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Integrated task and motion planning has emerged as a challenging problem in sequential decision making, where a robot needs to compute high-level strategy and low-level motion plans for solving complex tasks. While high-level strategies…
We formulate some simple conditions under which a Markov chain may be approximated by the solution to a differential equation, with quantifiable error probabilities. The role of a choice of coordinate functions for the Markov chain is…
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
Recently, the centroidal momentum dynamics has received substantial attention to plan dynamically consistent motions for robots with arms and legs in multi-contact scenarios. However, it is also non convex which renders any optimization…
To tackle the difficulties faced by both stochastic dynamic programming and scenario tree methods, we present some variational approach for numerical solution of stochastic optimal control problems. We consider two different interpretations…
Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…
This paper deals with the finite horizon optimal control problem for discrete-time Markov jump linear system with input delay. The correlation among the jumping parameters and the input delay are considered simultaneously, which forms the…
We define a class of "optimal" coordinate systems by requiring that the deviation from an exact Robertson-Walker metric is "as small as possible" within a given four dimensional volume. The optimization is performed by minimizing several…
Optimal control problems can be solved via a one-shot (single) optimization or a sequence of optimization using dynamic programming (DP). However, the computation of their global optima often faces NP-hardness, and thus only locally optimal…
A Markov process is registered. At random moment $\theta$ the distribution of observed sequence changes. Using probability maximizing approach the optimal stopping rule for detecting the change is identified. Some explicit solution is…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
In this paper, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state…
Optimization problems with stochastic dominance constraints provide a possibility to shape risk by selecting a benchmark random outcome with a desired distribution. The comparison of the relevant random outcomes to the respective benchmarks…
This paper considers a class of convex optimization problems where both, the objective function and the constraints, have a continuously varying dependence on time. Our goal is to develop an algorithm to track the optimal solution as it…
The standard approach in solving stochastic equations is eigenvector decomposition. Using separation ansatz $P(i,t)=u(i)e^{\mu t}$ one obtains standard equation for eigenvectors $Ku=\mu u$, where $K$ is the rate matrix of the master…
We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a…
This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…