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Rather than augmenting rewards with penalties for undesired behavior, Constrained Partially Observable Markov Decision Processes (CPOMDPs) plan safely by imposing inviolable hard constraint value budgets. Previous work performing online…
It is common to address the curse of dimensionality in Markov decision processes (MDPs) by exploiting low-rank representations. This motivates much of the recent theoretical study on linear MDPs. However, most approaches require a given…
Time bounded reachability is a fundamental problem in model checking continuous-time Markov chains (CTMCs) and Markov decision processes (CTMDPs) for specifications in continuous stochastic logics. It can be computed by numerically solving…
We consider the problem belief-state monitoring for the purposes of implementing a policy for a partially-observable Markov decision process (POMDP), specifically how one might approximate the belief state. Other schemes for belief-state…
In this paper, we develop a Topological Approximate Dynamic Programming (TADP) method for planningin stochastic systems modeled as Markov Decision Processesto maximize the probability of satisfying high-level systemspecifications expressed…
We study finite memory belief approximation for partially observable (PO) stochastic optimal control (SOC) problems. While belief states are sufficient for SOC in partially observable Markov decision processes (POMDPs), they are generally…
We revisit closed-loop performance guarantees for Model Predictive Control in the deterministic and stochastic cases, which extend to novel performance results applicable to receding horizon control of Partially Observable Markov Decision…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
We study the $(\varepsilon, \delta)$-PAC policy identification problem in finite-horizon episodic Markov Decision Processes. Existing approaches provide finite-time guarantees for approximate settings ($\varepsilon>0$) but suffer from high…
Stability under model predictive control (MPC) schemes is frequently ensured by terminal ingredients. Employing a (control) Lyapunov function as the terminal cost constitutes a common choice. Learning-based methods may be used to construct…
We consider synthesis of control policies that maximize the probability of satisfying given temporal logic specifications in unknown, stochastic environments. We model the interaction between the system and its environment as a Markov…
Markov decision processes (MDPs) is viewed as an optimization of an objective function over certain linear operators over general function spaces. A new existence result is established for the existence of optimal policies in general MDPs,…
We consider partially observable Markov decision processes (POMDPs) with {\omega}-regular conditions specified as parity objectives. The class of {\omega}-regular languages extends regular languages to infinite strings and provides a robust…
A standard objective in partially-observable Markov decision processes (POMDPs) is to find a policy that maximizes the expected discounted-sum payoff. However, such policies may still permit unlikely but highly undesirable outcomes, which…
Algorithms developed under stationary Markov Decision Processes (MDPs) often face challenges in non-stationary environments, and infinite-horizon formulations may not directly apply to finite-horizon tasks. To address these limitations, we…
Policy gradient methods are widely used in reinforcement learning. Yet, the nonconvexity of policy optimization poses significant challenges in understanding the global convergence of policy gradient methods. For a class of finite-horizon…
We study the computational complexity of the infinite-horizon discounted-reward Markov Decision Problem (MDP) with a finite state space $|\mathcal{S}|$ and a finite action space $|\mathcal{A}|$. We show that any randomized algorithm needs a…
We propose policy gradient algorithms for robust infinite-horizon Markov decision processes (MDPs) with non-rectangular uncertainty sets, thereby addressing an open challenge in the robust MDP literature. Indeed, uncertainty sets that…
Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a…
Partially Observable Markov Decision Processes (POMDPs) provide an efficient way to model real-world sequential decision making processes. Motivated by the problem of maintenance and inspection of a group of infrastructure components with…