Related papers: Dynamic Programming in Probability Spaces via Opti…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes,…
We consider a two-road dynamic routing game where the state of one of the roads (the "risky road") is stochastic and may change over time. This generates room for experimentation. A central planner may wish to induce some of the (finite…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
We prove a Pontryagin Maximum Principle for optimal control problems in the space of probability measures, where the dynamics is given by a transport equation with non-local velocity. We formulate this first-order optimality condition using…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
The paper extends an impulsive control-theoretical framework towards dynamic systems in the space of measures. We consider a transport equation describing the time-evolution of a conservative "mass" (probability measure), which represents…
We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability…
This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem…
Coordination of dynamical routes can alleviate traffic congestion and is essential for the coming era of autonomous self-driving cars. However, dynamical route coordination is difficult and many existing routing protocols are either static…
A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure…
We analyze a power distribution line with high penetration of distributed generation and strong variations of power consumption and generation levels. In the presence of uncertainty the statistical description of the system is required to…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…
This article addresses the problem of data-driven numerical optimal control for unknown nonlinear systems. In our scenario, we suppose to have the possibility of performing multiple experiments (or simulations) on the system. Experiments…