Related papers: Measurable Monte Carlo Search Error Bounds

Monte Carlo Exploring Starts (MCES), which aims to learn the optimal policy using only sample returns, is a simple and natural algorithm in reinforcement learning which has been shown to converge under various conditions. However, the…

The analysis of online least squares estimation is at the heart of many stochastic sequential decision making problems. We employ tools from the self-normalized processes to provide a simple and self-contained proof of a tail bound of a…

We study the stochastic multi-armed bandit problem when one knows the value $\mu^{(\star)}$ of an optimal arm, as a well as a positive lower bound on the smallest positive gap $\Delta$. We propose a new randomized policy that attains a…

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 present a new algorithm based on posterior sampling for learning in constrained Markov decision processes (CMDP) in the infinite-horizon undiscounted setting. The algorithm achieves near-optimal regret bounds while being advantageous…

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 prove a bound on the finite sample error of sequential Monte Carlo (SMC) on static spaces using the $L_2$ distance between interpolating distributions and the mixing times of Markov kernels. This result is unique in that it is the first…

We present an algorithm based on posterior sampling (aka Thompson sampling) that achieves near-optimal worst-case regret bounds when the underlying Markov Decision Process (MDP) is communicating with a finite, though unknown, diameter. Our…

Markov chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities?…

We study how the regret guarantees of nonstochastic multi-armed bandits can be improved, if the effective range of the losses in each round is small (e.g. the maximal difference between two losses in a given round). Despite a recent…

Much current research in AI and games is being devoted to Monte Carlo search (MCS) algorithms. While the quest for a single unified MCS algorithm that would perform well on all problems is of major interest for AI, practitioners often know…

Monte-Carlo Tree Search (MCTS) typically uses multi-armed bandit (MAB) strategies designed to minimize cumulative regret, such as UCB1, as its selection strategy. However, in the root node of the search tree, it is more sensible to minimize…

We present a new Monte Carlo Tree Search (MCTS) algorithm to solve the stochastic orienteering problem with chance constraints, i.e., a version of the problem where travel costs are random, and one is assigned a bound on the tolerable…

We study finite-armed semiparametric bandits, where each arm's reward combines a linear component with an unknown, potentially adversarial shift. This model strictly generalizes classical linear bandits and reflects complexities common in…

This paper concerns error bounds for recursive equations subject to Markovian disturbances. Motivating examples abound within the fields of Markov chain Monte Carlo (MCMC) and Reinforcement Learning (RL), and many of these algorithms can be…

In this research note, we revisit the bandits with expert advice problem. Under a restricted feedback model, we prove a lower bound of order $\sqrt{K T \ln(N/K)}$ for the worst-case regret, where $K$ is the number of actions, $N>K$ the…

Bayesian optimization is a popular framework for efficiently tackling black-box search problems. As a rule, these algorithms operate by iteratively choosing what to evaluate next until some predefined budget has been exhausted. We…

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…

We consider the framework of stochastic multi-armed bandit problems and study the possibilities and limitations of forecasters that perform an on-line exploration of the arms. These forecasters are assessed in terms of their simple regret,…

A standard assumption in Reinforcement Learning is that the agent observes every visited state-action pair in the associated Markov Decision Process (MDP), along with the per-step rewards. Strong theoretical results are known in this…