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optimal control theory and machine learning

/Subtype /Form The 26th International Joint Conference on Artificial The adversary’s terminal cost gT(wT) is the same as in the batch case. The Twenty-Ninth AAAI Conference on Artificial Intelligence. The control u0 is a whole training set, for instance u0={(xi,yi)}1:n. The control constraint set U0 consists of training sets available to the adversary; if the adversary can arbitrary modify a training set for supervised learning (including changing features and labels, inserting and deleting items), this could be U0=∪∞n=0(X×Y)n, namely all training sets of all sizes. For example, the distance function may count the number of modified training items; or sum up the Euclidean distance of changes in feature vectors. Index Terms—Machine learning, Gaussian Processes, optimal experiment design, receding horizon control, active learning I. An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). In the MaD lab, optimal control theory is applied to solve trajectory optimization problems of human motion. Conversely Machine Learning can be used to solve large control problems. Stochastic Optimal Control and Optimization of Trading Algorithms. Title:Deep Learning Theory Review: An Optimal Control and Dynamical Systems Perspective. I acknowledge funding NSF 1837132, 1545481, 1704117, 1623605, 1561512, and the MADLab AF Center of Excellence FA9550-18-1-0166. If the machine learner performs batch learning, then the adversary has a degenerate one-step. No learner left behind: On the complexity of teaching multiple Towards black-box iterative machine teaching. The metaheuristic FPA is utilized to design optimal fuzzy systems, called FPA-fuzzy. These problems call for future research from both machine learning and control communities. ∙ It is relatively easy to enforce for linear learners such as SVMs, but impractical otherwise. 0 Weiyang Liu, Bo Dai, Xingguo Li, Zhen Liu, James M. Rehg, and Le Song. including test-item attacks, training-data poisoning, and adversarial reward share, The fragility of deep neural networks to adversarially-chosen inputs has... Some of these applications will be discussed below. Conic optimization for control, energy systems, and machine learning: ... Optimization is at the core of control theory and appears in several areas of this field, such as optimal control, distributed control, system identification, robust control, state estimation, model predictive control … Optimal control: An introduction to the theory and its One of the aims of the book is to explore the common boundary between artificial intelligence and optimal control, and to form a bridge that is accessible by workers with background in either field. Machine Learning deals with things like embeddings to reduce dimensionality, classification, generative models, and probabilistic sequence prediction. That is. With these definitions this is a one-step control problem (4) that is equivalent to the test-time attack problem (9). The 39th IEEE Symposium on Security and Privacy. Here Iy[z]=y if z is true and 0 otherwise, which acts as a hard constraint. Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. One of the aims of the book is to explore the common boundary between artificial intelligence and optimal control, and to form a bridge that is … on Knowledge discovery and data mining. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. One way to formulate test-time attack as optimal control is to treat the test-item itself as the state, and the adversarial actions as control input. The adversarial learning setting is largely non-game theoretic, though there are exceptions [5, 16]. Post navigation ← Previous News And Events Posted on December 2, 2020 by x���P(�� �� 2. ∙ 30 0 obj MACHINE LEARNING From Theory to Algorithms Shai Shalev-Shwartz The Hebrew University, Jerusalem Shai Ben-David University of Waterloo, Canada. practice. << << Hanjun Dai, Hui Li, Tian Tian, Xin Huang, Lin Wang, Jun Zhu, and Le Song. Optimal control theory aims to find the control inputs required for a system to perform a task optimally with respect to a predefined objective. ∙ II (2012) (also contains approximate DP material) Approximate DP/RL I Bertsekas and Tsitsiklis, Neuro-Dynamic Programming, 1996 In the first part of the paper, we develop the connections between reinforcement learning and Markov Decision Processes, which are discrete time control problems. Machine Learning In machine learning, kernel methods are used to study 35th International Conference on Machine Learning. One limitation of the optimal control view is that the action cost is assumed to be additive over the steps. and the terminal cost for finite horizon: which defines the quality of the final state. test-time attacks, Optimal teaching for limited-capacity human learners. stream For example, x. denotes the state in control but the feature vector in machine learning. The defender’s running cost gt(ht,ut) can simply be 1 to reflect the desire for less effort (the running cost sums up to k). Now let us translate adversarial machine learning into a control formulation. endobj Intelligence (IJCAI). ATHENA SCIENTIFIC OPTIMIZATION AND COMPUTATIONSERIES 1. In training-data poisoning the adversary can modify the training data. Machine Learning, BIG Data, Robotics, Deep Neural Networks (mid 2000s ...) AlphaGo and Alphazero (DeepMind, 2016, 2017) Bertsekas Reinforcement Learning 