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We study a general class of PageRank optimization problems which consist in finding an optimal outlink strategy for a web site subject to design constraints. We consider both a continuous problem, in which one can choose the intensity of a…
This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
We propose a novel constrained reinforcement learning method for finding optimal policies in Markov Decision Processes while satisfying temporal logic constraints with a desired probability throughout the learning process. An…
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…
We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem…
In this paper, we propose a novel solution for the distributed unconstrained optimization problem where the total cost is the summation of time-varying local cost functions of a group networked agents. The objective is to track the optimal…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
We investigate a singular-optimal stopping stochastic control problem driven by self-exciting dynamics governed by a Hawkes process. In the continuous-time setting, we show that the optimization problem reduces to solving a variational…
This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex…
We derive the explicit solutions to singular stochastic control problems of the monotone follower type with (a) an expected discounted criterion, (b) an expected ergodic criterion and (c) a pathwise ergodic criterion. These problems have…
Motivated, in particular, by the entropy-regularized optimal transport problem, we consider convex optimization problems with linear equality constraints, where the dual objective has Lipschitz $p$-th order derivatives, and develop two…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
Consider a discrete-time optimal selection problem where one observes a sequence of independent Bernoulli trials and receives a nonnegative reward upon stopping on a success. The aim is to find a single-choice strategy that maximises the…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
We consider the problem of computing optimal policies in average-reward Markov decision processes. This classical problem can be formulated as a linear program directly amenable to saddle-point optimization methods, albeit with a number of…
We consider the non-linear optimal multiple stopping problem under general conditions on the non-linear evaluation operators, which might depend on two time indices: the time of evaluation/assessment and the horizon (when the reward or loss…
In this paper, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A sophisticated solution is proposed and is well-defined for any time setting with general flows of objectives. A…
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…
We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by non-autonomous methods via open-loop damping (e.g.,…