Related papers: Optimal stopping under model uncertainty: randomiz…
In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…
We analyze an optimal stopping problem with random maturity under a nonlinear expectation with respect to a weakly compact set of mutually singular probabilities $\mathcal{P}$. The maturity is specified as the hitting time to level $0$ of…
This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of…
Conventional robust H2/H-infinity control minimizes the worst-case performance, often leading to a conservative design driven by very rare parametric configurations. To reduce this conservatism while taking advantage of the stochastic…
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…
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…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
We develop an approach for solving time-consistent risk-sensitive stochastic optimization problems using model-free reinforcement learning (RL). Specifically, we assume agents assess the risk of a sequence of random variables using dynamic…
In this paper we consider stopping problems for continuous-time Markov chains under a general risk-sensitive optimization criterion for problems with finite and infinite time horizon. More precisely our aim is to maximize the certainty…
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is…
From an optimizer's perspective, achieving the global optimum for a general nonconvex problem is often provably NP-hard using the classical worst-case analysis. In the case of Cox's proportional hazards model, by taking its statistical…
This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
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…
In this paper, we address the real-time risk-bounded safety verification problem of continuous-time state trajectories of autonomous systems in the presence of uncertain time-varying nonlinear safety constraints. Risk is defined as the…
In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
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 consider a class of discretionary stopping problems within the $G$-framework. We first establish the well-definedness of the stopping problem under the $G$-expectation, by showing the quasi-continuity of the stopped process. We then…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…