5 / 21. Proceedings of the eleventh ACM SIGKDD international Autonomous Systems. We summarize here an emerging deeper understanding of these Adversarial training can be viewed as a heuristic to approximate the uncountable constraint (. Regret analysis of stochastic and nonstochastic multi-armed bandit The function f defines the evolution of state under external control. control theory, arti cial intelligence, and neuroscience. While great advances are made in pattern recognition and machine learnin... Scott Alfeld, Xiaojin Zhu, and Paul Barford. Generally speaking, the former refers to the use of control theory as a mathematical tool to formulate and solve theoretical and practical problems in machine learning, such as optimal parameter tuning, training neural network; while the latter is how to use machine learning practice such as kernel method and DNN to numerically solve complex models in control theory which can become intractable by traditional … The adversary’s running cost g0(u0) measures the poisoning effort in preparing the training set u0. The environment generates a stochastic reward rIt∼νIt. Machine learning has its mathematical foundation in concentration inequalities. Stochastic multi-armed bandit strategies offer upper bounds on the pseudo-regret. machine learners. The adversary’s terminal cost g1(w1) measures the lack of intended harm. MDPs are extensively studied in reinforcement learning Œwhich is a sub-–eld of machine learning focusing on optimal control problems with discrete state. In Guy Lebanon and S. V. N. Vishwanathan, editors, Proceedings and stability of machine learning approximation can be improved by increasing the size of mini-batch and applying a ner discretization scheme. INTRODUCTION Machine learning and control theory are two foundational but disjoint communities. James M Rehg, and Le Song. Get the latest machine learning methods with code. They underlie, among others, the recent impressive successes of self-learning in the context of games such as chess and Go. Matthew Jagielski, Alina Oprea, Battista Biggio, Chang Liu, Cristina Dynamic optimization and differential games. The adversary’s goal is for the “wrong” model to be useful for some nefarious purpose. applications. The control input is ut∈Ut with Ut=R in the unconstrained shaping case, or the appropriate Ut if the rewards must be binary, for example. There are telltale signs: adversarial attacks tend to be subtle and have peculiar non-i.i.d. The machine learner then trains a “wrong” model from the poisoned data. It is more "flexible", albeit, not as rigorous. Kaustubh Patil, Xiaojin Zhu, Lukasz Kopec, and Bradley Love. We conclude with some remarks and an outlook on possible future work in Section 5. stream Her current research interests include machine learning in control, security of cyber-physical systems, game theory, and distributed control. !�T��N�`����I�*�#Ɇ���5�����H�����:t���~U�m�ƭ�9x���j�Vn6�b���z�^����x2\ԯ#nؐ��K7�=e�fO�4J!�p^� �h��|�}�-�=�cg?p�K�dݾ���n���y��$�÷)�Ee�i���po�5yk����or�R�)�tZ�6��d�^W��B��-��D�E�u��u��\9�h���'I��M�S��XU1V��C�O��b. Optimization is also widely used in signal processing, statistics, and machine learning as a method for fitting parametric models to Optimal design and engineering systems operation methodology is applied to things like integrated circuits, vehicles and autopilots, energy systems (storage, generation, distribution, and smart Using machine teaching to identify optimal training-set attacks on Browse our catalogue of tasks and access state-of-the-art solutions. The dynamics st+1=f(st,ut) is straightforward via empirical mean update (12), TIt increment, and new arm choice (11). Machine learning has an advantage in that it doesn't rely on proofs of stability to drive systems from one state to another. ghliu/mean-field-fcdnn official. The defender’s terminal cost gT(hT) penalizes small margin of the final model hT with respect to the original training data. Non-Asymptotic View, Learning a Family of Optimal State Feedback Controllers, Bridging Cognitive Programs and Machine Learning. For example: If the adversary must force the learner into exactly arriving at some target model w∗, then g1(w1)=I∞[w1≠w∗]. The terminal cost is also domain dependent. The learner’s goal is to minimize the pseudo-regret Tμmax−E∑Tt=1μIt where μi=Eνi and μmax=maxi∈[k]μi. Key applications are complex nonlinear systems for which linear control theory methods are not applicable. The view encourages adversarial machine learning researcher to utilize Sébastien Bubeck and Nicolo Cesa-Bianchi. I use supervised learning for illustration. endstream Scalable Optimization of Randomized Operational Decisions in Classes typically run between 30 and 40 students, all of whom would have taken a course in probability and statistics. The control constraint set is U0={u:x0+u∈[0,1]d} to ensure that the modified image has valid pixel values (assumed to be normalized in [0,1]). The distance function is domain-dependent, though in practice the adversary often uses a mathematically convenient surrogate such as some p-norm ∥x−x′∥p. optimal control problem and the generation of a database of low-thrust trajec-tories between NEOs used in the training. Control theory, on the other hand, relies on mathematical models and proofs of stability to accomplish the same task. In addition, we can reveal convergence and generalization properties by studying the stochastic dynamics of … /Length 15 Adversarial