Related papers: Finite-Sample Analysis of the Monte Carlo Explorin…
Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum…
We study the problem of pure exploration in matching markets under uncertain preferences, where the goal is to identify a stable matching with confidence parameter $\delta$ and minimal sample complexity. Agents learn preferences via…
We revisit the Reinforce policy gradient algorithm from the literature. Note that this algorithm typically works with cost returns obtained over random length episodes obtained from either termination upon reaching a goal state (as with…
With the aim of improving performance in Markov Decision Problem in an Off-Policy setting, we suggest taking inspiration from what is done in Offline Reinforcement Learning (RL). In Offline RL, it is a common practice during policy learning…
Policy optimization is an effective reinforcement learning approach to solve continuous control tasks. Recent achievements have shown that alternating online and offline optimization is a successful choice for efficient trajectory reuse.…
Reverse Monte Carlo (RMC) is an algorithm that incorporates stochastic modification of the action as part of the process that updates the fields in a Monte Carlo simulation. Such update moves have the potential of lowering or eliminating…
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions,…
While traditional distributionally robust optimization (DRO) aims to minimize the maximal risk over a set of distributions, Agarwal and Zhang (2022) recently proposed a variant that replaces risk with excess risk. Compared to DRO, the new…
We establish the geometric ergodicity of the preconditioned Hamiltonian Monte Carlo (HMC) algorithm defined on an infinite-dimensional Hilbert space, as developed in [Beskos et al., Stochastic Process. Appl., 2011]. This algorithm can be…
Background: Designing amino acid sequences that are stable in a given target structure amounts to maximizing a conditional probability. A straightforward approach to accomplish this is a nested Monte Carlo where the conformation space is…
We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…
We present an extension of Monte Carlo Tree Search (MCTS) that strongly increases its efficiency for trees with asymmetry and/or loops. Asymmetric termination of search trees introduces a type of uncertainty for which the standard upper…
In Bayesian inference, we seek to compute information about random variables such as moments or quantiles on the basis of {available data} and prior information. When the distribution of random variables is {intractable}, Monte Carlo (MC)…
Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…
Adaptive importance samplers are adaptive Monte Carlo algorithms to estimate expectations with respect to some target distribution which \textit{adapt} themselves to obtain better estimators over a sequence of iterations. Although it is…
Most reinforcement learning practitioners evaluate their policies with online Monte Carlo estimators for either hyperparameter tuning or testing different algorithmic design choices, where the policy is repeatedly executed in the…
The optimized certainty equivalent (OCE) is a family of risk measures that cover important examples such as entropic risk, conditional value-at-risk and mean-variance models. In this paper, we propose a new episodic risk-sensitive…
Importance Sampling (IS), an effective variance reduction strategy in Monte Carlo (MC) simulation, is frequently utilized for Bayesian inference and other statistical challenges. Quasi-Monte Carlo (QMC) replaces the random samples in MC…