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Rachel Kalpana Kalaimani

Publications and source records attributed to Rachel Kalpana Kalaimani.

10 recordsLinked to original sources

Distributed Federated Learning by Alternating Periods of Training

Federated learning is a privacy-focused approach towards machine learning where models are trained on client devices with locally available data and aggregated at a central server. However, the dependence on a single central server is challenging in the case of a large number of clients and even poses the risk of a single point of failure. To address these critical limitations of scalability and fault-tolerance, we present a distributed approach to federated learning comprising multiple servers with inter-server communication capabilities. While providing a fully decentralized approach, the designed framework retains the core federated learning structure where each server is associated with a disjoint set of clients with server-client communication capabilities. We propose a novel DFL (Distributed Federated Learning) algorithm which uses alternating periods of local training on the client data followed by global training among servers. We show that the DFL algorithm, under a suitable choice of parameters, ensures that all the servers converge to a common model value within a small tolerance of the ideal model, thus exhibiting effective integration of local and global training models. Finally, we illustrate our theoretical claims through numerical simulations.

cs.LG↗

Optimal Pinning Control for Synchronization over Temporal Networks

In this paper, we address the finite time synchronization of a network of dynamical systems with time-varying interactions modeled using temporal networks. We synchronize a few nodes initially using external control inputs. These nodes are termed as pinning nodes. The other nodes are synchronized by interacting with the pinning nodes and with each other. We first provide sufficient conditions for the network to be synchronized. Then we formulate an optimization problem to minimize the number of pinning nodes for synchronizing the entire network. Finally, we address the problem of maximizing the number of synchronized nodes when there are constraints on the number of nodes that could be pinned. We show that this problem belongs to the class of NP-hard problems and propose a greedy heuristic. We illustrate the results using numerical simulations.

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Distributed ADMM with linear updates over directed networks

We propose a distributed version of the Alternating Direction Method of Multipliers (ADMM) with linear updates for directed networks. We show that if the objective function of the minimization problem is smooth and strongly convex, our distributed ADMM algorithm achieves a geometric rate of convergence to the optimal point. Our algorithm exploits the robustness inherent to ADMM by not enforcing accurate consensus, thereby significantly improving the convergence rate. We illustrate this by numerical examples, where we compare the performance of our algorithm with that of state-of-the-art ADMM methods over directed graphs.

math.OC↗

Online Distributed Algorithm for Optimal Power Flow problem with Regret Analysis

We investigate the distributed DC-Optimal Power Flow (DC-OPF) problem for a dynamic and uncertain environment. The unpredictable supply of renewable resources and varying prices of the electricity market are a few factors responsible for the uncertainty. We propose to address this problem using the framework of online convex optimization, where the cost functions are not known apriori because of the uncertainty and are revealed only incrementally over time. We also consider a distributed setting, where each agent (generators and loads) in the power network is only privy to their own local objectives and constraints but can communicate with their neighbours. A distributed online algorithm is proposed based on the modified primal-dual approach. The performance of the online algorithm is evaluated using the regret (static) function, which is the difference between the actual cost incurred by employing the proposed algorithm and the optimal fixed decision in hindsight. Since we deal with a constrained optimization problem, analogous to the notion of regret the accumulation of the constraint violation is also calculated at each step. We establish a sub-linear bound on the static regret and constraint violation under suitable assumptions on step-size and cost function. Finally, we use the standard IEEE-14 bus system to demonstrate the performance of our algorithm.

math.OC↗

Resilient Dynamic Average Consensus based on Trusted agents

In this paper, we address the discrete-time dynamic average consensus (DAC) of a multi-agent system in the presence of adversarial attacks. The adversarial attack is considered to be of Byzantine type, which compromises the computation capabilities of the agent and sends arbitrary false data to its neighbours. We assume a few of the agents cannot be compromised by adversaries, which we term trusted agents. We first formally define resilient DAC in the presence of Byzantine adversaries. Then we propose our novel Resilient Dynamic Average Consensus (ResDAC) algorithm that ensures the trusted and ordinary agents achieve resilient DAC in the presence of adversarial agents. The only requirements are that of the trusted agents forming a connected dominating set and the first-order differences of the reference signals being bounded. We do not impose any restriction on the tolerable number of adversarial agents that can be present in the network. We also do not restrict the reference signals to be bounded. Finally, we provide numerical simulations to illustrate the effectiveness of the proposed ResDAC algorithm.

