Session: Advances in Network Optimization and Cooperative Learning
Chair: Cesar A Uribe
Cluster: Multi-agent Optimization and Games
Talk 1: Optimally Improving Cooperative Learning in a Social Settin
Speaker: Shahrzad Haddadan
Abstract: We consider a cooperative learning scenario where a collection of networked agents with individually owned classifiers update their predictions, for the same classification task, through communication or observations of each other’s predictions. Clearly if highly influential vertices use erroneous classifiers, there will be a negative effect on the accuracy of all the agents in the network. We ask the following question: how can we optimally fix the prediction of a few classifiers so as maximize the overall accuracy in the entire network. To this end we consider an aggregate and an egalitarian objective function. We show a polynomial time algorithm for optimizing the aggregate objective function, and show that optimizing the egalitarian objective function is NP-hard. Furthermore, we develop approximation algorithms for the egalitarian improvement. The performance of all of our algorithms are guaranteed by mathematical analysis and backed by experiments on synthetic and real data.
Talk 2: The engineering potential of fish research: swimming upstream to new solutions
Speaker: Daniel Burbano
Abstract: Millions of years of evolution have endowed animals with refined and elegant mechanisms to orient and navigate in complex environments. Elucidating the underpinnings of these processes is of critical importance not only in biology to understand migration and survival but also for engineered network systems to aid the development of bio-inspired algorithms for estimation and control. Particularly interesting is the study of fish navigation where different cues, such as vision and hydrodynamics are integrated and fed back to generate locomotion. Little is known, however, about the information pathways and the integration process underlying complex navigation problems. This talk will discuss recent advances in data-driven mathematical models based on potential flow theory, stochastic differential equations, and control theory describing fish navigation. In addition, we will discuss how biological insights gained from this research can be applied to robot navigation with zero-order optimization and estimation and control problems in network systems
Talk 3: An Optimal Transport Approach for Network Regression
Speaker: Alex Zalles
Abstract: We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on Fr\'echet means and propose a network regression method using the Wasserstein metric. We show that when representing graphs as multivariate Gaussian distributions, the network regression problem requires the computation of a Riemannian center of mass (i.e., Fr\'echet means). Fr\'echet means with non-negative weights translates into a barycenter problem and can be efficiently computed using fixed point iterations. Although the convergence guarantees of fixed-point iterations for the computation of Wasserstein affine averages remain an open problem, we provide evidence of convergence in a large number of synthetic and real-data scenarios. Extensive numerical results show that the proposed approach improves existing procedures by accurately accounting for graph size, topology, and sparsity in synthetic experiments. Additionally, real-world experiments using the proposed approach result in higher Coefficient of Determination () values and lower mean squared prediction error (MSPE), cementing improved prediction capabilities in practice.
