Related papers: On Structural Properties of Risk-Averse Optimal St…
This paper studies the long-time behavior of optimal solutions for a class of linear-convex optimal control problems. We focus on a partial exponential turnpike property, established without imposing controllability or stabilizability…
Nonsmooth composite optimization problems under uncertainty are prevalent in various scientific and engineering applications. We consider risk-neutral composite optimal control problems, where the objective function is the sum of a…
We first derive a general integral-turnpike property around a set for infinite-dimensional non-autonomous optimal control problems with any possible terminal state constraints, under some appropriate assumptions. Roughly speaking, the…
In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
Autonomous systems are increasingly deployed in real-world environments, where they must achieve high performance while maintaining safety under state and input constraints. Although Model Predictive Control (MPC) provides a principled…
We consider a control problem for a finite-state Markov system whose performance is evaluated by a coherent Markov risk measure. For each policy, the risk of a state is approximated by a function of its features, thus leading to a…
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…
We study a class of dynamically consistent risk measures that robustify a time-homogeneous Markovian reference model by allowing for distributional uncertainty in its transition laws. We start from one-step convex risk evaluations in which…
We discuss importance sampling of exit problems that involve unbounded stopping times; examples are mean first passage times, transition rates or committor probabilities in molecular dynamics. The naive application of variance minimization…
Multistage risk-averse optimal control problems with nested conditional risk mappings are gaining popularity in various application domains. Risk-averse formulations interpolate between the classical expectation-based stochastic and minimax…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
This paper studies convergence properties of optimal values and actions for discounted and average-cost Markov Decision Processes (MDPs) with weakly continuous transition probabilities and applies these properties to the stochastic…
We consider a class of time-inhomogeneous optimal stopping problems and we provide sufficient conditions on the data of the problem that guarantee monotonicity of the optimal stopping boundary. In our setting, time-inhomogeneity stems not…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the…
We consider the control problem with \textit{exit time}. Unlike the Bolza and Mayer problems, in this problem the terminal time of the trajectories is not fixed, but it is the first time at which they reach a given closed subset -…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
In this article, we propose a novel characterization of law-invariant and coherent risk measures, based on a generalized optimal transport problem in which the second marginal of the admissible plans is not fixed, but required to lie within…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…