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Distributed Estimation over Directed Graphs Resilient to Sensor Spoofing

This paper addresses the problem of distributed estimation of an unknown dynamic parameter by a multi-agent system over a directed communication network in the presence of an adversarial attack on the agents' sensors. The mode of attack of the adversaries is to corrupt the sensor measurements of some of the agents, while the communication and information processing capabilities of those agents remain unaffected. To ensure that all the agents, both normal as well as those under attack, are able to correctly estimate the parameter value, the Resilient Estimation through Weight Balancing (REWB) algorithm is introduced. The only condition required for the REWB algorithm to guarantee resilient estimation is that at any given point in time, less than half of the total number of agents are under attack. The paper discusses the development of the REWB algorithm using the concepts of weight balancing of directed graphs, and the consensus+innovations approach for linear estimation. Numerical simulations are presented to illustrate the performance of our algorithm over directed graphs under different conditions of adversarial attacks.

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ADMM based Distributed State Observer Design under Sparse Sensor Attacks

This paper considers the design of a distributed state-observer for discrete-time Linear Time-Invariant (LTI) systems in the presence of sensor attacks. We assume there is a network of observer nodes, communicating with each other over an undirected graph, each with partial measurements of the output corrupted by some adversarial attack. We address the case of sparse attacks where the attacker targets a small subset of sensors. An algorithm based on Alternating Direction Method of Multipliers (ADMM) is developed which provides an update law for each observer which ensures convergence of each observer node to the actual state asymptotically.

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Distributed Online Optimization with Byzantine Adversarial Agents

We study the problem of non-constrained, discrete-time, online distributed optimization in a multi-agent system where some of the agents do not follow the prescribed update rule either due to failures or malicious intentions. None of the agents have prior information about the identities of the faulty agents and any agent can communicate only with its immediate neighbours. At each time step, a locally Lipschitz strongly convex cost function is revealed locally to all the agents and the non-faulty agents update their states using their local information and the information obtained from their neighbours. We measure the performance of the online algorithm by comparing it to its offline version, when the cost functions are known apriori. The difference between the same is termed as regret. Under sufficient conditions on the graph topology, the number and location of the adversaries, the defined regret grows sublinearly. We further conduct numerical experiments to validate our theoretical results.

math.OC↗

Distributed Optimization of Average Consensus Containment with Multiple Stationary Leaders

In this paper, we consider the problem of containment control of multi-agent systems with multiple stationary leaders, interacting over a directed network. While, containment control refers to just ensuring that the follower agents reach the convex hull of the leaders states, we focus on the problem where the followers achieve a consensus to the average values of the leaders states. We propose an algorithm that can be implemented in a distributed manner to achieve the above consensus among followers. Next we optimize the convergence rate of the followers to the average consensus by proper choice of weights for the interaction graph. This optimization is also performed in a distributed manner using Alternating Direction Method of Multipliers (ADMM). Finally, we complement our results by illustrating them with numerical examples.

math.OC↗

Distributed computation of fast consensus weights using ADMM

We consider the problem of achieving average consensus among multiple agents, where the inter-agent communication network is depicted by a graph. We consider the discrete-time consensus protocol where each agent updates its value as a weighted average of its own value and those of its neighbours. Given a graph, it is known that there exists a set of 'optimal weights' such that the agents reach average consensus asymptotically with an optimal rate of convergence. However, existing methods require the knowledge of the entire graph to compute these optimal weights. We propose a method for each agent to compute its set of optimal weights locally, i.e., each agent only has to know who are its neighbours. The method is derived by solving a matrix norm minimization problem subject to linear constraints in a distributed manner using the Alternating Direction Method of Multipliers (ADMM). We illustrate our results using numerical examples and compare our method with an existing method called the Metropolis weights, which are also computed locally.

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