Related papers: Rough Path Approaches to Stochastic Control, Filte…
We present two different approaches to stochastic integration in frictionless model free financial mathematics. The first one is in the spirit of It\^o's integral and based on a certain topology which is induced by the outer measure…
``When in a difficult situation, it is sometimes better to give up and start all over again''. While this empirical truth has been regularly observed in a wide range of circumstances, quantifying the effectiveness of such a heuristic…
This paper presents a joint optimisation framework for optimal estimation and stochastic optimal control with imperfect information. It provides a estimation and control scheme that can be decomposed into a classical optimal estimation step…
In this paper, we focus on the problem of robustifying reinforcement learning (RL) algorithms with respect to model uncertainties. Indeed, in the framework of model-based RL, we propose to merge the theory of constrained Markov decision…
This paper investigates the exact controllability problem for multi-dimensional stochastic first-order symmetric hyperbolic systems with control inputs acting in two distinct ways: an internal control applied to the diffusion term and a…
In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic differential equations. We…
We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…
We introduce a notion of rough paths on embedded submanifolds and demonstrate that this class of rough paths is natural. On the way we develop a notion of rough integration and an efficient and intrinsic theory of rough differential…
We present an approach for approximately solving discrete-time stochastic optimal-control problems by combining direct trajectory optimization, deterministic sampling, and policy optimization. Our feedback motion-planning algorithm uses a…
In the real-world, self-driving vehicles are required to achieve steering maneuvers in both uncontrolled and uncertain environments while maintaining high levels of safety and passengers' comfort. Ignoring these requirements would…
In this article, we present a general methodology for control problems driven by the Brownian motion filtration including non-Markovian and non-semimartingale state processes controlled by mutually singular measures. The main result of this…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
In this paper we make a survey on the so called randomization method, a recent methodology to study stochastic optimization problems. It allows to represent the value function of an optimal control problem by a suitable backward stochastic…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
We introduce a sequential learning algorithm to address a robust controller tuning problem, which in effect, finds (with high probability) a candidate solution satisfying the internal performance constraint to a chance-constrained program…
In this article, we show how the theory of rough paths can be used to provide a notion of solution to a class of nonlinear stochastic PDEs of Burgers type that exhibit too high spatial roughness for classical analytical methods to apply. In…
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value…
This paper offers a critical view of the "worst-case" approach that is the cornerstone of robust control design. It is our contention that a blind acceptance of worst-case scenarios may lead to designs that are actually more dangerous than…
In this paper, we consider optimal control of stochastic differential equations subject to an expected path constraint. The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs. In…
Using rough path theory, we provide a pathwise foundation for stochastic It\^o integration, which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To…