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Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…

Policy gradients methods apply to complex, poorly understood, control problems by performing stochastic gradient descent over a parameterized class of polices. Unfortunately, even for simple control problems solvable by standard dynamic…

This paper is concerned with the computing efficiency of model predictive control (MPC) problems for dynamical systems with both rate and amplitude constraints on the inputs. Instead of augmenting the decision variables of the underlying…

Projects consist of interconnected dimensions such as objective, time, resource and environment. Use of these dimensions in a controlled way and their effective scheduling brings the project success. Project scheduling process includes…

Gradient-based (a.k.a. `first order') optimization algorithms are routinely used to solve large scale non-convex problems. Yet, it is generally hard to predict their effectiveness. In order to gain insight into this question, we revisit the…

Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…

Recent studies on transfer learning have shown that selectively fine-tuning a subset of layers or customizing different learning rates for each layer can greatly improve robustness to out-of-distribution (OOD) data and retain generalization…

This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…

The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…

In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…

We study the distributed optimization problem over a graphon with a continuum of nodes, which is regarded as the limit of the distributed networked optimization as the number of nodes goes to infinity. Each node has a private local cost…

Gromov--Wasserstein optimal transport (GWOT) aligns metric measure spaces by matching their within-domain relational structures, but large-scale GWOT remains challenging because its objective is nonconvex and projection onto the transport…

The potential benefit of migrating software design from Structured to Object Oriented Paradigm is manifolded including modularity, manageability and extendability. This design migration should be automated as it will reduce the time…

This paper proposes a distributed stochastic algorithm with variance reduction for general smooth non-convex finite-sum optimization, which has wide applications in signal processing and machine learning communities. In distributed setting,…

We consider policy gradient methods for stochastic optimal control problem in continuous time. In particular, we analyze the gradient flow for the control, viewed as a continuous time limit of the policy gradient method. We prove the global…

Stochastic kinetic models describe systems across biology, chemistry, and physics where discrete events and small populations render deterministic approximations inadequate. Parameter inference and inverse design in these systems require…

We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…

Exact Gaussian Process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure…

This paper presents a novel distributed formulation of the min-max optimization problem. Such a formulation enables enhanced flexibility among agents when optimizing their maximization variables. To address the problem, we propose two…

One important feature of complex systems are problem domains that have many local minima and substructure. Biological systems manage these local minima by switching between different subsystems depending on their environmental or…