Related papers: Resetting in Stochastic Optimal Control
The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the…
In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
Without exact knowledge of the true system dynamics, optimal control of non-linear continuous-time systems requires careful treatment under epistemic uncertainty. In this work, we translate a probabilistic interpretation of the Pontryagin…
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
This paper bridges some of the gap between optimal planning and reinforcement learning (RL), both of which share roots in dynamic programming applied to sequential decision making or optimal control. Whereas planning typically favors…
Adaptive optimal control of nonlinear dynamic systems with deterministic and known dynamics under a known undiscounted infinite-horizon cost function is investigated. Policy iteration scheme initiated using a stabilizing initial control is…
This paper considers an opportunistic scheduling problem over a renewal system. A controller observes a random event at the beginning of each renewal frame and then chooses an action in response to the event, which affects the duration of…
Overconservatism has long been recognized as a major issue with robust optimization, despite its key advantages of tractability, performance guarantee, and limited information. To address this issue, a new criterion is proposed that can…
Optimized certainty equivalents (OCEs) is a family of risk measures widely used by both practitioners and academics. This is mostly due to its tractability and the fact that it encompasses important examples, including entropic risk…
We present and characterize a method to accelerate the relaxation of a Brownian object between two distinct equilibrium states. Instead of relying on a deterministic time-dependent control parameter, we use stochastic resetting to guide and…
Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
The mean completion time of a stochastic process may be rendered finite and minimised by a judiciously chosen restart protocol, which may either be stochastic or deterministic. Here we study analytically an arbitrary stochastic search…
We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a…
This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime-switching is introduced. The decision-makers either harvest or renew with finite…
This paper considers online optimization for a system that performs a sequence of back-to-back tasks. Each task can be processed in one of multiple processing modes that affect the duration of the task, the reward earned, and an additional…
Policy gradient (PG) methods are successful approaches to deal with continuous reinforcement learning (RL) problems. They learn stochastic parametric (hyper)policies by either exploring in the space of actions or in the space of parameters.…
Optimal control deals with optimization problems in which variables steer a dynamical system, and its outcome contributes to the objective function. Two classical approaches to solving these problems are Dynamic Programming and the…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…