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In this study, we derive Probably Approximately Correct (PAC) bounds on the asymptotic sample-complexity for RL within the infinite-horizon Markov Decision Process (MDP) setting that are sharper than those in existing literature. The…
Multi-objective optimization models that encode ordered sequential constraints provide a solution to model various challenging problems including encoding preferences, modeling a curriculum, and enforcing measures of safety. A recently…
The theory of reinforcement learning has focused on two fundamental problems: achieving low regret, and identifying $\epsilon$-optimal policies. While a simple reduction allows one to apply a low-regret algorithm to obtain an…
We study model-based learning of finite-window policies in tabular partially observable Markov decision processes (POMDPs). A common approach to learning under partial observability is to approximate unbounded history dependencies using…
Markov decision processes (MDPs) describe sequential decision-making processes; MDP policies return for every state in that process an advised action. Classical algorithms can efficiently compute policies that are optimal with respect to,…
Safety is a fundamental challenge in reinforcement learning (RL), particularly in real-world applications such as autonomous driving, robotics, and healthcare. To address this, Constrained Markov Decision Processes (CMDPs) are commonly used…
This paper proposes a novel termination criterion, termed the advantage gap function, for finite state and action Markov decision processes (MDP) and reinforcement learning (RL). By incorporating this advantage gap function into the design…
This paper considers the best policy identification (BPI) problem in online Constrained Markov Decision Processes (CMDPs). We are interested in algorithms that are model-free, have low regret, and identify an approximately optimal policy…
Many real-world applications, such as those in medical domains, recommendation systems, etc, can be formulated as large state space reinforcement learning problems with only a small budget of the number of policy changes, i.e., low…
The constrained Markov decision process (CMDP) framework emerges as an important reinforcement learning approach for imposing safety or other critical objectives while maximizing cumulative reward. However, the current understanding of how…
We consider the problem of learning an $\varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Given access to a generative model, we achieve rate-optimal sample…
We study policy iteration for infinite-horizon Markov decision processes. It has recently been shown policy iteration style algorithms have exponential lower bounds in a two player game setting. We extend these lower bounds to Markov…
In this paper, we are concerned with a worst-case complexity analysis of a-posteriori algorithms for unconstrained multiobjective optimization. Specifically, we propose an algorithmic framework that generates sets of points by means of…
We study the computational complexity of decision problems in $k$-level linear programming (LP). Seminal work by Jeroslow establishes that determining whether the optimal objective value of a $k$-level LP is at least as good as a given…
Optimizing a partially observable Markov decision process (POMDP) policy is challenging. The policy graph improvement (PGI) algorithm for POMDPs represents the policy as a fixed size policy graph and improves the policy monotonically. Due…
In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…
We study the sample complexity of the plug-in approach for learning $\varepsilon$-optimal policies in average-reward Markov decision processes (MDPs) with a generative model. The plug-in approach constructs a model estimate then computes an…
We consider the optimal sample complexity theory of tabular reinforcement learning (RL) for maximizing the infinite horizon discounted reward in a Markov decision process (MDP). Optimal worst-case complexity results have been developed for…
Model-free reinforcement learning algorithms combined with value function approximation have recently achieved impressive performance in a variety of application domains. However, the theoretical understanding of such algorithms is limited,…
We study countably infinite MDPs with parity objectives. Unlike in finite MDPs, optimal strategies need not exist, and may require infinite memory if they do. We provide a complete picture of the exact strategy complexity of…