We consider the distributed optimization problem where a group of agents seeks to cooperatively compute the optimizer of the average of local functions. To solve this problem, we propose a novel algorithm which adjusts the ratio between the number of communications and computations to achieve fast convergence. In particular, the …
We consider the unconstrained 0-1 polynomial optimization problem where its hypergraph representation contains a beta-cycle. First, we show that almost all known cutting planes for this problem have Chvátal rank 1. We then exploit these inequalities to derive new cutting planes that generally have Chvátal rank 2. This novel class …
We consider the problem of estimating the species tree from large numbers of unrooted gene tree topologies in the presence of incomplete lineage sorting, a phenomenon which enforces heterogeneity among the set of gene trees. This phenomenon is modeled with the Multispecies Coalescent Process. We make progress towards deriving a …
We address the problem of modifying a dataset so as to minimize mutual information about sensitive attributes in the released version, while maintaining a specified level of utility. This can be formulated as an optimization problem over distributions, and we attempt to solve it in a data-driven manner using adversarially …
In this talk, we review several challenges that one can encounter while solving a smooth nonconvex optimization problem. For each of these issues, we develop a practical variant on the popular trust-region method with second-order guarantees. We first consider the case of a large number of problem variables. By resorting …