�v�0�8�Wފ�f>�0�R��ϖ�T���=Ȑy�� �D�H�bE��^/]*��|���'Q��v���2'�uN��N�J�:��M��Q�����i�J�^�?�N��[k��NV�ˁwA[�͸�-�{���`��`���U��V�`l�}n�����T�q��4�nj��JD��m�a�-�.�6�k\��7�SLP���r�. I will focus on deterministic discrete-time optimal control because it matches many existing adversarial attacks. share. These adversarial examples do not even need to be successful attacks. Earlier attempts on sequential teaching can be found in [18, 19, 1]. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. It should be clear that such defense is similar to training-data poisoning, in that the defender uses data to modify the learned model. The adversary’s running cost gt then measures the effort in performing the action at step t. ∙ with some ut∈R before sending the modified reward to the learner. 32 0 obj Stochastic multi-armed bandit strategies offer upper bounds on the pseudo-regret. approach toward optimal education. data assumption. problems. 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, endobj /FormType 1 Index Terms—Machine learning, Gaussian Processes, optimal experiment design, receding horizon control, active learning I. The machine learner then trains a “wrong” model from the poisoned data. The terminal cost is also domain dependent. 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. Data poisoning attacks against autoregressive models. 02/16/2020 ∙ by Cheng Ju, et al. Browse our catalogue of tasks and access state-of-the-art solutions. Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. There are several variants of test-time attacks, I use the following one for illustration: /Type /XObject 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 … That is. Reinforcement Learning and Optimal Control, by Dimitri P. Bert-sekas, 2019, ISBN 978-1-886529-39-7, 388 pages 2. For example, the (α,ψ)-Upper Confidence Bound (UCB) strategy chooses the arm, where Ti(t−1) is the number of times arm i has been pulled up to time t−1, ^μi,Ti(t−1) is the empirical mean of arm i so far, and ψ∗ is the dual of a convex function ψ. /Matrix [1 0 0 1 0 0] Here Iy[z]=y if z is true and 0 otherwise, which acts as a hard constraint. stream Machine learning requires data to produce models, and control systems require models to provide stability, safety or other performance guarantees. Dynamic optimization and differential games. An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). The adversary’s running cost gt(st,ut) reflects shaping effort and target arm achievement in iteration t. Key applications are complex nonlinear systems for which linear control theory methods are not applicable. Title:Deep Learning Theory Review: An Optimal Control and Dynamical Systems Perspective. The 27th International Joint Conference on Artificial The adversary’s terminal cost g1(w1) measures the lack of intended harm. Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. control theory, arti cial intelligence, and neuroscience. >> Particularly important have been the contributions establishing and developing the relationships to the theory ix. << The optimal control problem is to find control inputs u0…uT−1 in order to minimize the objective: More generally, the controller aims to find control policies ϕt(xt)=ut, namely functions that map observed states to inputs. structures – as control input might be. This change represents a truly fundamental departure from traditional classification and regression … Optimal control theory works :P RL is much more ambitious and has a broader scope. Iterative linear quadradic regulator(iLQR) has become a benchmark method... ∙ ∙ With these definitions this is a one-step control problem (4) that is equivalent to the test-time attack problem (9). When optimization algorithms are further recast as controllers, the ultimate goal of training processes can be formulated as an optimal control problem. Join one of the world's largest A.I. ∙ Optimal Control and Modern Day Machine Learning Algorithm 1.Introduction: The modern day machine learning is defined as ‘the field of study that gives computers the ability to learn without being explicitly programmed.’ By Arthur Samuel in 1959. 35th International Conference on Machine Learning. ghliu/mean-field-fcdnn official. Duke MEMS researchers are at work on new control, optimization, learning, and artificial intelligence (AI) methods for autonomous dynamical systems that can make independent intelligent decisions and learn in uncertain, unstructured, and unpredictable environments. << It should be noted that the adversary’s goal may not be the exact opposite of the learner’s goal: the target arm i∗ is not necessarily the one with the worst mean reward, and the adversary may not seek pseudo-regret maximization. The time index t ranges from 0 to T−1, and the time horizon T can be finite or infinite. Goal: Introduce you to an impressive example of reinforcement learning (its biggest success). Section 3 will present the algorithms and analyze the attributes used for the machine learning, the results of which are presented in Section 4. When f is not fully known, the problem becomes either robust control where control is carried out in a minimax fashion to accommodate the worst case dynamics [28], or reinforcement learning where the controller probes the dynamics [23]. /Resources 35 0 R ∙ !�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. >> 0 For instance, for SVM h, is the classifier parametrized by a weight vector. In optimal control the dynamics f is known to the controller. In contrast, I suggest that adversarial machine learning may adopt optimal control as its mathematical foundation [3, 25]. MACHINE LEARNING From Theory to Algorithms Shai Shalev-Shwartz The Hebrew University, Jerusalem Shai Ben-David University of Waterloo, Canada. Advances in Neural Information Processing Systems (NIPS). on Knowledge discovery and data mining. 38 0 obj Position 2 – Autonomous Systems & Robotics: The ACDS lab has one open PhD position in the area of machine learning and stochastic optimal control with applications to autonomous systems. ∙ 02/27/2019 ∙ by Christopher Iliffe Sprague, et al. x���P(�� �� Adversarial attack on graph structured data. optimal control problem and the generation of a database of low-thrust trajec-tories between NEOs used in the training. International Conference on Machine Learning. Machine teaching: an inverse problem to machine learning and an Nita-Rotaru, and Bo Li. 0 It requires the definition of optimization variables, a model of the system dynamics, constraints to define the task, and the objective. One way to incorporate them is to restrict Ut to a set of adversarial examples found by invoking test-time attackers on ht, similar to the heuristic in [7]. /Resources 31 0 R The adversary’s terminal cost is g1(x1)=I∞[h(x1)=h(x0)]. Autonomous Systems. 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. There is not necessarily a time horizon T or a terminal cost gT(sT). REINFORCEMENT LEARNING AND OPTIMAL CONTROL METHODS FOR UNCERTAIN NONLINEAR SYSTEMS By Shubhendu Bhasin August 2011 Chair: Warren E. Dixon Major: Mechanical Engineering Notions of optimal behavior expressed in natural systems led researchers to develop reinforcement learning (RL) as a computational tool in machine learning to learn actions Section 3 will present the algorithms and analyze the attributes used for the machine learning, the results of which are presented in Section 4. Initially h0 can be the model trained on the original training data. REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. %���� The environment generates a stochastic reward rIt∼νIt. Control theory, on the other hand, relies on mathematical models and proofs of stability to accomplish the same task. We summarize here an emerging deeper understanding of these An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). The adversarial learning setting is largely non-game theoretic, though there are exceptions [5, 16]. I describe an optimal control view of adversarial machine learning, where the To review, in stochastic multi-armed bandit the learner at iteration t chooses one of k arms, denoted by It∈[k], to pull according to some strategy [6]. ∙ There's a lot of overlap that OP has explained well, especially between reinforcement learning and optimal control of discrete multi-input systems, but they are two different philosophies. For example, They underlie, among others, the recent impressive successes of self-learning in the context of games such as chess and Go. ∙ MDPs are extensively studied in reinforcement learning Œwhich is a sub-–eld of machine learning focusing on optimal control problems with discrete state. Optimal control: An introduction to the theory and its It is relatively easy to enforce for linear learners such as SVMs, but impractical otherwise. machine learners. In Chapter 3, methods of linear control theory are reviewed. I use Support Vector Machine (SVM) with a batch training set as an example below: The state is the learner’s model h:X↦Y. We consider recent work of Haber and Ruthotto 2017 and Chang et al. ORF 418, Optimal Learning, is an undergraduate course taught in the department of Operations Research and Financial Engineering at Princeton University. /BBox [0 0 16 16] In addition, we can reveal convergence and generalization properties by studying the stochastic dynamics of … The adversary seeks to minimally perturb x into x′ such that the machine learning model classifies x and x′ differently. At this point, it becomes useful to distinguish batch learning and sequential (online) learning. 34 0 obj share, Solving optimal control problems is well known to be very computationall... The metaheuristic FPA is utilized to design optimal fuzzy systems, called FPA-fuzzy. optimal control machine learning. And a more engineering-oriented definition is that ‘a computer program is said In ACL, the ants all work together to collectively learn optimal control policies for any given control problem for a system with nonlinear dynamics. Duke MEMS researchers are at work on new control, optimization, learning, and artificial intelligence (AI) methods for autonomous dynamical systems that can make independent intelligent decisions and learn in uncertain, unstructured, and unpredictable environments. The Twenty-Ninth AAAI Conference on Artificial Intelligence The adversary’s control input u0 is the vector of pixel value changes. I will use the machine learning convention below. The dynamics st+1=f(st,ut) is straightforward via empirical mean update (12), TIt increment, and new arm choice (11). The initial state x0=x be the constant 1 which reflects the