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In this paper, we present a new MTL framework that searches for structures optimized for multiple tasks with diverse graph topologies and shares features among tasks. We design a restricted DAG-based central network with read-in/read-out…
We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…
This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…
We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an…
One fundamental problem in decentralized multi-agent optimization is the trade-off between gradient/sampling complexity and communication complexity. We propose new algorithms whose gradient and sampling complexities are graph topology…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and…
This paper studies the unconstrained nonconvex-strongly-convex bilevel optimization problem. A common approach to solving this problem is to alternately update the upper-level and lower-level variables using (biased) stochastic gradients or…
Distributed Optimization is an increasingly important subject area with the rise of multi-agent control and optimization. We consider a decentralized stochastic optimization problem where the agents on a graph aim to asynchronously optimize…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
Nonconvex minimax problems appear frequently in emerging machine learning applications, such as generative adversarial networks and adversarial learning. Simple algorithms such as the gradient descent ascent (GDA) are the common practice…
In this paper, we study zeroth-order algorithms for nonconvex minimax problems with coupled linear constraints under the deterministic and stochastic settings, which have attracted wide attention in machine learning, signal processing and…
An optimization algorithm for a group of nonsmooth nonconvex problems inspired by two-stage stochastic programming problems is proposed. The main challenges for these problems include (1) the problems lack the popular lower-type properties…
We develop a new consensus-based distributed algorithm for solving learning problems with feature partitioning and non-smooth convex objective functions. Such learning problems are not separable, i.e., the associated objective functions…
When facing graph signal processing tasks, the workhorse assumption is that the graph describing the support of the signals is known. However, in many relevant applications the available graph suffers from observation errors and…
This paper studies graph-based active learning, where the goal is to reconstruct a binary signal defined on the nodes of a weighted graph, by sampling it on a small subset of the nodes. A new sampling algorithm is proposed, which…
We consider a decentralized optimization problem for networks affected by communication delays. Examples of such networks include collaborative machine learning, sensor networks, and multi-agent systems. To mimic communication delays, we…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
Structural learning, which aims to learn directed acyclic graphs (DAGs) from observational data, is foundational to causal reasoning and scientific discovery. Recent advancements formulate structural learning into a continuous optimization…
In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…