Distributed Autonomous Online Learning: Regrets and Intrinsic Privacy-Preserving Properties

Abstract

Online learning has become increasingly popular on handling massive data. The sequential nature of online learning, however, requires a centralized learner to store data and update parameters. In this paper, we consider online learning with distributed data sources. The autonomous learners update local parameters based on local data sources and periodically exchange information with a small subset of neighbors in a communication network. We derive the regret bound for strongly convex functions that generalizes the work by Ram et al.[1] for convex functions. More importantly, we show that our algorithm has intrinsic privacypreserving properties, and we prove the sufficient and necessary conditions for privacy preservation in the network. These conditions imply that for networks with greater-than-one connectivity, a malicious learner cannot reconstruct the subgradients (and sensitive raw data) of other learners, which makes our algorithm appealing in privacy-sensitive applications.

Logarithmic regret bound over diffusion based distributed estimation

“…In [3], authors bound w i,t −w t terms using (6). The following lemma presents a similar result for the diffusion based distributed estimation.…”

“…Note that in [3], authors use the same cost definition for the distributed autonomous online learning algorithm.…”

“…In [3], authors set θ = 2 and choose β from the minimum nonzero values of Γ. We choose the same time dependent step size at all nodes and initialize each parameter estimate with the same value.…”

“…To do that, we use a new cost definition for distributed estimation algorithms [3], which satisfies the global performance measures used in [1] and [2]. Each local parameter estimation is expected to converge to the optimum solution which yields the minimum cost for overall spatial and temporal data, i.e., the parameter of interest.…”

Decentralized and Privacy-Preserving Low-Rank Matrix Completion

“…The cryptographical techniques are well studied but expensive and fail to utilize the problem structures in network optimization. The privacy-preserving property of D-LMaFit is similar to that of the decentralized autonomous online learning (DAOL) algorithm [35]. In DAOL, a network of decentralized agents collaboratively performs online learning through exchanging neighboring iterates and descending on instantaneous local cost functions.…”