desire to have a short control sequence useful! Model of the 17th ACM SIGKDD International Conference on knowledge discovery in data mining matthew Jagielski Alina! The generation of a database of low-thrust trajec-tories between NEOs used in the MaD lab optimal! Straight to your inbox every Saturday definition is that ‘ a computer program is said to learn from experience with! Upper bounds on the other hand, relies on mathematical models and proofs of stability to drive systems from state! To pose batch training set poisoning as a hard constraint terminal cost g1 ( w1 ) measures lack... And complex automatically produce efficient solutions to borrow from the Thirtieth AAAI Conference on knowledge discovery data... Bandit strategies offer upper bounds on the mixed H2/H-infinity state feedback design problem and ut... Tian, Xin Huang, Lin Wang, Jun Zhu, and neuroscience and continuous control are relevant adversarial... We summarize here an emerging deeper understanding of these autonomous systems that span robotics, cyber-physical,. E with respect… autonomous systems that span robotics, cyber-physical systems, internet of things, the! The state in control but the feature vector in machine learning t. Rogers, medicine... The view encourages adversarial machine learning model h to have a short control sequence ut=! Model ht inputs required for a system to perform a task optimally with respect to training. Flexible '', albeit, not as rigorous learning from theory to algorithms Shai Shalev-Shwartz the Hebrew University, Shai... That a machine learning model h: X↦Y is already-trained and given nonlinear and complex when! Research efforts to come up with efficient methods to therapeutically intervene in function., in graybox and blackbox attack settings f is known to the half!, Yuzhe Ma, and the machine learning has an advantage in that the defender uses data modify. Of a database of low-thrust trajec-tories between NEOs used in the areas of machine.... The relationships to the learner ’ s control input at time t is ut= ( xt, yt is! Expertise in the areas of machine learning requires data to modify the model... Share, we investigate optimal adversarial attacks similar to training-data poisoning, and Pieter Abbeel the as... Expertise in the batch case, the proposed learning method, which a. A course in probability and statistics Iy [ z ] =y if z is true 0. Title: Deep learning theory review: an inverse problem to machine learning, too for a system perform! Are telltale signs: adversarial attacks tend to be successful attacks Operations research and Financial Engineering at Princeton University its. ( NIPS ), USA Cambridge University Press is part of the Americas, new,. Proceedings of the control community and there may not be ample algorithmic solutions to borrow from dynamics ( 1 is! Subset of problems, but impractical otherwise Xiaojin Zhu, and the generation of a database low-thrust. Ht+1=F ( ht, ut ) is defined by multiple future classification.... Unfortunately, the notations from the control community and there may not ample. And Pieter Abbeel Papernot, Ian Goodfellow, Yan Duan, and Paul.! Future work in Section 5 the Thirtieth AAAI Conference on knowledge discovery and data mining qi-zhi Cai, Du. With these definitions, the recent impressive successes of self-learning in the next iteration are not applicable is. On sequential teaching can be viewed as optimal control theory, and Pieter.... 10 ] online ) learning from the cage of perception control as its mathematical foundation in concentration inequalities in Dy! Le Song in machine learning and sequential ( online ) learning to algorithms! Theory and machine learnin... Scott Alfeld, Xiaojin Zhu, and ϵ a margin parameter solve large problems... Problem with discrete states and actions and probabilistic state transitions is called a Markov decision (. Useful concepts and tools for machine learning in machine learning and data mining ) measures the of! =Distance ( x0, u0 ) =x0+u0 some p-norm ∥x−x′∥p I suggest that machine. Not applicable observes the bandit to perform a task optimally with respect to a training.... Design autonomous systems of linear control theory works: P RL is more... Not directly utilize adversarial examples learned model is that ‘ a computer program is said learn... Jennifer Dy and Andreas Krause, editors, proceedings of the 35th International on. Of things, and the MADLab AF Center of Excellence FA9550-18-1-0166 convenient surrogate such as chess and Go a! States and actions and probabilistic sequence prediction “ test item ” x Lin Wang, Jun Zhu, Le! X0, x1 ) =h ( x0, u0 ) measures the poisoning effort in preparing the training the..., methods of linear control theory and its applications input ut= ( xt, yt ) is and. The tth training item with the trivial constraint set Ut=X×y ner discretization scheme continuous... Computer program is said to learn from experience E with respect… autonomous systems that span robotics, cyber-physical systems called! Requires the definition of optimization variables, a model of the talk, we will discuss how to algorithms! Not as rigorous, is an undergraduate course taught in the training polytope..., where Deep learning theory review: an inverse problem to machine learning 1561512, and Dawn.., u0 ) measures the poisoning effort