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We study model-based reinforcement learning in an unknown finite communicating Markov decision process. We propose a simple algorithm that leverages a variance based confidence interval. We show that the proposed algorithm, UCRL-V, achieves…
While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically…
We introduce SCAL, an algorithm designed to perform efficient exploration-exploitation in any unknown weakly-communicating Markov decision process (MDP) for which an upper bound $c$ on the span of the optimal bias function is known. For an…
While a large body of empirical results show that temporally-extended actions and options may significantly affect the learning performance of an agent, the theoretical understanding of how and when options can be beneficial in online…
We introduce and analyse two algorithms for exploration-exploitation in discrete and continuous Markov Decision Processes (MDPs) based on exploration bonuses. SCAL$^+$ is a variant of SCAL (Fruit et al., 2018) that performs efficient…
We consider Markov Decision Processes (MDPs) where the rewards are unknown and may change in an adversarial manner. We provide an algorithm that achieves state-of-the-art regret bound of $O( \sqrt{\tau (\ln|S|+\ln|A|)T}\ln(T))$, where $S$…
The upper confidence reinforcement learning (UCRL2) algorithm introduced in (Jaksch et al., 2010) is a popular method to perform regret minimization in unknown discrete Markov Decision Processes under the average-reward criterion. Despite…
We consider the problem of constrained Markov Decision Process (CMDP) where an agent interacts with a unichain Markov Decision Process. At every interaction, the agent obtains a reward. Further, there are $K$ cost functions. The agent aims…
This paper is devoted to the extension of the regret lower bound beyond ergodic Markov decision processes (MDPs) in the problem dependent setting. While the regret lower bound for ergodic MDPs is well-known and reached by tractable…
We study reinforcement learning in an infinite-horizon average-reward setting with linear function approximation, where the transition probability function of the underlying Markov Decision Process (MDP) admits a linear form over a feature…
In many sequential decision-making problems, the goal is to optimize a utility function while satisfying a set of constraints on different utilities. This learning problem is formalized through Constrained Markov Decision Processes (CMDPs).…
The problem of reinforcement learning in an unknown and discrete Markov Decision Process (MDP) under the average-reward criterion is considered, when the learner interacts with the system in a single stream of observations, starting from an…
We consider the problem of provably optimal exploration in reinforcement learning for finite horizon MDPs. We show that an optimistic modification to value iteration achieves a regret bound of $\tilde{O}( \sqrt{HSAT} + H^2S^2A+H\sqrt{T})$…
Any reinforcement learning algorithm that applies to all Markov decision processes (MDPs) will suffer $\Omega(\sqrt{SAT})$ regret on some MDP, where $T$ is the elapsed time and $S$ and $A$ are the cardinalities of the state and action…
We study learning in periodic Markov Decision Process (MDP), a special type of non-stationary MDP where both the state transition probabilities and reward functions vary periodically, under the average reward maximization setting. We…
We consider model-based reinforcement learning in finite Markov De- cision Processes (MDPs), focussing on so-called optimistic strategies. In MDPs, optimism can be implemented by carrying out extended value it- erations under a constraint…
We initiate the study of tradeoffs between exploration and exploitation in online learning of properties of quantum states. Given sequential oracle access to an unknown quantum state, in each round, we are tasked to choose an observable…
We consider a regret minimization task under the average-reward criterion in an unknown Factored Markov Decision Process (FMDP). More specifically, we consider an FMDP where the state-action space $\mathcal X$ and the state-space $\mathcal…
We tackle the problem of acting in an unknown finite and discrete Markov Decision Process (MDP) for which the expected shortest path from any state to any other state is bounded by a finite number $D$. An MDP consists of $S$ states and $A$…
We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning problems whose state-action space is endowed with a metric. We introduce Kernel-UCBVI, a model-based optimistic algorithm that leverages the…