Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRobust Deep Learning as Optimal Control: Insights and Convergence Guarantees
110
0
0.0
(
0
)
Added by
Jacob Seidman
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This mechanism can be formulated as a min-max optimization problem, where the adversary seeks to maximize the loss function using an iterative first-order algorithm while the learner attempts to minimize it. However, finding adversarial examples in this way causes excessive computational overhead during training. By interpreting the min-max problem as an optimal control problem, it has recently been shown that one can exploit the compositional structure of neural networks in the optimization problem to improve the training time significantly. In this paper, we provide the first convergence analysis of this adversarial training algorithm by combining techniques from robust optimal control and inexact oracle methods in optimization. Our analysis sheds light on how the hyperparameters of the algorithm affect the its stability and convergence. We support our insights with experiments on a robust classification problem.
rate research
Read More
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a maximum condition, we reformulate the original control problem as a new one. Three algorithms are proposed to solve the new control problem. Numerical results for different examples demonstrate the effectiveness of our proposed algorithms, especially in high dimensional cases. And an important application of this method is to calculate the sub-linear expectations, which correspond to a kind of fully nonlinear PDEs.
We present a simple model-free control algorithm that is able to robustly learn and stabilize an unknown discrete-time linear system with full control and state feedback subject to arbitrary bounded disturbance and noise sequences. The controller does not require any prior knowledge of the system dynamics, disturbances, or noise, yet it can guarantee robust stability and provides asymptotic and worst-case bounds on the state and input trajectories. To the best of our knowledge, this is the first model-free algorithm that comes with such robust stability guarantees without the need to make any prior assumptions about the system. We would like to highlight the new convex geometry-based approach taken towards robust stability analysis which served as a key enabler in our results. We will conclude with simulation results that show that despite the generality and simplicity, the controller demonstrates good closed-loop performance.
The combination of machine learning with control offers many opportunities, in particular for robust control. However, due to strong safety and reliability requirements in many real-world applications, providing rigorous statistical and control-theoretic guarantees is of utmost importance, yet difficult to achieve for learning-based control schemes. We present a general framework for learning-enhanced robust control that allows for systematic integration of prior engineering knowledge, is fully compatible with modern robust control and still comes with rigorous and practically meaningful guarantees. Building on the established Linear Fractional Representation and Integral Quadratic Constraints framework, we integrate Gaussian Process Regression as a learning component and state-of-the-art robust controller synthesis. In a concrete robust control example, our approach is demonstrated to yield improved performance with more data, while guarantees are maintained throughout.
The traditional notion of generalization---i.e., learning a hypothesis whose empirical error is close to its true error---is surprisingly brittle. As has recently been noted in [DFH+15b], even if several algorithms have this guarantee in isolation, the guarantee need not hold if the algorithms are composed adaptively. In this paper, we study three notions of generalization---increasing in strength---that are robust to postprocessing and amenable to adaptive composition, and examine the relationships between them. We call the weakest such notion Robust Generalization. A second, intermediate, notion is the stability guarantee known as differential privacy. The strongest guarantee we consider we call Perfect Generalization. We prove that every hypothesis class that is PAC learnable is also PAC learnable in a robustly generalizing fashion, with almost the same sample complexity. It was previously known that differentially private algorithms satisfy robust generalization. In this paper, we show that robust generalization is a strictly weaker concept, and that there is a learning task that can be carried out subject to robust generalization guarantees, yet cannot be carried out subject to differential privacy. We also show that perfect generalization is a strictly stronger guarantee than differential privacy, but that, nevertheless, many learning tasks can be carried out subject to the guarantees of perfect generalization.
In stochastic dynamic environments, team stochastic games have emerged as a versatile paradigm for studying sequential decision-making problems of fully cooperative multi-agent systems. However, the optimality of the derived policies is usually sensitive to the model parameters, which are typically unknown and required to be estimated from noisy data in practice. To mitigate the sensitivity of the optimal policy to these uncertain parameters, in this paper, we propose a model of robust team stochastic games, where players utilize a robust optimization approach to make decisions. This model extends team stochastic games to the scenario of incomplete information and meanwhile provides an alternative solution concept of robust team optimality. To seek such a solution, we develop a learning algorithm in the form of a Gauss-Seidel modified policy iteration and prove its convergence. This algorithm, compared with robust dynamic programming, not only possesses a faster convergence rate, but also allows for using approximation calculations to alleviate the curse of dimensionality. Moreover, some numerical simulations are presented to demonstrate the effectiveness of the algorithm by generalizing the game model of social dilemmas to sequential robust scenarios.
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
