A Survey of Monte Carlo Methods for Noisy and Costly Densities With Application to Reinforcement Learning and ABC

Author:

Llorente Fernando1ORCID,Martino Luca23ORCID,Read Jesse4,Delgado‐Gómez David5ORCID

Affiliation:

1. Department of Electrical Engineering Stony Brook University Stony Brook NY USA

2. Department of Signal Processing Universidad Rey Juan Carlos Fuenlabrada Spain

3. Departamento de Economia e Impresa Università di Catania Catania Italy

4. Computer Science Laboratory École Polytechnique Palaiseau France

5. Department of Statistics Universidad Carlos III de Madrid Leganés Spain

Abstract

SummaryThis survey gives an overview of Monte Carlo methodologies using surrogate models, for dealing with densities that are intractable, costly, and/or noisy. This type of problem can be found in numerous real‐world scenarios, including stochastic optimisation and reinforcement learning, where each evaluation of a density function may incur some computationally‐expensive or even physical (real‐world activity) cost, likely to give different results each time. The surrogate model does not incur this cost, but there are important trade‐offs and considerations involved in the choice and design of such methodologies. We classify the different methodologies into three main classes and describe specific instances of algorithms under a unified notation. A modular scheme that encompasses the considered methods is also presented. A range of application scenarios is discussed, with special attention to the likelihood‐free setting and reinforcement learning. Several numerical comparisons are also provided.

Publisher

Wiley

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