Cihan Tepedelenlioglu

Sai Zhang, Cihan Tepedelenlioglu, Mahesh K. Banavar et al.

A distributed consensus algorithm for estimating the maximum value of the initial measurements in a sensor network with communication noise is proposed. In the absence of communication noise, max estimation can be done by updating the state value with the largest received measurements in every iteration at each sensor. In the presence of communication noise, however, the maximum estimate will incorrectly drift and the estimate at each sensor will diverge. As a result, a soft-max approximation together with a non-linear consensus algorithm is introduced herein. A design parameter controls the trade-off between the soft-max error and convergence speed. An analysis of this trade-off gives a guideline towards how to choose the design parameter for the max estimate. We also show that if some prior knowledge of the initial measurements is available, the consensus process can converge faster by using an optimal step size in the iterative algorithm. A shifted non-linear bounded transmit function is also introduced for faster convergence when sensor nodes have some prior knowledge of the initial measurements. Simulation results corroborating the theory are also provided.

Gowtham Muniraju, Cihan Tepedelenlioglu, Andreas Spanias

A novel distributed algorithm for estimating the maximum of the node initial state values in a network, in the presence of additive communication noise is proposed. Conventionally, the maximum is estimated locally at each node by updating the node state value with the largest received measurements in every iteration. However, due to the additive channel noise, the estimate of the maximum at each node drifts at each iteration and this results in nodes diverging from the true max value. Max-plus algebra is used as a tool to study this ergodic process. The subadditive ergodic theorem is invoked to establish a constant growth rate for the state values due to noise, which is studied by analyzing the max-plus Lyapunov exponent of the product of noise matrices in a max-plus semiring. The growth rate of the state values is upper bounded by a constant which depends on the spectral radius of the network and the noise variance. Upper and lower bounds are derived for both fixed and random graphs. Finally, a two-run algorithm robust to additive noise in the network is proposed and its variance is analyzed using concentration inequalities. Simulation results supporting the theory are also presented.

Sivaraman Dasarathan, Cihan Tepedelenlioglu, Mahesh Banavar et al.

A distributed average consensus algorithm robust to a wide range of impulsive channel noise distributions is proposed. This work is the first of its kind in the literature to propose a consensus algorithm which relaxes the requirement of finite moments on the communication noise. It is shown that the nodes reach consensus asymptotically to a finite random variable whose expectation is the desired sample average of the initial observations with a variance that depends on the step size of the algorithm and the receiver nonlinear function. The asymptotic performance is characterized by deriving the asymptotic covariance matrix using results from stochastic approximation theory. Simulations corroborate our analytical findings and highlight the robustness of the proposed algorithm.

Jongmin Lee, Cihan Tepedelenlioglu, Andreas Spanias

A quantile is defined as a value below which random draws from a given distribution falls with a given probability. In a centralized setting where the cumulative distribution function (CDF) is unknown, the empirical CDF (ECDF) can be used to estimate such quantiles after aggregating the data. In a fully distributed sensor network, however, it is challenging to estimate quantiles. This is because each sensor node observes local measurement data with limited storage and data transmission power which make it difficult to obtain the global ECDF. This paper proposes consensus-based quantile estimation for such a distributed network. The states of the proposed algorithm are recursively updated with two-steps at each iteration: one is a local update based on the measurement data and the current state, and the other is averaging the updated states with neighboring nodes. We consider the realistic case of communication links between nodes being corrupted by independent random noise. It is shown that the estimated state sequence is asymptotically unbiased and converges toward the sample quantile in the mean-square sense. The two step-size sequences corresponding to the averaging and local update steps result in a mixed-time scale algorithm with proper decay rates in order to achieve convergence. We also provide applications to distributed estimation of trimmed mean, computation of median, maximum, or minimum values and identification of outliers through simulation.

Abdullah Basar Akbay, Cihan Tepedelenlioglu

This study considers a federated learning setup where cost-sensitive and strategic agents train a learning model with a server. During each round, each agent samples a minibatch of training data and sends his gradient update. As an increasing function of his minibatch size choice, the agent incurs a cost associated with the data collection, gradient computation and communication. The agents have the freedom to choose their minibatch size and may even opt out from training. To reduce his cost, an agent may diminish his minibatch size, which may also cause an increase in the noise level of the gradient update. The server can offer rewards to compensate the agents for their costs and to incentivize their participation but she lacks the capability of validating the true minibatch sizes of the agents. To tackle this challenge, the proposed reward mechanism evaluates the quality of each agent's gradient according to the its distance to a reference which is constructed from the gradients provided by other agents. It is shown that the proposed reward mechanism has a cooperative Nash equilibrium in which the agents determine the minibatch size choices according to the requests of the server.

Gowtham Muniraju, Bhavya Kailkhura, Jayaraman J. Thiagarajan et al.

Sampling one or more effective solutions from large search spaces is a recurring idea in machine learning, and sequential optimization has become a popular solution. Typical examples include data summarization, sample mining for predictive modeling and hyper-parameter optimization. Existing solutions attempt to adaptively trade-off between global exploration and local exploitation, wherein the initial exploratory sample is critical to their success. While discrepancy-based samples have become the de facto approach for exploration, results from computer graphics suggest that coverage-based designs, e.g. Poisson disk sampling, can be a superior alternative. In order to successfully adopt coverage-based sample designs to ML applications, which were originally developed for 2-d image analysis, we propose fundamental advances by constructing a parameterized family of designs with provably improved coverage characteristics, and by developing algorithms for effective sample synthesis. Using experiments in sample mining and hyper-parameter optimization for supervised learning, we show that our approach consistently outperforms existing exploratory sampling methods in both blind exploration, and sequential search with Bayesian optimization.