance the network performance. We investigate the approach for both static and mobile networ…
For sequential stochastic control problems with standard Borel measurement and control action spaces, we introduce a general (universally applicable) dynamic programming formulation, establish its well-posedness, and provide new existence results for optimal policies. Our dynamic program builds in part on Witsenhausen's standard form, but with a different formulation for the state, action, and transition dynamics. Using recent results on measurability properties of strategic measures in decentralized control, we obtain a standard Borel controlled Markov model. This allows for a well-defined dy…
Decentralized control of mobile robotic sensor networks is a fundamental problem in robotics that has attracted intensive research in recent decades. Most of the existing works dealt with two-dimensional spaces. This report is concerned with the problem of decentralized self-deployment of mobile robotic sensor networks in three-dimensional environments. The first part of the report investigates the problem of complete sensing coverage in three-dimensional spaces. We propose a decentralized random algorithm to drive mobile robotic sensors on the vertices of a truncated octahedral grid for compl…
We study the decentralized consensus and stochastic optimization problems with compressed communications over static directed graphs. We propose an iterative gradient-based algorithm that compresses messages according to a desired compression ratio. The proposed method provably reduces the communication overhead on the network at every communication round. Contrary to existing literature, we allow for arbitrary compression ratios in the communicated messages. We show a linear convergence rate for the proposed method on the consensus problem. Moreover, we provide explicit convergence rates for …
