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We study policy optimization problems for deterministic Markov decision processes (MDPs) with metric state and action spaces, which we refer to as Metric Policy Optimization Problems (MPOPs). Our goal is to establish theoretical results on…
For combinatorial optimization problems, model-based paradigms such as mixed-integer programming (MIP) and constraint programming (CP) aim to decouple modeling and solving a problem: the `holy grail' of declarative problem solving. We…
For combinatorial optimization problems, model-based approaches such as mixed-integer programming (MIP) and constraint programming (CP) aim to decouple modeling and solving a problem: the 'holy grail' of declarative problem solving. We…
Low-rank methods for semidefinite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are hard to implement…
This paper proposes a comprehensive hierarchical control framework for autonomous decision-making arising in robotics and autonomous systems. In a typical hierarchical control architecture, high-level decision making is often characterised…
There is a growing need for computational tools to automatically design and verify autonomous systems, especially complex robotic systems involving perception, planning, control, and hardware in the autonomy stack. Differentiable…
Partially observable Markov decision processes (POMDPs) provide a modeling framework for autonomous decision making under uncertainty and imperfect sensing, e.g. robot manipulation and self-driving cars. However, optimal control of POMDPs…
The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…
Many sequential decision problems can be formulated as Markov Decision Processes (MDPs) where the optimal value function (or cost-to-go function) can be shown to satisfy a monotone structure in some or all of its dimensions. When the state…
MPI applications matter. However, with the advent of many-core processors, traditional MPI applications are challenged to achieve satisfactory performance. This is due to the inability of these applications to respond to load imbalances, to…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
We propose a novel data-driven neural network (NN) optimization framework for solving an optimal stochastic control problem under stochastic constraints. Customized activation functions for the output layers of the NN are applied, which…
Differential Dynamic Programming (DDP) is an efficient computational tool for solving nonlinear optimal control problems. It was originally designed as a single shooting method and thus is sensitive to the initial guess supplied. This work…
Spatial puzzles composed of rigid objects, flexible strings and holes offer interesting domains for reasoning about spatial entities that are common in the human daily-life's activities. The goal of this work is to investigate the automated…
Dual control denotes a class of control problems where the parameters governing the system are imperfectly known. The challenge is to find the optimal balance between probing, i.e. exciting the system to understand it more, and caution,…
We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…
This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…
Modern Machine Learning (ML) training on large-scale datasets is a very time-consuming workload. It relies on the optimization algorithm Stochastic Gradient Descent (SGD) due to its effectiveness, simplicity, and generalization performance.…
This paper describes open-source scientific contributions in python surrounding the numerical solutions to hyperbolic Hamilton-Jacobi (HJ) partial differential equations viz., their implicit representation on co-dimension one surfaces;…
Computationally efficient nonlinear model predictive control relies on elaborate discrete-time optimal control problem (OCP) formulations trading off accuracy with respect to the continuous-time problem and associated computational burden.…