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This paper develops a comprehensive extension of the $\Lambda$-set framework for optimal control, introducing second-order $\Lambda$-sets and generalizing the theory to non-smooth, hybrid, and stochastic hybrid systems. We first establish…
This paper considers deployment problems where a mobile robotic network must optimize its configuration in a distributed way in order to minimize a steady-state cost function that depends on the spatial distribution of certain probabilistic…
The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…
In this work we study the method of Bregman projections for deterministic and stochastic convex feasibility problems with three types of control sequences for the selection of sets during the algorithmic procedure: greedy, random, and…
Nonsmooth nonconvex optimization problems broadly emerge in machine learning and business decision making, whereas two core challenges impede the development of efficient solution methods with finite-time convergence guarantee: the lack of…
Consider the following multi-phase project management problem. Each project is divided into several phases. All projects enter the next phase at the same point chosen by the decision maker based on observations up to that point. Within each…
By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…
Multi-model inference covers a wide range of modern statistical applications such as variable selection, model confidence set, model averaging and variable importance. The performance of multi-model inference depends on the availability of…
Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…
Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore,…
In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…
We consider stochastic gradient descent (SGD) for least-squares regression with potentially several passes over the data. While several passes have been widely reported to perform practically better in terms of predictive performance on…
Preliminary spacecraft trajectory optimization is a parameter dependent global search problem that aims to provide a set of solutions that are of high quality and diverse. In the case of numerical solution, it is dependent on the original…
This paper considers the problem of reachability analysis of control systems with optimal controllers, as a first step towards verifying the safety and correctness of such systems. Despite their appeal in guaranteeing task satisfaction…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
IIn this paper, we study a partially observed progressive optimal control problem of forward-backward stochastic differential equations with random jumps, where the control domain is not necessarily convex, and the control variable enter…
A long-standing and difficult problem in, e.g., condensed matter physics is how to find the ground state of a complex many-body system where the potential energy surface has a large number of local minima. Spin systems containing complex…
While the optimization landscape of policy gradient methods has been recently investigated for partially observed linear systems in terms of both static output feedback and dynamical controllers, they only provide convergence guarantees to…
This paper deals with a new accelerated path integral method, which iteratively searches optimal controls with a small number of iterations. This study is based on the recent observations that a path integral method for reinforcement…
In this paper we develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the…