Shivanshu Tripathi

Shivanshu Tripathi, Maziar Raissi

We study online optimization problems in which the cost function depends on latent, time-varying parameters that are unmeasurable and governed by unknown dynamics. Specifically, we consider a strongly convex cost function whose linear term evolves according to unknown linear stochastic dynamics, while the algorithm has access only to finite noisy gradient measurements. We propose a solution that uses control theoretic tools to reconstruct the latent parameters from gradient observations using a Gauss-Markov estimator, then identifies the parameter dynamics using an instrumental-variable estimator, and finally forecasts the parameters to compute the future minimizer. We provide a bound on the expected tracking error. We illustrate the effectiveness of our algorithm on a series of numerical examples.

Darshan Gadginmath, Shivanshu Tripathi, Fabio Pasqualetti

This study addresses the challenge of online learning in contexts where agents accumulate disparate data, face resource constraints, and use different local algorithms. This paper introduces the Switched Online Learning Algorithm (SOLA), designed to solve the heterogeneous online learning problem by amalgamating updates from diverse agents through a dynamic switching mechanism contingent upon their respective performance and available resources. We theoretically analyze the design of the selecting mechanism to ensure that the regret of SOLA is bounded. Our findings show that the number of changes in selection needs to be bounded by a parameter dependent on the performance of the different local algorithms. Additionally, two test cases are presented to emphasize the effectiveness of SOLA, first on an online linear regression problem and then on an online classification problem with the MNIST dataset.