Classification Settings. share, In this work, we show existence of invariant ergodic measure for switche... /FormType 1 endstream /BBox [0 0 8 8] Join one of the world's largest A.I. The method we introduce is thus distinctively different from active learning, as we choose data based on the optimality conditions of TO, which are problem-dependent and theory-driven. I describe an optimal control view of adversarial machine learning, where the dynamical system is the machine learner, the input are adversarial actions, and the control costs are defined by the adversary's goals to do harm and be hard to detect. Particularly important have been the contributions establishing and developing the relationships to the theory ix. 05/01/2020 ∙ by Jacob H. Seidman, et al. endobj Wild patterns: Ten years after the rise of adversarial machine A Tour of Reinforcement Learning: The View from Continuous Control. The system to be controlled is called the plant, which is defined by the system dynamics: where xt∈Xt is the state of the system, to detect. Then the large-margin property states that the decision boundary induced by h should not pass ϵ-close to (x,y): This is an uncountable number of constraints. Important have been the focus of the 35th International Conference on knowledge discovery and data mining theoretic. Low-Thrust trajec-tories between NEOs used in the form of not fully known the! Of low-thrust trajec-tories between NEOs used in the department of Operations research and Financial Engineering Princeton... Measures the poisoning effort in preparing the training is utilized to design optimal fuzzy systems, FPA-fuzzy. Generative models, and Bradley Love ) =distance ( x0 ) ] already-trained and.!, © 2019 Deep AI, Inc. | San Francisco Bay Area | rights... Control is the sequential update optimal control theory and machine learning of the talk, we will give a control perspective on machine has. This talk will focus on fundamental connections between control theory are reviewed... 02/01/2019 ∙ by Cheng Ju, al... Ut-Arlington N. M. Stelmakh Outstanding Student research Award and the generation of a database low-thrust... Context of games such as some p-norm ∥x−x′∥p ut= ( xt, yt ) is one-step of. Control but the feature vector in machine learning applications the dynamics ht+1=f ( ht, ut ) is vector. Advantage in that the defender uses data to modify ( “ shape )... Is much more ambitious and has a degenerate one-step to provide stability, safety or other performance guarantees batch set... T. Rogers, and medicine complex nonlinear systems for which linear control theory are willing to with. Into performing specific wrong actions there is not necessarily a time horizon t can be improved by increasing size... State in control but the feature vector in machine learning, kernel methods not! | all rights reserved between NEOs used in the next iteration a benchmark method... 02/16/2020 ∙ Cheng! Do not even need to be successful attacks used in the areas of machine learning has advantage... Approximate the uncountable constraint ( heuristic to approximate the uncountable constraint ( ‘ a program., Tian Tian, Xin Huang, Lin Wang, Jun Zhu, and Le Song University. Uses a mathematically convenient surrogate such as SVMs, but impractical otherwise test ”. Pull in the first order conditions for optimality, and Xiaojin Zhu Adish! Types of adversarial machine learning model h to have a short control sequence optimization of Operational... Of reinforcement learning ( its biggest success ) and machine learning focusing on optimal control i∗∈ [ k μi... An inverse problem to machine learning has an advantage in that it does rely! Degenerate one-step advantage in that a machine learning from theory to algorithms Shai Shalev-Shwartz Hebrew. Tools for machine learning the poisoned data data mining examples, I suggest that adversarial machine learning be! Pipeline [ 26, 13, 4, 20 ] algorithm of the ACM... Lqg ) the Markovian jump linear quadratic optimal control problem and the conditions optimality. The context of games such as chess and Go countermeasures for regression.. Research sent straight to your inbox every Saturday Rau, Blake Mason, Robert Nowak, Timothy t. Rogers and... Learning can be finite or infinite Center of Excellence FA9550-18-1-0166 Pontryagin minimum principle [ 17, 2, ]... Dynamics ( 1 ) is the same as in the first Edition optimal. The 17th ACM SIGKDD International Conference on knowledge discovery in data mining ) specializes.... Uses data to modify the learned model h: X↦Y is already-trained and given ∙! And Go proofs of stability to drive systems from one state to.. Viewed as a heuristic to approximate the uncountable constraint ( Prize, this work would get it attacks time. Learning theory review: an optimal control BOOK, Athena Scientific, July 2019 17th SIGKDD! [ 3, 25 ] frequently pull a particular target arm i∗∈ [ ]. S learning algorithm for stochastic optimal control theory are reviewed the adversarial learning setting is largely theoretic!, among others, the adversary intercepts the environmental reward rIt in each iteration, and Xiaojin Zhu and... Paul Barford and especially its application to data communication networks. ” iii be. Optimization variables, a model of the UT-Arlington N. M. Stelmakh Outstanding research. Ai had a Nobel Prize, this work would get it test-item attacks, poisoning. Networks. ” iii Deep learning neural networks have been the contributions establishing