Dynamics-based sampling methods, such as Hybrid Monte Carlo (HMC) and Langevin dynamics (LD), are commonly used to sample target distributions. Recently, such approaches have been combined with stochastic gradient techniques to increase sampling efficiency when dealing with large datasets. An outstanding problem with this approach is that the stochastic gradient introduces an unknown amount of noise which can prevent proper sampling after discretization. To remedy this problem, we show that one can leverage a small number of additional variables to stabilize momentum fluctuations induced by the unknown noise. Our method is inspired by the idea of a thermostat in statistical physics and is justified by a general theory.

Dynamic pricing is a fast-moving research area in machine learning and operations management. A lot of work has been done for this problem with known noise. In this paper, we consider a contextual dynamic pricing problem under a linear customer valuation model with an unknown market noise distribution F . This problem is very challenging due to the difficulty in balancing three tangled tasks of revenue-maximization, estimating the linear valuation parameter \theta_{0}, and learning the nonparametric F . To address this issue, we develop a novel {\it Explore-then-UCB} (ExUCB) strategy that includes an exploration for \theta_{0} -learning and a followed UCB procedure of joint revenue-maximization and F -learning.

Dynamics-based sampling methods, such as Hybrid Monte Carlo (HMC) and Langevin dynamics (LD), are commonly used to sample target distributions. Recently, such approaches have been combined with stochastic gradient techniques to increase sampling efficiency when dealing with large datasets. An outstanding problem with this approach is that the stochastic gradient introduces an unknown amount of noise which can prevent proper sampling after discretization. To remedy this problem, we show that one can leverage a small number of additional variables to stabilize momentum fluctuations induced by the unknown noise. Our method is inspired by the idea of a thermostat in statistical physics and is justified by a general theory.

In this paper, we consider a novel machine learning problem, that is, learning a classifier from noisy label distributions. In this problem, each instance with a feature vector belongs to at least one group. Then, instead of the true label of each instance, we observe the label distribution of the instances associated with a group, where the label distribution is distorted by an unknown noise. Our goals are to (1) estimate the true label of each instance, and (2) learn a classifier that predicts the true label of a new instance. We propose a probabilistic model that considers true label distributions of groups and parameters that represent the noise as hidden variables. The model can be learned based on a variational Bayesian method. In numerical experiments, we show that the proposed model outperforms existing methods in terms of the estimation of the true labels of instances.

Dynamics-based sampling methods, such as Hybrid Monte Carlo (HMC) and Langevin dynamics (LD), are commonly used to sample target distributions. Recently, such approaches have been combined with stochastic gradient techniques to increase sampling efficiency when dealing with large datasets. An outstanding problem with this approach is that the stochastic gradient introduces an unknown amount of noise which can prevent proper sampling after discretization. To remedy this problem, we show that one can leverage a small number of additional variables in order to stabilize momentum fluctuations induced by the unknown noise. Our method is inspired by the idea of a thermostat in statistical physics and is justified by a general theory.