Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDeep Learning Theory Review: An Optimal Control and Dynamical Systems Perspective
68
0
0.0
(
0
)
Added by
Guan-Horng Liu
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align existing branches of deep learning theory through the lens of dynamical system and optimal control. By viewing deep neural networks as discrete-time nonlinear dynamical systems, we can analyze how information propagates through layers using mean field theory. When optimization algorithms are further recast as controllers, the ultimate goal of training processes can be formulated as an optimal control problem. In addition, we can reveal convergence and generalization properties by studying the stochastic dynamics of optimization algorithms. This viewpoint features a wide range of theoretical study from information bottleneck to statistical physics. It also provides a principled way for hyper-parameter tuning when optimal control theory is introduced. Our framework fits nicely with supervised learning and can be extended to other learning problems, such as Bayesian learning, adversarial training, and specific forms of meta learning, without efforts. The review aims to shed lights on the importance of dynamics and optimal control when developing deep learning theory.
rate research
Read More
As power systems are undergoing a significant transformation with more uncertainties, less inertia and closer to operation limits, there is increasing risk of large outages. Thus, there is an imperative need to enhance grid emergency control to maintain system reliability and security. Towards this end, great progress has been made in developing deep reinforcement learning (DRL) based grid control solutions in recent years. However, existing DRL-based solutions have two main limitations: 1) they cannot handle well with a wide range of grid operation conditions, system parameters, and contingencies; 2) they generally lack the ability to fast adapt to new grid operation conditions, system parameters, and contingencies, limiting their applicability for real-world applications. In this paper, we mitigate these limitations by developing a novel deep meta reinforcement learning (DMRL) algorithm. The DMRL combines the meta strategy optimization together with DRL, and trains policies modulated by a latent space that can quickly adapt to new scenarios. We test the developed DMRL algorithm on the IEEE 300-bus system. We demonstrate fast adaptation of the meta-trained DRL polices with latent variables to new operating conditions and scenarios using the proposed method and achieve superior performance compared to the state-of-the-art DRL and model predictive control (MPC) methods.
This paper focuses on finding reinforcement learning policies for control systems with hard state and action constraints. Despite its success in many domains, reinforcement learning is challenging to apply to problems with hard constraints, especially if both the state variables and actions are constrained. Previous works seeking to ensure constraint satisfaction, or safety, have focused on adding a projection step to a learned policy. Yet, this approach requires solving an optimization problem at every policy execution step, which can lead to significant computational costs. To tackle this problem, this paper proposes a new approach, termed Vertex Networks (VNs), with guarantees on safety during exploration and on learned control policies by incorporating the safety constraints into the policy network architecture. Leveraging the geometric property that all points within a convex set can be represented as the convex combination of its vertices, the proposed algorithm first learns the convex combination weights and then uses these weights along with the pre-calculated vertices to output an action. The output action is guaranteed to be safe by construction. Numerical examples illustrate that the proposed VN algorithm outperforms vanilla reinforcement learning in a variety of benchmark control tasks.
In this work, we study the problem of learning partially observed linear dynamical systems from a single sample trajectory. A major practical challenge in the existing system identification methods is the undesirable dependency of their required sample size on the system dimension: roughly speaking, they presume and rely on sample sizes that scale linearly with respect to the system dimension. Evidently, in high-dimensional regime where the system dimension is large, it may be costly, if not impossible, to collect as many samples from the unknown system. In this paper, we will remedy this undesirable dependency on the system dimension by introducing an $ell_1$-regularized estimation method that can accurately estimate the Markov parameters of the system, provided that the number of samples scale logarithmically with the system dimension. Our result significantly improves the sample complexity of learning partially observed linear dynamical systems: it shows that the Markov parameters of the system can be learned in the high-dimensional setting, where the number of samples is significantly smaller than the system dimension. Traditionally, the $ell_1$-regularized estimators have been used to promote sparsity in the estimated parameters. By resorting to the notion of weak sparsity, we show that, irrespective of the true sparsity of the system, a similar regularized estimator can be used to reduce the sample complexity of learning partially observed linear systems, provided that the true system is inherently stable.
Traditional methods for solvability region analysis can only have inner approximations with inconclusive conservatism. Machine learning methods have been proposed to approach the real region. In this letter, we propose a deep active learning framework for power system solvability prediction. Compared with the passive learning methods where the training is performed after all instances are labeled, the active learning selects most informative instances to be label and therefore significantly reduce the size of labeled dataset for training. In the active learning framework, the acquisition functions, which correspond to different sampling strategies, are defined in terms of the on-the-fly posterior probability from the classifier. The IEEE 39-bus system is employed to validate the proposed framework, where a two-dimensional case is illustrated to visualize the effectiveness of the sampling method followed by the full-dimensional numerical experiments.
In this effort, a novel operator theoretic framework is developed for data-driven solution of optimal control problems. The developed methods focus on the use of trajectories (i.e., time-series) as the fundamental unit of data for the resolution of optimal control problems in dynamical systems. Trajectory information in the dynamical systems is embedded in a reproducing kernel Hilbert space (RKHS) through what are called occupation kernels. The occupation kernels are tied to the dynamics of the system through the densely defined Liouville operator. The pairing of Liouville operators and occupation kernels allows for lifting of nonlinear finite-dimensional optimal control problems into the space of infinite-dimensional linear programs over RKHSs.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