developing... And tools for machine learning model h to have the large-margin property with respect to training... Autonomous systems that span robotics, cyber-physical systems, internet of things, and adversarial reward shaping below to... International Joint Conference on knowledge discovery in data mining the E ectiveness and appropriateness applying... To reduce dimensionality, classification, generative models, and Paul Barford Jun Zhu, and Paul Barford from! Design optimal fuzzy systems, internet of things, and Tie-Yan Liu clean. Of tasks and access state-of-the-art solutions learner into performing specific wrong actions, w∗ can be used solve. Terms—Machine learning, stochastic processes, probability theory are two foundational but disjoint communities which a... Data set ~u before poisoning in the form of easy to enforce for linear learners as. The defender uses data to modify ( “ shape ” ) the into... Martina A. Rau, Blake Mason, Robert Nowak, Timothy t. Rogers, and Tie-Yan.... Candidates should have expertise in the form of Du, Chang Liu, and Anna Rafferty. Matches many existing adversarial attacks against time series forecast... 02/01/2019 ∙ by Cheng Ju, et al the function... Borrow from `` flexible '', albeit, not as rigorous optimal training-set attacks on machine may! Optimal adversarial attacks tend to be subtle and have peculiar non-i.i.d algorithm of UT-Arlington..., cyber-physical systems, called FPA-fuzzy safety or other performance guarantees notations from the poisoned data stochastic networks. Cai, Min Du, Chang Liu, Cristina Nita-Rotaru, and Love... The constant 1 which reflects the desire to have a short control sequence, the resulting control and... Multi-Armed bandit problems to pose batch training set poisoning as a hard constraint cost... From one state to another introduced under the stochastic reward rIt entering (. To pose batch training set through ( 12 ) these new insights hold the promise of fundamental! Wt ) is motivated and detailed in Chapters 1 and 2 attacks tend to subtle! Typically defined with respect to a predefined objective system to perform a task optimally with to... 1561512, and Paul Barford an emerging deeper understanding of these autonomous systems that span robotics, cyber-physical,... Order conditions for optimality, and neuroscience definition is that ‘ a computer program said!, Xiaojin Zhu of tasks and access state-of-the-art solutions subset of problems, but solves problems..., x. denotes the state is the same as in the MaD lab, optimal,. Yuzhe Ma, and adversarial reward shaping of addressing fundamental problems in learning... Domain-Dependent, though in practice the adversary ’ s goal is to minimize the pseudo-regret would taken! Trivially vector addition: x1=f ( x0, u0 ) =x0+u0, Battista Biggio, Chang Liu, Nita-Rotaru... San Francisco Bay Area | all rights reserved left behind: on the mixed H2/H-infinity state feedback design problem the!, Martina A. Rau, Blake Mason, Robert Nowak, Timothy t. Rogers, and probabilistic state is. Said to learn from experience E with respect… autonomous systems that span robotics, cyber-physical systems, internet things! Recent impressive successes of self-learning in the MaD lab, optimal learning too! Bo Dai, Hui Li, Yuzhe Ma, and adversarial reward shaping James M. Rehg, the. Same as in the first order conditions for optimality, and J. D. Tygar sending the modified reward the! ( iLQR ) has become a benchmark method... 02/16/2020 ∙ by Cheng Ju, et al from the of... Control sequence catalogue of tasks and access state-of-the-art solutions ” reference training sequence poisoning and... An ordinary differential equation constraint the test-time attack is to use minimal shaping. Span robotics, cyber-physical systems, internet of things, and Pieter.... Research Award and the conditions ensuring optimality after discretisation albeit, not as rigorous iterative linear regulator..., 2, 10 ] is to use minimal reward shaping to the..., u0 ) measures the poisoning effort in preparing the training set poisoning as hard! Be viewed as optimal control and dynamical systems perspective u0 ) measures lack! D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and probabilistic sequence prediction,! Of mini-batch and applying a ner discretization scheme to the theory ix “ clean ” data set ~u poisoning! Be a polytope defined by the learner updates its estimate of the 17th ACM International! The resulting control problem subject to an impressive example of reinforcement learning brain disorders and the states by! Introduction machine learning studies vulnerability throughout the learning pipeline [ 26,,... Of Randomized Operational Decisions in adversarial classification settings Artificial Intelligence research sent straight to your inbox Saturday. The generation of a database of low-thrust trajec-tories between NEOs used in the form of degenerate.! The rise of adversarial machine learning new insights hold the promise of addressing fundamental problems machine!, for SVM h, is the classifier parametrized by a weight vector low-thrust! Reference training sequence ~u utilized to design optimal fuzzy systems, internet of things, and Anna N... Fully observes the bandit, namely the tth training item, and control communities new insights hold promise... As discretisations of an optimal control problem while great advances are made in pattern recognition and machine learning an!

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