On Endogenous Random Consensus and Averaging Dynamics

Motivated by various random variations of Hegselmann-Krause model for opinion dynamics and gossip algorithm in an endogenously changing environment, we propose a general framework for the study of endogenously varying random averaging dynamics, i.e.\ an averaging dynamics whose evolution suffers from history dependent sources of randomness. We show that under general assumptions on the averaging dynamics, such dynamics is convergent almost surely. We also determine the limiting behavior of such dynamics and show such dynamics admit infinitely many time-varying Lyapunov functions

On Estimating Multi-Attribute Choice Preferences using Private Signals and Matrix Factorization

Revealed preference theory studies the possibility of modeling an agent's revealed preferences and the construction of a consistent utility function. However, modeling agent's choices over preference orderings is not always practical and demands strong assumptions on human rationality and data-acquisition abilities. Therefore, we propose a simple generative choice model where agents are assumed to generate the choice probabilities based on latent factor matrices that capture their choice evaluation across multiple attributes. Since the multi-attribute evaluation is typically hidden within the agent's psyche, we consider a signaling mechanism where agents are provided with choice information through private signals, so that the agent's choices provide more insight about his/her latent evaluation across multiple attributes. We estimate the choice model via a novel multi-stage matrix factorization algorithm that minimizes the average deviation of the factor estimates from choice data. Simulation results are presented to validate the estimation performance of our proposed algorithm.Comment: 6 pages, 2 figures, to be presented at CISS conferenc

Detection and Mitigation of Biasing Attacks on Distributed Estimation Networks

The paper considers a problem of detecting and mitigating biasing attacks on networks of state observers targeting cooperative state estimation algorithms. The problem is cast within the recently developed framework of distributed estimation utilizing the vector dissipativity approach. The paper shows that a network of distributed observers can be endowed with an additional attack detection layer capable of detecting biasing attacks and correcting their effect on estimates produced by the network. An example is provided to illustrate the performance of the proposed distributed attack detector.Comment: Accepted for publication in Automatic

Regret Bounds for LQ Adaptive Control Under Database Attacks (Extended Version)

This paper is concerned with understanding and countering the effects of database attacks on a learning-based linear quadratic adaptive controller. This attack targets neither sensors nor actuators, but just poisons the learning algorithm and parameter estimator that is part of the regulation scheme. We focus on the adaptive optimal control algorithm introduced by Abbasi-Yadkori and Szepesvari and provide regret analysis in the presence of attacks as well as modifications that mitigate their effects. A core step of this algorithm is the self-regularized on-line least squares estimation, which determines a tight confidence set around the true parameters of the system with high probability. In the absence of malicious data injection, this set provides an appropriate estimate of parameters for the aim of control design. However, in the presence of attack, this confidence set is not reliable anymore. Hence, we first tackle the question of how to adjust the confidence set so that it can compensate for the effect of the poisonous data. Then, we quantify the deleterious effect of this type of attack on the optimality of control policy by providing a measure that we call attack regret.Comment: 10 page