Related papers: On Skolem-hardness and saturation points in Markov…

The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…

We consider the problem of controlling a fully specified Markov decision process (MDP), also known as the planning problem, when the state space is very large and calculating the optimal policy is intractable. Instead, we pursue the more…

We study the problem of online learning in a class of Markov decision processes known as linearly solvable MDPs. In the stationary version of this problem, a learner interacts with its environment by directly controlling the state…

Partially Observable Markov Decision Processes (POMDPs) are powerful models for sequential decision making under transition and observation uncertainties. This paper studies the challenging yet important problem in POMDPs known as the…

There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both…

The problem of constrained Markov decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its utilities/costs. A new primal-dual approach is…

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…

A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…

In this paper, we consider the optimal stopping problem on semi-Markov processes (SMPs) with finite horizon, and aim to establish the existence and computation of optimal stopping times. To achieve the goal, we first develop the main…

Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…

We revisit the problem of finding optimal strategies for deterministic Markov Decision Processes (DMDPs), and a closely related problem of testing feasibility of systems of $m$ linear inequalities on $n$ real variables with at most two…

In this paper, we consider a modified version of the control problem in a model free Markov decision process (MDP) setting with large state and action spaces. The control problem most commonly addressed in the contemporary literature is to…

We are interested in risk constraints for infinite horizon discrete time Markov decision processes (MDPs). Starting with average reward MDPs, we show that increasing concave stochastic dominance constraints on the empirical distribution of…

Robust Markov decision processes (MDPs) aim to handle changing or partially known system dynamics. To solve them, one typically resorts to robust optimization methods. However, this significantly increases computational complexity and…

Markov decision processes (MDPs) and simple stochastic games (SSGs) provide a rich mathematical framework to study many important problems related to probabilistic systems. MDPs and SSGs with finite-horizon objectives, where the goal is to…

With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion…

We study the Safe Reinforcement Learning (SRL) problem using the Constrained Markov Decision Process (CMDP) formulation in which an agent aims to maximize the expected total reward subject to a safety constraint on the expected total value…

We consider a class of optimization problems over stochastic variables where the algorithm can learn information about the value of any variable through a series of costly steps; we model this information acquisition process as a Markov…

Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…

We study the online estimation of the optimal policy of a Markov decision process (MDP). We propose a class of Stochastic Primal-Dual (SPD) methods which exploit the inherent minimax duality of Bellman equations. The SPD methods update a…