Related papers: Regret Bounds for Information-Directed Reinforceme…
We present an algorithm based on the \emph{Optimism in the Face of Uncertainty} (OFU) principle which is able to learn Reinforcement Learning (RL) modeled by Markov decision process (MDP) with finite state-action space efficiently. By…
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…
We establish a connection between the stability of mirror descent and the information ratio by Russo and Van Roy [2014]. Our analysis shows that mirror descent with suitable loss estimators and exploratory distributions enjoys the same…
We give a simple optimistic algorithm for which it is easy to derive regret bounds of $\tilde{O}(\sqrt{t_{\rm mix} SAT})$ after $T$ steps in uniformly ergodic Markov decision processes with $S$ states, $A$ actions, and mixing time parameter…
Modern tasks in reinforcement learning have large state and action spaces. To deal with them efficiently, one often uses predefined feature mapping to represent states and actions in a low-dimensional space. In this paper, we study…
We study the Bayesian regret of the renowned Thompson Sampling algorithm in contextual bandits with binary losses and adversarially-selected contexts. We adapt the information-theoretic perspective of \cite{RvR16} to the contextual setting…
This paper develops a viable notion of learning for sampling-based algorithms that applies in broader settings than previously considered. More specifically, we model a discounted infinite-horizon MDPs with Borel state and action spaces,…
In many sequential decision problems, an agent performs a repeated task. He then suffers regret and obtains information that he may use in the following rounds. However, sometimes the agent may also obtain information and avoid suffering…
Strong worst-case performance bounds for episodic reinforcement learning exist but fortunately in practice RL algorithms perform much better than such bounds would predict. Algorithms and theory that provide strong problem-dependent bounds…
We develop a model selection approach to tackle reinforcement learning with adversarial corruption in both transition and reward. For finite-horizon tabular MDPs, without prior knowledge on the total amount of corruption, our algorithm…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…
We develop a new approach to obtaining high probability regret bounds for online learning with bandit feedback against an adaptive adversary. While existing approaches all require carefully constructing optimistic and biased loss…
Deep reinforcement learning has achieved impressive successes yet often requires a very large amount of interaction data. This result is perhaps unsurprising, as using complicated function approximation often requires more data to fit, and…
We study the performance of the Thompson Sampling algorithm for logistic bandit problems. In this setting, an agent receives binary rewards with probabilities determined by a logistic function, $\exp(\beta \langle a, \theta…
Reinforcement learning (RL) has traditionally been understood from an episodic perspective; the concept of non-episodic RL, where there is no restart and therefore no reliable recovery, remains elusive. A fundamental question in…
The expected regret of any reinforcement learning algorithm is lower bounded by $\Omega\left(\sqrt{DXAT}\right)$ for undiscounted returns, where $D$ is the diameter of the Markov decision process, $X$ the size of the state space, $A$ the…
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…
This paper initiates the study of data-dependent regret bounds in constrained MAB settings. These bounds depend on the sequence of losses that characterize the problem instance. Thus, they can be much smaller than classical…
In order to make good decision under uncertainty an agent must learn from observations. To do so, two of the most common frameworks are Contextual Bandits and Markov Decision Processes (MDPs). In this paper, we study whether there exist…
We analyze the Bayesian regret of the Gaussian process posterior sampling reinforcement learning (GP-PSRL) algorithm. Posterior sampling is an effective heuristic for decision-making under uncertainty that has been used to develop…