Related papers: Risk averse stochastic programming: time consisten…
Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For…
This work provides a novel convergence analysis for stochastic optimization in terms of stopping times, addressing the practical reality that algorithms are often terminated adaptively based on observed progress. Unlike prior approaches,…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We consider discrete-time infinite horizon deterministic optimal control problems with nonnegative cost per stage, and a destination that is cost-free and absorbing. The classical linear-quadratic regulator problem is a special case. Our…
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 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…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
Standard Markovian optimal stopping problems are consistent in the sense that the first entrance time into the stopping set is optimal for each initial state of the process. Clearly, the usual concept of optimality cannot in a…
We consider control of uncertain linear time-varying stochastic systems from the perspective of regret minimization. Specifically, we focus on the problem of designing a feedback controller that minimizes the loss relative to a clairvoyant…
The paper [12] examines a concept of equilibrium policies instead of optimal controls in stochastic optimization to analyze a mean-variance portfolio selection problem. We follow the same approach in order to investigate the Merton…
Linear dynamical systems that obey stochastic differential equations are canonical models. While optimal control of known systems has a rich literature, the problem is technically hard under model uncertainty and there are hardly any…
This paper establishes a rigorous connection between regularized discrete-time reinforcement learning (RL) and continuous-time stochastic optimal control. Specifically, classical RL algorithms are typically solving a regularized…
In this paper, we consider a class of stochastic optimal control problems with risk constraints that are expressed as bounded probabilities of failure for particular initial states. We present here a martingale approach that diffuses a risk…
An optimal control problem is considered for a stochastic differential equation containing a state-dependent regime switching, with a recursive cost functional. Due to the non-exponential discounting in the cost functional, the problem is…
We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite…
Motion planning is a fundamental problem and focuses on finding control inputs that enable a robot to reach a goal region while safely avoiding obstacles. However, in many situations, the state of the system may not be known but only…
In this paper, we study a time-inconsistent stochastic optimal control problem with a recursive cost functional by a multi-person hierarchical differential game approach. An equilibrium strategy of this problem is constructed and a…
We propose a risk measurement approach for a risk-averse stochastic problem. We provide results that guarantee that our problem has a solution. We characterize and explore the properties of the argmin as a risk measure and the minimum as a…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman's optimality principle and Pontryagin's maximum principle, and their modern exposition with…