Laboratoire de systemes adaptatifs

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Hidden Markov Modeling Over Graphs

Virginia Bordignon, Mert Kayaalp, Ali H. Sayed, Stefan Vlaski

This work proposes a multi-agent filtering algorithm over graphs for finite-state hidden Markov models (HMMs), which can be used for sequential state estimation or for tracking opinion formation over dynamic social networks. We show that the difference from the optimal centralized Bayesian solution is asymptotically bounded for geometrically ergodic transition models. Experiments illustrate the theoretical findings and in particular, demonstrate the superior performance of the proposed algorithm compared to a state-of-the-art social learning algorithm.

IEEE2022

Regularized Diffusion Adaptation via Conjugate Smoothing

Ali H. Sayed, Stefan Vlaski

The purpose of this article is to develop and study a decentralized strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability distribution, while the regularizers are assumed deterministic, but are not required to be differentiable or even continuous. The individual, regularized, cost functions are distributed across a strongly connected network of agents, and the Pareto optimal solution is sought by appealing to a multiagent diffusion strategy. To this end, the regularizers are smoothed by means of infimal convolution, and it is shown that the Pareto solution of the approximate smooth problem can be made arbitrarily close to the solution of the original nonsmooth problem. Performance bounds are established under conditions that are weaker than assumed before in the literature and, hence, applicable to a broader class of adaptation and learning problems.

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Distributed Meta-Learning with Networked Agents

Mert Kayaalp, Ali H. Sayed, Stefan Vlaski

Meta-learning aims to improve efficiency of learning new tasks by exploiting the inductive biases obtained from related tasks. Previous works consider centralized or federated architectures that rely on central processors, whereas, in this paper, we propose a decentralized meta-learning scheme where the data and the computations are distributed across a network of agents. We provide convergence results for non-convex environments and illustrate the theoretical findings with experiments.

EUROPEAN ASSOC SIGNAL SPEECH & IMAGE PROCESSING-EURASIP2021