1,081 research outputs found
Constructing Parsimonious Analytic Models for Dynamic Systems via Symbolic Regression
Developing mathematical models of dynamic systems is central to many
disciplines of engineering and science. Models facilitate simulations, analysis
of the system's behavior, decision making and design of automatic control
algorithms. Even inherently model-free control techniques such as reinforcement
learning (RL) have been shown to benefit from the use of models, typically
learned online. Any model construction method must address the tradeoff between
the accuracy of the model and its complexity, which is difficult to strike. In
this paper, we propose to employ symbolic regression (SR) to construct
parsimonious process models described by analytic equations. We have equipped
our method with two different state-of-the-art SR algorithms which
automatically search for equations that fit the measured data: Single Node
Genetic Programming (SNGP) and Multi-Gene Genetic Programming (MGGP). In
addition to the standard problem formulation in the state-space domain, we show
how the method can also be applied to input-output models of the NARX
(nonlinear autoregressive with exogenous input) type. We present the approach
on three simulated examples with up to 14-dimensional state space: an inverted
pendulum, a mobile robot, and a bipedal walking robot. A comparison with deep
neural networks and local linear regression shows that SR in most cases
outperforms these commonly used alternative methods. We demonstrate on a real
pendulum system that the analytic model found enables a RL controller to
successfully perform the swing-up task, based on a model constructed from only
100 data samples
Black-Box Data-efficient Policy Search for Robotics
The most data-efficient algorithms for reinforcement learning (RL) in
robotics are based on uncertain dynamical models: after each episode, they
first learn a dynamical model of the robot, then they use an optimization
algorithm to find a policy that maximizes the expected return given the model
and its uncertainties. It is often believed that this optimization can be
tractable only if analytical, gradient-based algorithms are used; however,
these algorithms require using specific families of reward functions and
policies, which greatly limits the flexibility of the overall approach. In this
paper, we introduce a novel model-based RL algorithm, called Black-DROPS
(Black-box Data-efficient RObot Policy Search) that: (1) does not impose any
constraint on the reward function or the policy (they are treated as
black-boxes), (2) is as data-efficient as the state-of-the-art algorithm for
data-efficient RL in robotics, and (3) is as fast (or faster) than analytical
approaches when several cores are available. The key idea is to replace the
gradient-based optimization algorithm with a parallel, black-box algorithm that
takes into account the model uncertainties. We demonstrate the performance of
our new algorithm on two standard control benchmark problems (in simulation)
and a low-cost robotic manipulator (with a real robot).Comment: Accepted at the IEEE/RSJ International Conference on Intelligent
Robots and Systems (IROS) 2017; Code at
http://github.com/resibots/blackdrops; Video at http://youtu.be/kTEyYiIFGP
Approximate Dynamic Programming with Gaussian Processes
In general, it is difficult to determine an optimal closed-loop policy in nonlinear control problems with continuous-valued state and control domains. Hence, approximations are often inevitable. The standard method of discretizing states and controls suffers from the curse of dimensionality and strongly depends on the chosen temporal sampling rate. In this paper, we introduce Gaussian process dynamic programming (GPDP) and determine an approximate globally optimal closed-loop policy. In GPDP, value functions in the Bellman recursion of the dynamic programming algorithm are modeled using Gaussian processes. GPDP returns an optimal statefeedback for a finite set of states. Based on these outcomes, we learn a possibly discontinuous closed-loop policy on the entire state space by switching between two independently trained Gaussian processes. A binary classifier selects one Gaussian process to predict the optimal control signal. We show that GPDP is able to yield an almost optimal solution to an LQ problem using few sample points. Moreover, we successfully apply GPDP to the underpowered pendulum swing up, a complex nonlinear control problem
Data-Efficient Reinforcement Learning with Probabilistic Model Predictive Control
Trial-and-error based reinforcement learning (RL) has seen rapid advancements
in recent times, especially with the advent of deep neural networks. However,
the majority of autonomous RL algorithms require a large number of interactions
with the environment. A large number of interactions may be impractical in many
real-world applications, such as robotics, and many practical systems have to
obey limitations in the form of state space or control constraints. To reduce
the number of system interactions while simultaneously handling constraints, 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 then
use MPC to find a control sequence that minimises the expected long-term cost.
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 does not only achieve
state-of-the-art data efficiency, but also is a principled way for RL in
constrained environments.Comment: Accepted at AISTATS 2018
Benchmarking Deep Reinforcement Learning for Continuous Control
Recently, researchers have made significant progress combining the advances
in deep learning for learning feature representations with reinforcement
learning. Some notable examples include training agents to play Atari games
based on raw pixel data and to acquire advanced manipulation skills using raw
sensory inputs. However, it has been difficult to quantify progress in the
domain of continuous control due to the lack of a commonly adopted benchmark.
In this work, we present a benchmark suite of continuous control tasks,
including classic tasks like cart-pole swing-up, tasks with very high state and
action dimensionality such as 3D humanoid locomotion, tasks with partial
observations, and tasks with hierarchical structure. We report novel findings
based on the systematic evaluation of a range of implemented reinforcement
learning algorithms. Both the benchmark and reference implementations are
released at https://github.com/rllab/rllab in order to facilitate experimental
reproducibility and to encourage adoption by other researchers.Comment: 14 pages, ICML 201
A Practical and Conceptual Framework for Learning in Control
We propose a fully Bayesian approach for efficient reinforcement learning (RL) in Markov decision processes with continuous-valued state and action spaces when no expert knowledge is available. Our framework is based on well-established ideas from statistics and machine learning and learns fast since it carefully models, quantifies, and incorporates available knowledge when making decisions. The key ingredient of our framework is a probabilistic model, which is implemented using a Gaussian process (GP), a distribution over functions. In the context of dynamic systems, the GP models the transition function. By considering all plausible transition functions simultaneously, we reduce model bias, a problem that frequently occurs when deterministic models are used. Due to its generality and efficiency, our RL framework can be considered a conceptual and practical approach to learning models and controllers whe
PILCO: A Model-Based and Data-Efficient Approach to Policy Search
In this paper, we introduce PILCO, a practical, data-efficient model-based policy search method. PILCO reduces model bias, one of the key problems of model-based reinforcement learning, in a principled way. By learning a probabilistic dynamics model and explicitly incorporating model uncertainty into long-term planning, PILCO can cope with very little data and facilitates learning from scratch in only a few trials. Policy evaluation is performed in closed form using state-of-the-art approximate inference. Furthermore, policy gradients are computed analytically for policy improvement. We report unprecedented learning efficiency on challenging and high-dimensional control tasks. Copyright 2011 by the author(s)/owner(s)
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