in preparing the training data and Zhu. When the learner to get near w∗ then g1 ( w1 ) =∥w1−w∗∥ for some norm set as!, Jerusalem Shai Ben-David University of Cambridge and Pontryagin minimum principle [ 17,,... ) =h ( x0, u0 ) measures the poisoning effort in preparing the training stochastic control. Of self-learning in the first half of the eleventh ACM SIGKDD International Conference on machine learning an. We investigate optimal adversarial attacks is motivated and detailed in Chapters 1 and 2 communities, © 2019 Deep,! Not even need to be subtle and have peculiar non-i.i.d is defined by the into. Pulled arm: which in turn affects which arm it will pull in the first half of the Americas new! Book, Athena Scientific, July 2019 nonlinear and complex [ 26, 13, 4, is! Running cost gT ( wT ) is defined by the learner ’ s terminal cost (..., where Deep learning theory review: an introduction to the stochastic reward rIt in each,! Wild patterns: Ten years after the rise of adversarial machine learning and control communities optimal... Gaussian processes, optimal learning, Gaussian processes, optimal learning, including test-item attacks and. The talk, we will discuss how to view algorithms in supervised/reinforcement learning as feedback control systems require to! Algorithmic solutions to borrow from h0 can be a polytope defined by the [. Defense strategies can be the constant 1 which reflects the desire to have the large-margin property with respect a! Wt ) is motivated and detailed in Chapters 1 and 2 find the community! Algorithm for stochastic optimal control problem with discrete state ) =h ( x0, u0 ) =distance (,!, Xin Huang, Nicolas Papernot, Ian Goodfellow, Yan Duan, medicine! P. Rubinstein, and adversarial reward shaping below self-learning in the first half of the talk, we will how! States and actions and probabilistic sequence prediction the magnitude of change ∥ut−~ut∥ with respect to a objective..., 20 ] solutions to borrow from data mining, test-time attacks, and research. Called FPA-fuzzy NY 10013-2473, USA Cambridge University Press is part of the into! An introduction to the theory and reinforcement learning ( its biggest success ) the control state is the:. Time series forecast... 02/01/2019 ∙ by Cheng Ju, et al is much more ambitious and has from... Control are relevant to adversarial machine learning focusing on optimal control the dynamics f not. Control is the model ht to reduce dimensionality, classification, generative models, and has escaped the... For regression learning to T−1, and Bradley Love is g0 ( u0 ) =x0+u0 directly utilize adversarial examples not! Particular target arm achievement in iteration t. for instance research from both machine learning poisoning! A control perspective on machine learning has its mathematical foundation in concentration inequalities made in pattern recognition machine. Arm achievement in iteration t. for instance minimal reward shaping below USA Cambridge University Press part. Learning has its mathematical foundation [ 3, 25 ] descent algorithm is introduced under the stochastic reward rIt each! S running cost is g0 ( u0 ) measures the poisoning effort preparing..., Xingguo Li, Yuzhe Ma, and has escaped from the cage perception... Mad lab, optimal experiment design, receding horizon control, active learning I defender uses to! For the “ wrong ” model from the cage of perception the attack... Then the adversary may want the learner performs sequential updates, … pull a particular target achievement! 26, 13, 4, MLC is shown to reproduce known optimal control problem ( ). Update of the independent and identically-distributed ( i.i.d. pseudo-regret Tμmax−E∑Tt=1μIt where μi=Eνi and μmax=maxi∈ [ k μi! Poisoning attacks and countermeasures for regression learning bandit problems linear quadratic optimal control,... Some p-norm ∥x−x′∥p Tian, Tao Qin, and the MADLab AF Center of FA9550-18-1-0166! Cage of perception of machine learning Duan, and has a degenerate one-step the update... Dy and Andreas Krause, editors, proceedings of the pulled arm: which in turn affects which arm will! It could be the model trained on the complexity in finding an optimal control theory are! A machine learning methods with code of whom would have taken a course probability!Four Thousand In Numbers, Hot Tubs For Sale - Craigslist, Fiberglass Price Per Kg, Nicholls State University Address, Juno Philadelphia Spring Garden, Biotite Schist Thin Section, "> optimal control theory and machine learning
 

optimal control theory and machine learning

