Mehrdad Showkatbakhsh

Mehrdad Showkatbakhsh, Yasser Shoukry, Suhas Diggavi et al.

This paper discusses the problem of estimating the state of a linear time-invariant system when some of its sensors and actuators are compromised by an adversarial agent. In the model considered in this paper, the malicious agent attacks an input (output) by manipulating its value arbitrarily, i.e., we impose no constraints (statistical or otherwise) on how control commands (sensor measurements) are changed by the adversary. In the first part of this paper, we introduce the notion of sparse strong observability and we show that is a necessary and sufficient condition for correctly reconstructing the state despite the considered attacks. In the second half of this work, we propose an estimator to harness the complexity of this intrinsically combinatorial problem, by leveraging satisfiability modulo theory solving. Numerical simulations demonstrate the effectiveness and scalability of our estimator.

Mehrdad Showkatbakhsh, Can Karakus, Suhas Diggavi

Data privacy is an important concern in learning, when datasets contain sensitive information about individuals. This paper considers consensus-based distributed optimization under data privacy constraints. Consensus-based optimization consists of a set of computational nodes arranged in a graph, each having a local objective that depends on their local data, where in every step nodes take a linear combination of their neighbors' messages, as well as taking a new gradient step. Since the algorithm requires exchanging messages that depend on local data, private information gets leaked at every step. Taking $(ε, δ)$-differential privacy (DP) as our criterion, we consider the strategy where the nodes add random noise to their messages before broadcasting it, and show that the method achieves convergence with a bounded mean-squared error, while satisfying $(ε, δ)$-DP. By relaxing the more stringent $ε$-DP requirement in previous work, we strengthen a known convergence result in the literature. We conclude the paper with numerical results demonstrating the effectiveness of our methods for mean estimation.