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This paper considers an infinite-horizon Markov decision process (MDP) that allows for general non-exponential discount functions, in both discrete and continuous time. Due to the inherent time inconsistency, we look for a randomized…
We study the synthesis of a policy in a Markov decision process (MDP) following which an agent reaches a target state in the MDP while minimizing its total discounted cost. The problem combines a reachability criterion with a discounted…
We consider a Markov decision process with deterministic state transition dynamics, adversarially generated rewards that change arbitrarily from round to round, and a bandit feedback model in which the decision maker only observes the…
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…
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…
We study discrete-time discounted constrained Markov decision processes (CMDPs) on Borel spaces with unbounded reward functions. In our approach the transition probability functions are weakly or set-wise continuous. The reward functions…
Continuous-time Markov decision processes are an important class of models in a wide range of applications, ranging from cyber-physical systems to synthetic biology. A central problem is how to devise a policy to control the system in order…
We study regret minimization for infinite-horizon average-reward Markov Decision Processes (MDPs) under cost constraints. We start by designing a policy optimization algorithm with carefully designed action-value estimator and bonus term,…
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…
Optimal policies in Markov decision processes (MDPs) are very sensitive to model misspecification. This raises serious concerns about deploying them in high-stake domains. Robust MDPs (RMDP) provide a promising framework to mitigate…
We propose and analyze a temporal concatenation heuristic for solving large-scale finite-horizon Markov decision processes (MDP), which divides the MDP into smaller sub-problems along the time horizon and generates an overall solution by…
This paper investigates a series of optimization problems for one-counter Markov decision processes (MDPs) and integer-weighted MDPs with finite state space. Specifically, it considers problems addressing termination probabilities and…
We consider a multi-hypothesis testing problem involving a K-armed bandit. Each arm's signal follows a distribution from a vector exponential family. The actual parameters of the arms are unknown to the decision maker. The decision maker…
A labelled Markov decision process (MDP) is a labelled Markov chain with nondeterminism; i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by…
We study the common generalization of Markov decision processes (MDPs) with sets of transition probabilities, known as robust MDPs (RMDPs). A standard goal in RMDPs is to compute a policy that maximizes the expected return under an…
A wide variety of queueing systems can be naturally modeled as infinite-state Markov Decision Processes (MDPs). In the reinforcement learning (RL) context, a variety of algorithms have been developed to learn and optimize these MDPs. At the…
We consider fair resource allocation in sequential decision-making environments modeled as weakly coupled Markov decision processes, where resource constraints couple the action spaces of $N$ sub-Markov decision processes (sub-MDPs) that…
Recently, several studies (Zhou et al., 2021a; Zhang et al., 2021b; Kim et al., 2021; Zhou and Gu, 2022) have provided variance-dependent regret bounds for linear contextual bandits, which interpolates the regret for the worst-case regime…
This note describes sufficient conditions under which total-cost and average-cost Markov decision processes (MDPs) with general state and action spaces, and with weakly continuous transition probabilities, can be reduced to discounted MDPs.…
This paper considers what we propose to call multi-gear bandits, which are Markov decision processes modeling a generic dynamic and stochastic project fueled by a single resource and which admit multiple actions representing gears of…