200 research outputs found
Structured Hammerstein-Wiener Model Learning for Model Predictive Control
This paper aims to improve the reliability of optimal control using models
constructed by machine learning methods. Optimal control problems based on such
models are generally non-convex and difficult to solve online. In this paper,
we propose a model that combines the Hammerstein-Wiener model with input convex
neural networks, which have recently been proposed in the field of machine
learning. An important feature of the proposed model is that resulting optimal
control problems are effectively solvable exploiting their convexity and
partial linearity while retaining flexible modeling ability. The practical
usefulness of the method is examined through its application to the modeling
and control of an engine airpath system.Comment: 6 pages, 3 figure
Convex Identifcation of Stable Dynamical Systems
This thesis concerns the scalable application of convex optimization to data-driven modeling of dynamical systems, termed system identi cation in the control community. Two problems commonly arising in system identi cation are model instability (e.g. unreliability of long-term, open-loop predictions), and nonconvexity of quality-of- t criteria, such as simulation error (a.k.a. output error). To address these problems, this thesis presents convex parametrizations of stable dynamical systems, convex quality-of- t criteria, and e cient algorithms to optimize the latter over the former. In particular, this thesis makes extensive use of Lagrangian relaxation, a technique for generating convex approximations to nonconvex optimization problems. Recently, Lagrangian relaxation has been used to approximate simulation error and guarantee nonlinear model stability via semide nite programming (SDP), however, the resulting SDPs have large dimension, limiting their practical utility. The rst contribution of this thesis is a custom interior point algorithm that exploits structure in the problem to signi cantly reduce computational complexity. The new algorithm enables empirical comparisons to established methods including Nonlinear ARX, in which superior generalization to new data is demonstrated. Equipped with this algorithmic machinery, the second contribution of this thesis is the incorporation of model stability constraints into the maximum likelihood framework. Speci - cally, Lagrangian relaxation is combined with the expectation maximization (EM) algorithm to derive tight bounds on the likelihood function, that can be optimized over a convex parametrization of all stable linear dynamical systems. Two di erent formulations are presented, one of which gives higher delity bounds when disturbances (a.k.a. process noise) dominate measurement noise, and vice versa. Finally, identi cation of positive systems is considered. Such systems enjoy substantially simpler stability and performance analysis compared to the general linear time-invariant iv Abstract (LTI) case, and appear frequently in applications where physical constraints imply nonnegativity of the quantities of interest. Lagrangian relaxation is used to derive new convex parametrizations of stable positive systems and quality-of- t criteria, and substantial improvements in accuracy of the identi ed models, compared to existing approaches based on weighted equation error, are demonstrated. Furthermore, the convex parametrizations of stable systems based on linear Lyapunov functions are shown to be amenable to distributed optimization, which is useful for identi cation of large-scale networked dynamical systems
Recurrent Neural Network Training with Convex Loss and Regularization Functions by Extended Kalman Filtering
This paper investigates the use of extended Kalman filtering to train
recurrent neural networks with rather general convex loss functions and
regularization terms on the network parameters, including
-regularization. We show that the learning method is competitive with
respect to stochastic gradient descent in a nonlinear system identification
benchmark and in training a linear system with binary outputs. We also explore
the use of the algorithm in data-driven nonlinear model predictive control and
its relation with disturbance models for offset-free closed-loop tracking.Comment: 21 pages, 3 figures, submitted for publicatio
A Behavioral Approach to Robust Machine Learning
Machine learning is revolutionizing almost all fields of science and technology and has been proposed as a pathway to solving many previously intractable problems such as autonomous driving and other complex robotics tasks. While the field has demonstrated impressive results on certain problems, many of these results have not translated to applications in physical systems, partly due to the cost of system fail-
ure and partly due to the difficulty of ensuring reliable and robust model behavior. Deep neural networks, for instance, have simultaneously demonstrated both incredible performance in game playing and image processing, and remarkable fragility. This combination of high average performance and a catastrophically bad worst case performance presents a serious danger as deep neural networks are currently being
used in safety critical tasks such as assisted driving.
In this thesis, we propose a new approach to training models that have built in robustness guarantees. Our approach to ensuring stability and robustness of the models trained is distinct from prior methods; where prior methods learn a model and then attempt to verify robustness/stability, we directly optimize over sets of
models where the necessary properties are known to hold.
Specifically, we apply methods from robust and nonlinear control to the analysis and synthesis of recurrent neural networks, equilibrium neural networks, and recurrent equilibrium neural networks. The techniques developed allow us to enforce properties such as incremental stability, incremental passivity, and incremental l2 gain bounds / Lipschitz bounds. A central consideration in the development of our model sets is the difficulty of fitting models. All models can be placed in the image of a convex set, or even R^N , allowing useful properties to be easily imposed during the training procedure via simple interior point methods, penalty methods, or unconstrained optimization.
In the final chapter, we study the problem of learning networks of interacting models with guarantees that the resulting networked system is stable and/or monotone, i.e., the order relations between states are preserved. While our approach to learning in this chapter is similar to the previous chapters, the model set that we propose has a separable structure that allows for the scalable and distributed identification of large-scale systems via the alternating directions method of multipliers (ADMM)
Optimization's Neglected Normative Commitments
Optimization is offered as an objective approach to resolving complex,
real-world decisions involving uncertainty and conflicting interests. It drives
business strategies as well as public policies and, increasingly, lies at the
heart of sophisticated machine learning systems. A paradigm used to approach
potentially high-stakes decisions, optimization relies on abstracting the real
world to a set of decision(s), objective(s) and constraint(s). Drawing from the
modeling process and a range of actual cases, this paper describes the
normative choices and assumptions that are necessarily part of using
optimization. It then identifies six emergent problems that may be neglected:
1) Misspecified values can yield optimizations that omit certain imperatives
altogether or incorporate them incorrectly as a constraint or as part of the
objective, 2) Problematic decision boundaries can lead to faulty modularity
assumptions and feedback loops, 3) Failing to account for multiple agents'
divergent goals and decisions can lead to policies that serve only certain
narrow interests, 4) Mislabeling and mismeasurement can introduce bias and
imprecision, 5) Faulty use of relaxation and approximation methods,
unaccompanied by formal characterizations and guarantees, can severely impede
applicability, and 6) Treating optimization as a justification for action,
without specifying the necessary contextual information, can lead to ethically
dubious or faulty decisions. Suggestions are given to further understand and
curb the harms that can arise when optimization is used wrongfully.Comment: 14 pages, 1 figure, presentation at FAccT2
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