Probabilistic models for data efficient reinforcement learning
File(s)
Author(s)
Kamthe, Sanket
Type
Thesis
Abstract
Trial-and-error based reinforcement learning (RL) has seen rapid advancements
in recent times, especially with the advent of deep neural networks. However, the
standard deep learning methods often overlook the progress made in control theory
by treating systems as black-box. We propose a model-based RL framework based
on probabilistic Model Predictive Control (MPC). In particular, we propose to learn
a probabilistic transition model using Gaussian Processes (GPs) to incorporate model
uncertainty into long-term predictions, thereby, reducing the impact of model errors. We
provide theoretical guarantees for first-order optimality in the GP-based transition models
with deterministic approximate inference for long-term planning. We demonstrate that
our approach not only achieves the state-of-the-art data efficiency, but also is a principled
way for RL in constrained environments.
When the true state of the dynamical system cannot be fully observed the standard
model based methods cannot be directly applied. For these systems an additional step of
state estimation is needed. We propose distributed message passing for state estimation in
non-linear dynamical systems. In particular, we propose to use expectation propagation
(EP) to iteratively refine the state estimate, i.e., the Gaussian posterior distribution on the
latent state. We show two things: (a) Classical Rauch-Tung-Striebel (RTS) smoothers,
such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS),
are special cases of our message passing scheme; (b) running the message passing
scheme more than once can lead to significant improvements over the classical RTS
smoothers. We show the explicit connection between message passing with EP and
well-known RTS smoothers and provide a practical implementation of the suggested
algorithm. Furthermore, we address convergence issues of EP by generalising this
framework to damped updates and the consideration of general 𝛼-divergences.
Probabilistic models can also be used to generate synthetic data. In model based RL
we use ’synthetic’ data as a proxy to real environments and in order to achieve high data
efficiency. The ability to generate high-fidelity synthetic data is crucial when available
(real) data is limited as in RL or where privacy and data protection standards allow
only for limited use of the given data, e.g., in medical and financial data-sets. Current
state-of-the-art methods for synthetic data generation are based on generative models,
such as Generative Adversarial Networks (GANs). Even though GANs have achieved
remarkable results in synthetic data generation, they are often challenging to interpret.
Furthermore, GAN-based methods can suffer when used with mixed real and categorical
variables. Moreover, the loss function (discriminator loss) design itself is problem
specific, i.e., the generative model may not be useful for tasks it was not explicitly trained
for. In this paper, we propose to use a probabilistic model as a synthetic data generator.
Learning the probabilistic model for the data is equivalent to estimating the density of
the data. Based on the copula theory, we divide the density estimation task into two parts,
i.e., estimating univariate marginals and estimating the multivariate copula density over
the univariate marginals. We use normalising flows to learn both the copula density and
univariate marginals. We benchmark our method on both simulated and real data-sets in
terms of density estimation as well as the ability to generate high-fidelity synthetic data.
in recent times, especially with the advent of deep neural networks. However, the
standard deep learning methods often overlook the progress made in control theory
by treating systems as black-box. We propose a model-based RL framework based
on probabilistic Model Predictive Control (MPC). In particular, we propose to learn
a probabilistic transition model using Gaussian Processes (GPs) to incorporate model
uncertainty into long-term predictions, thereby, reducing the impact of model errors. We
provide theoretical guarantees for first-order optimality in the GP-based transition models
with deterministic approximate inference for long-term planning. We demonstrate that
our approach not only achieves the state-of-the-art data efficiency, but also is a principled
way for RL in constrained environments.
When the true state of the dynamical system cannot be fully observed the standard
model based methods cannot be directly applied. For these systems an additional step of
state estimation is needed. We propose distributed message passing for state estimation in
non-linear dynamical systems. In particular, we propose to use expectation propagation
(EP) to iteratively refine the state estimate, i.e., the Gaussian posterior distribution on the
latent state. We show two things: (a) Classical Rauch-Tung-Striebel (RTS) smoothers,
such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS),
are special cases of our message passing scheme; (b) running the message passing
scheme more than once can lead to significant improvements over the classical RTS
smoothers. We show the explicit connection between message passing with EP and
well-known RTS smoothers and provide a practical implementation of the suggested
algorithm. Furthermore, we address convergence issues of EP by generalising this
framework to damped updates and the consideration of general 𝛼-divergences.
Probabilistic models can also be used to generate synthetic data. In model based RL
we use ’synthetic’ data as a proxy to real environments and in order to achieve high data
efficiency. The ability to generate high-fidelity synthetic data is crucial when available
(real) data is limited as in RL or where privacy and data protection standards allow
only for limited use of the given data, e.g., in medical and financial data-sets. Current
state-of-the-art methods for synthetic data generation are based on generative models,
such as Generative Adversarial Networks (GANs). Even though GANs have achieved
remarkable results in synthetic data generation, they are often challenging to interpret.
Furthermore, GAN-based methods can suffer when used with mixed real and categorical
variables. Moreover, the loss function (discriminator loss) design itself is problem
specific, i.e., the generative model may not be useful for tasks it was not explicitly trained
for. In this paper, we propose to use a probabilistic model as a synthetic data generator.
Learning the probabilistic model for the data is equivalent to estimating the density of
the data. Based on the copula theory, we divide the density estimation task into two parts,
i.e., estimating univariate marginals and estimating the multivariate copula density over
the univariate marginals. We use normalising flows to learn both the copula density and
univariate marginals. We benchmark our method on both simulated and real data-sets in
terms of density estimation as well as the ability to generate high-fidelity synthetic data.
Version
Open Access
Date Issued
2020-12
Date Awarded
2021-11
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
Advisor
Deisenroth, Marc
Publisher Department
Computing
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)