Related papers: Martingale Characterizations of Risk-Averse Stocha…
Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first…
Time-consistency is an essential requirement in risk sensitive optimal control problems to make rational decisions. An optimization problem is time consistent if its solution policy does not depend on the time sequence of solving the…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
In this work, we address the problem of learning provably stable neural network policies for stochastic control systems. While recent work has demonstrated the feasibility of certifying given policies using martingale theory, the problem of…
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…
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,…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
This paper enhances the pricing of derivatives as well as optimal control problems to a level comprising risk. We employ nested risk measures to quantify risk, investigate the limiting behavior of nested risk measures within the classical…
We propose some machine-learning-based algorithms to solve hedging problems in incomplete markets. Sources of incompleteness cover illiquidity, untradable risk factors, discrete hedging dates and transaction costs. The proposed algorithms…
In this paper, we aim to solve Bayesian Risk Optimization (BRO), which is a recently proposed framework that formulates simulation optimization under input uncertainty. In order to efficiently solve the BRO problem, we derive nested…
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…
This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite…
We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…
In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set…
Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations,…
We consider a class of stochastic control problems where the state process is a probability measure-valued process satisfying an additional martingale condition on its dynamics, called measure-valued martingales (MVMs). We establish the…
This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing $\tilde{N}$ perturbed rollouts around the nominal dynamics to estimate the…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
This paper focuses on stochastic optimal control problems with constraints in law, which are rewritten as optimization (minimization) of probability measures problem on the canonical space. We introduce a penalized version of this type of…