5,168 research outputs found
On the Design of LQR Kernels for Efficient Controller Learning
Finding optimal feedback controllers for nonlinear dynamic systems from data
is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful
framework for direct controller tuning from experimental trials. For selecting
the next query point and finding the global optimum, BO relies on a
probabilistic description of the latent objective function, typically a
Gaussian process (GP). As is shown herein, GPs with a common kernel choice can,
however, lead to poor learning outcomes on standard quadratic control problems.
For a first-order system, we construct two kernels that specifically leverage
the structure of the well-known Linear Quadratic Regulator (LQR), yet retain
the flexibility of Bayesian nonparametric learning. Simulations of uncertain
linear and nonlinear systems demonstrate that the LQR kernels yield superior
learning performance.Comment: 8 pages, 5 figures, to appear in 56th IEEE Conference on Decision and
Control (CDC 2017
Stick-Breaking Policy Learning in Dec-POMDPs
Expectation maximization (EM) has recently been shown to be an efficient
algorithm for learning finite-state controllers (FSCs) in large decentralized
POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often
converge to maxima that are far from optimal. This paper considers a
variable-size FSC to represent the local policy of each agent. These
variable-size FSCs are constructed using a stick-breaking prior, leading to a
new framework called \emph{decentralized stick-breaking policy representation}
(Dec-SBPR). This approach learns the controller parameters with a variational
Bayesian algorithm without having to assume that the Dec-POMDP model is
available. The performance of Dec-SBPR is demonstrated on several benchmark
problems, showing that the algorithm scales to large problems while
outperforming other state-of-the-art methods
Optimizing the CVaR via Sampling
Conditional Value at Risk (CVaR) is a prominent risk measure that is being
used extensively in various domains. We develop a new formula for the gradient
of the CVaR in the form of a conditional expectation. Based on this formula, we
propose a novel sampling-based estimator for the CVaR gradient, in the spirit
of the likelihood-ratio method. We analyze the bias of the estimator, and prove
the convergence of a corresponding stochastic gradient descent algorithm to a
local CVaR optimum. Our method allows to consider CVaR optimization in new
domains. As an example, we consider a reinforcement learning application, and
learn a risk-sensitive controller for the game of Tetris.Comment: To appear in AAAI 201
Q-learning with Nearest Neighbors
We consider model-free reinforcement learning for infinite-horizon discounted
Markov Decision Processes (MDPs) with a continuous state space and unknown
transition kernel, when only a single sample path under an arbitrary policy of
the system is available. We consider the Nearest Neighbor Q-Learning (NNQL)
algorithm to learn the optimal Q function using nearest neighbor regression
method. As the main contribution, we provide tight finite sample analysis of
the convergence rate. In particular, for MDPs with a -dimensional state
space and the discounted factor , given an arbitrary sample
path with "covering time" , we establish that the algorithm is guaranteed
to output an -accurate estimate of the optimal Q-function using
samples. For instance, for a
well-behaved MDP, the covering time of the sample path under the purely random
policy scales as so the sample
complexity scales as Indeed, we
establish a lower bound that argues that the dependence of is necessary.Comment: Accepted to NIPS 201
Inverse Reinforcement Learning in Large State Spaces via Function Approximation
This paper introduces a new method for inverse reinforcement learning in
large-scale and high-dimensional state spaces. To avoid solving the
computationally expensive reinforcement learning problems in reward learning,
we propose a function approximation method to ensure that the Bellman
Optimality Equation always holds, and then estimate a function to maximize the
likelihood of the observed motion. The time complexity of the proposed method
is linearly proportional to the cardinality of the action set, thus it can
handle large state spaces efficiently. We test the proposed method in a
simulated environment, and show that it is more accurate than existing methods
and significantly better in scalability. We also show that the proposed method
can extend many existing methods to high-dimensional state spaces. We then
apply the method to evaluating the effect of rehabilitative stimulations on
patients with spinal cord injuries based on the observed patient motions.Comment: Experiment update
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