TMB: Automatic Differentiation and Laplace Approximation

TMB is an open source R package that enables quick implementation of complex nonlinear random effect (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, admb-project.org). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (~10^6) and parameters (~10^3). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems. The package and examples are available at http://tmb-project.org

Measure-valued differentiation for stationary Markov chains

http://staff.feweb.vu.nl/bheidergot

Optimization and sensitivity analysis of computer simulation models by the score function method

Experimental Design;Simulation;Optimization;Queueing Theory

A cyclo-stationary complex multichannel wiener filter for the prediction of wind speed and direction

This paper develops a linear predictor for application to wind speed and direction forecasting in time and across different sites. The wind speed and direction are modelled via the magnitude and phase of a complex-valued time-series. A multichannel adaptive filter is set to predict this signal, based on its past values and the spatio-temporal correlation between wind signals measured at numerous geographical locations. The time-varying nature of the underlying system and the annual cycle of seasons motivates the development of a cyclo-stationary Wiener filter, which is tested on hourly mean wind speed and direction data from 13 weather stations across the UK, and shown to provide an improvement over both stationary Wiener filtering and a recent auto-regressive approach

Risk-Sensitive Reinforcement Learning: A Constrained Optimization Viewpoint

The classic objective in a reinforcement learning (RL) problem is to find a policy that minimizes, in expectation, a long-run objective such as the infinite-horizon discounted or long-run average cost. In many practical applications, optimizing the expected value alone is not sufficient, and it may be necessary to include a risk measure in the optimization process, either as the objective or as a constraint. Various risk measures have been proposed in the literature, e.g., mean-variance tradeoff, exponential utility, the percentile performance, value at risk, conditional value at risk, prospect theory and its later enhancement, cumulative prospect theory. In this article, we focus on the combination of risk criteria and reinforcement learning in a constrained optimization framework, i.e., a setting where the goal to find a policy that optimizes the usual objective of infinite-horizon discounted/average cost, while ensuring that an explicit risk constraint is satisfied. We introduce the risk-constrained RL framework, cover popular risk measures based on variance, conditional value-at-risk and cumulative prospect theory, and present a template for a risk-sensitive RL algorithm. We survey some of our recent work on this topic, covering problems encompassing discounted cost, average cost, and stochastic shortest path settings, together with the aforementioned risk measures in a constrained framework. This non-exhaustive survey is aimed at giving a flavor of the challenges involved in solving a risk-sensitive RL problem, and outlining some potential future research directions