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Policy optimization is an effective reinforcement learning approach to solve continuous control tasks. Recent achievements have shown that alternating online and offline optimization is a successful choice for efficient trajectory reuse.…
This paper deals with unconstrained discounted continuous-time Markov decision processes in Borel state and action spaces. Under some conditions imposed on the primitives, allowing unbounded transition rates and unbounded (from both above…
In this review/tutorial article, we present recent progress on optimal control of partially observed Markov Decision Processes (POMDPs). We first present regularity and continuity conditions for POMDPs and their belief-MDP reductions, where…
We consider average-cost Markov decision processes (MDPs) with Borel state spaces, countable, discrete action spaces, and strictly unbounded one-stage costs. For the minimum pair approach, we introduce a new majorization condition on the…
This paper presents a new and straightforward procedure for solving bilinear quadratic optimal control problem. In this method, first the original optimal control problem is transformed into a nonlinear twopoint boundary value problem…
The Partially Observable Markov Decision Process has long been recognized as a rich framework for real-world planning and control problems, especially in robotics. However exact solutions in this framework are typically computationally…
In this work, we study discrete-time Markov decision processes (MDPs) under constraints with Borel state and action spaces and where all the performance functions have the same form of the expected total reward (ETR) criterion over the…
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…
We consider the problem of finding the best memoryless stochastic policy for an infinite-horizon partially observable Markov decision process (POMDP) with finite state and action spaces with respect to either the discounted or mean reward…
In this paper, we establish a general stochastic maximum principle for optimal control for systems described by a continuous-time Markov regime-switching stochastic recursive utilities model. The control domain is postulated not to be…
We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite…
Integrated task and motion planning has emerged as a challenging problem in sequential decision making, where a robot needs to compute high-level strategy and low-level motion plans for solving complex tasks. While high-level strategies…
In this paper, we consider a continuous-time Markov decision process (CTMDP) in Borel spaces, where the certainty equivalent with respect to the exponential utility of the total undiscounted cost is to be minimized. The cost rate is…
This paper presents a novel approach to pricing American options using piecewise diffusion Markov processes (PDifMPs), a type of generalised stochastic hybrid system that integrates continuous dynamics with discrete jump processes. Standard…
This paper studies discrete-time average-cost infinite-horizon Markov decision processes (MDPs) with Borel state and action sets. It introduces new sufficient conditions for { the} validity of optimality inequalities and optimality…
We present a new, tractable method for solving and analyzing risk-aware control problems over finite and infinite, discounted time-horizons where the dynamics of the controlled process are described as a martingale problem. Supposing…
Motivated by wide-ranging applications such as video delivery over networks using Multiple Description Codes, congestion control, and inventory management, we study the state-tracking of a Markovian random process with a known transition…
Filtering---estimating the state of a partially observable Markov process from a sequence of observations---is one of the most widely studied problems in control theory, AI, and computational statistics. Exact computation of the posterior…
This paper considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector field, polynomial Lagrangian and semialgebraic input and state constraints. The OCP is first relaxed as an…
In this paper, we consider the problem of periodic optimal control of nonlinear systems subject to online changing and periodically time-varying economic performance measures using model predictive control (MPC). The proposed economic MPC…