Global-Entropy Driven Exploration with Distributed Models under Sparsity Constraints

Abstract

This paper focuses on exploration when using different data distribution schemes and ADMM as a solver for swarms. By exploration, we mean the estimation of new measurement locations that are beneficial for the model estimation. In particular, the different distribution schemes are splitting-over-features or heterogeneous learning and splitting-over-examples or homogeneous learning. Each agent contributes a solution to solve the joint optimization problem by using ADMM and the consensus algorithm. This paper shows that some information is unknown to the individual agent, and thus, the estimation of new measurement positions is not possible without further communication. Therefore, this paper shows results for how to distribute only necessary information for a global exploration. We show the benefits between the proposed global exploration scheme and benchmark exploration schemes such as random walk and systematic traversing, i.e., meandering. The proposed waypoint estimation methods are then tested against each other and with other movement methods. This paper shows that a movement method, which considers the current information within the model, is superior to the benchmark movement methods.

Fast Model Predictive Control Based on Adaptive Alternating Direction Method of Multipliers

“…ADMM is a strong algorithm which can efficiently solve convex optimization problems, and it can decompose the global problem into several smaller and easy-to-solve local subproblems [30]. Because of its fast processing speed and good convergence performance, ADMM has received tremendous interest and approval for solving numerous problems in machine learning, statistics, and signal processing [17,[31][32][33].…”

Experimental Validation of Entropy-Driven Swarm Exploration under Sparsity Constraints with Sparse Bayesian Learning

“…The derivation of the distributed R-ARD (D-R-ARD) for SOF is shown in [14]. Here, we would like to show the main aspects of the distribution paradigm and the resulting algorithm.…”

“…, z T K ] T in (15) cannot be computed exactly. Instead it is upper-bounded [14] as z k ≤ z k , where z k is computed for each agent:…”

“…Note that due to the normality of the posterior pdf p(w|y), the term log|Σ w (X, Π)| is proportional to the entropy of w; thus, minimization of the criterion (30) would imply a reduction of the entropy of the parameter estimates. Note that in contrast to [14], the covariance matrix is not approximated here, but it is computed exactly based on the resulting probabilistic inference model. Our intention is now to evaluate and optimize (30) as a function of the new possible sampling location x.…”

“…For comparison, we will use non-Bayesian SOF and SOE formulations as discussed in [14]. As in these formulations, the ADMM algorithm [33] was used for estimation, we will refer to them as ADMM for SOF and ADMM for SOE, respectively.…”