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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…
The increasing use of autonomous and semi-autonomous agents in society has made it crucial to validate their safety. However, the complex scenarios in which they are used may make formal verification impossible. To address this challenge,…
The Markov decision process (MDP) provides a mathematical framework for modeling sequential decision-making problems, many of which are crucial to security and safety, such as autonomous driving and robot control. The rapid development of…
We consider the control of a Markov decision process (MDP) that undergoes an abrupt change in its transition kernel (mode). We formulate the problem of minimizing regret under control-switching based on mode change detection, compared to a…
Safe reinforcement learning (RL) is a promising approach for many real-world decision-making problems where ensuring safety is a critical necessity. In safe RL research, while expected cumulative safety constraints (ECSCs) are typically the…
In this paper we model basketball plays as episodes from team-specific non-stationary Markov decision processes (MDPs) with shot clock dependent transition probabilities. Bayesian hierarchical models are employed in the modeling and…
This paper presents a decentralized, online planning approach for scalable maneuver planning for large constellations. While decentralized, rule-based strategies have facilitated efficient scaling, optimal decision-making algorithms for…
Reinforcement learning algorithms are typically designed for generic Markov Decision Processes (MDPs), where any state-action pair can lead to an arbitrary transition distribution. In many practical systems, however, only a subset of the…
Novel advanced policy gradient (APG) algorithms, such as proximal policy optimization (PPO), trust region policy optimization, and their variations, have become the dominant reinforcement learning (RL) algorithms because of their ease of…
Energy Markov Decision Processes (EMDPs) are finite-state Markov decision processes where each transition is assigned an integer counter update and a rational payoff. An EMDP configuration is a pair s(n), where s is a control state and n is…
Significant digitalization of financial services in a short period of time has led to an urgent demand to have autonomous, transparent and real-time credit risk decision making systems. The traditional machine learning models are effective…
This paper presents a dynamic game framework to analyze the role of large banks in interbank markets. By extending existing models, we incorporate a large bank as a dynamic decision-maker interacting with multiple small banks. Using the…
We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…
The solution convergence of Markov Decision Processes (MDPs) can be accelerated by prioritized sweeping of states ranked by their potential impacts to other states. In this paper, we present new heuristics to speed up the solution…
A popular approach to solving a decision process with non-Markovian rewards (NMRDP) is to exploit a compact representation of the reward function to automatically translate the NMRDP into an equivalent Markov decision process (MDP) amenable…
Robust Markov decision processes (MDPs) provide a general framework to model decision problems where the system dynamics are changing or only partially known. Efficient methods for some \texttt{sa}-rectangular robust MDPs exist, using its…
A simple banking network model is proposed which features multiple waves of bank defaults and is analytically solvable in the limiting case of an infinitely large homogeneous network. The model is a collection of nodes representing…
Policy Iteration (PI) is a widely used family of algorithms to compute optimal policies for Markov Decision Problems (MDPs). We derive upper bounds on the running time of PI on Deterministic MDPs (DMDPs): the class of MDPs in which every…
A Tree Markov Decision Problem (T-MDP) is a finite-horizon MDP with a starting state $s_{1}$, in which every state is reachable from $s_{1}$ through exactly one state-action trajectory. T-MDPs arise naturally as abstractions of decision…
This paper investigates the limit behavior of Markov Decision Processes (MDPs) made of independent particles evolving in a common environment, when the number of particles goes to infinity. In the finite horizon case or with a discounted…