Session: Optimization for Robotics II
Chair: Panos Patrinos
Cluster: Optimization Applications (Communication, Energy, Health, ML, ...)
Talk 1: Graphs of Convex Sets with Applications to Robot Motion Planning
Speaker: Tobia Marcucci
Abstract: In this talk we introduce a novel modeling and computational framework for joint discrete and continuous decision making. We consider graphs where each vertex is associated with a convex optimization problem, and each edge couples two problems through additional convex costs and constraints. We call these Graphs of Convex Sets (GCS). Many classical problems in graph theory are naturally generalized to GCS, yielding a new class of problems at the interface of combinatorial and convex optimization with a wide variety of applications. For the solution of these problems, we present a unified technique that leverages perspective operators to formulate tight convex relaxations and strong mixed-integer formulations. In the second part of the presentation, we focus on the shortest-path problem in GCS and its application to robot motion planning. We present early experiments from Amazon Robotics, where our framework enables warehouse robots to move packages between bins nearly twice as fast as the current motion-planning solution.
Talk 2: Deep-Learning Aided Optimization for Decision-Making
Speaker: Evangelos Theodorou
Abstract: Optimization problems in robotics are typically nonlinear and nonconvex, while their scalability can range from few to millions of states and controls variables depending on the use case, the robotic system and the task in consideration. In this talk I will present a new class of algorithms for distributed optimization of multi-agent systems with emphasis on robotics applications. The primary goal is to out-perform existing algorithms in terms of convergence speed, optimality and scaling. To do so we will draw connections between iterative optimization algorithms and model-based deep learning approaches. These connections will allow us to develop neural networks architectures for learning to optimize that are interpretable, scalable and come with generalization guarantees. The interpretability arises from treating each iteration of an optimization method as layer with the corresponding tuning parameters treated as learnable parameters. Training of such architectures takes place in a supervised as well as semi-supervised learning fashion. We will show a range of applications of such neural network architectures including large-scale distributed optimal control, model predictive control, and network flow problems. The proposed architectures do not only improve performance, they also address a long-standing problem in industry and academia related to interpretability of neural network architectures when deployed to the real world.
Talk 3: Safe treatment of infeasible convex optimization problems via the augmented Lagrangian
Speaker: Roland Andrews
Abstract: This work focuses on constrained convex optimization problems. The augmented Lagrangian method is a popular algorithm designed to tackle such problems by solving sequences of unconstrained optimization problems. It is practically efficient and offers strong theoretical guarantees under minimal assumptions, provided that the feasible set associated with the constraints is non-empty. However, the infeasible setting for constrained optimization problems has only recently started to attract attention. This issue is particularly relevant in areas such as optimal control (e.g., Model Predictive Control) and machine learning (e.g., neural networks using convex optimization layers), where infeasibility frequently arises. Recent studies have approached this problem under various assumptions. In this work, we analyze the general case, relying solely on convexity as the key assumption. Our approach leverages the classical relationship between the augmented Lagrangian algorithm and the dual proximal point algorithm.