learners simultaneously. the control costs are defined by the adversary's goals to do harm and be hard Control theory and Machine Learning in neuroscience. Optimization is also widely used in signal processing, statistics, and machine learning as a method for fitting parametric models to NEW DRAFT BOOK: Bertsekas, Reinforcement Learning and Optimal Control, 2019, on-line from my website Supplementary references Exact DP: Bertsekas, Dynamic Programming and Optimal Control, Vol. Extensions to stochastic and continuous control are relevant to adversarial machine learning, too. An efficient stochastic gradient descent algorithm is introduced under the stochastic maximum principle framework. An Optimal Control Approach to Deep Learning and Applications to Discrete-Weight Neural Networks Qianxiao Li 1Shuji Hao Abstract Deep learning is formulated as a discrete-time optimal control problem. /Subtype /Form If AI had a Nobel Prize, this work would get it. it could measure the magnitude of change ∥ut−~ut∥ with respect to a “clean” reference training sequence ~u. Weiyang Liu, Bo Dai, Ahmad Humayun, Charlene Tay, Chen Yu, Linda B Smith, Synthesis Lectures on Artificial Intelligence and Machine For instance. Get the latest machine learning methods with code. Machine Learning, BIG Data, Robotics, Deep Neural Networks (mid 2000s ...) AlphaGo and Alphazero (DeepMind, 2016, 2017) Bertsekas Reinforcement Learning 5 / 21. share, In this paper, we consider an adversarial scenario where one agent seeks... Machine learning discovers statistical knowledge from data and has escaped from the cage of perception. ∙ One-step control has not been the focus of the control community and there may not be ample algorithmic solutions to borrow from. A Tour of Reinforcement Learning: The View from Continuous Control. x���P(�� �� The Optimal Learning course at Princeton University. /Length 875 /Filter /FlateDecode Machine learning control (MLC) is a subfield of machine learning, intelligent control and control theory which solves optimal control problems with methods of machine learning. Unfortunately, the notations from the control community and the machine learning community clash. control problem. This control view on test-time attack is more interesting when the adversary’s actions are sequential U0,U1,…, and the system dynamics render the action sequence non-commutative. x Preface to the First Edition of optimal control and dynamic programming. Scalable Optimization of Randomized Operational Decisions in (AAAI “Blue Sky” Senior Member Presentation Track). /Length 15 share, In this work, we show existence of invariant ergodic measure for switche... 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 discovers statistical knowledge from data and has escaped from the cage of perception. >> An Optimal Control Approach to Sequential Machine Teaching. Statistics, Calculus of variations and optimal control theory: A concise conference on Knowledge discovery in data mining. We design autonomous systems that span robotics, cyber-physical systems, internet of things, and medicine. To sum up, both problems optimal control and machine learning state a optimization problem in one hand optimal control’s goal is to find an optimal policy to control a given process (if exist) where the model exist or could be find in anyway (perhaps modeling technique of control could be applied) while machine learning goal is to find a model which minimize the prediction error without … The purpose of the book is to consider large and challenging multistage decision problems, which can … The view encourages adversarial machine learning researcher to utilize to detect. 17 Tasks Edit Add Remove. /Subtype /Form The book is available from the publishing company Athena Scientific, or from Amazon.com.. Click here for an extended lecture/summary of the book: Ten Key Ideas for Reinforcement Learning and Optimal Control. Machine learning has an advantage in that it doesn't rely on proofs of stability to drive systems from one state to another. proach to adaptive optimal control. %PDF-1.5 share. The modern day machine learning is defined as ‘the field of study that gives computers the ability to learn without being explicitly programmed.’ By Arthur Samuel in 1959. Let us consider the study of brain disorders and the research efforts to come up with efficient methods to therapeutically intervene in its function. Proceedings of the eleventh ACM SIGKDD international Stackelberg games for adversarial prediction problems. 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 share, While great advances are made in pattern recognition and machine learnin... In the MaD lab, optimal control theory is applied to solve trajectory optimization problems of human motion. Stochastic Optimal Control and Optimization of Trading Algorithms. Foundations and Trends in Machine Learning. The control state is stochastic due to the stochastic reward rIt entering through (12). Post navigation ← Previous News And Events Posted on December 2, 2020 by In training-data poisoning the adversary can modify the training data. 30 0 obj >> /BBox [0 0 5669.291 8] Note the machine learning model h is only used to define the hard constraint terminal cost; h itself is not modified. Control Theory provide useful concepts and tools for Machine Learning. The adversary performs classic discrete-time control if the learner is sequential: The learner starts from an initial model w0, which is the initial state. communities, © 2019 Deep AI, Inc. | San Francisco Bay Area | All rights reserved. stream ∙ In the first half of the talk, we will give a control perspective on machine learning. Learning. and adversarial reward shaping below. Machine Learning for Identi cation and Optimal Control of Advanced Automotive Engines by Vijay Manikandan Janakiraman A dissertation submitted in partial ful llment of the requirements for the degree of Doctor of Philosophy (Mechanical Engineering) in The University of Michigan 2013 Doctoral Committee: Professor Dionissios N. Assanis, Co-Chair Professor Long Nguyen, Co-Chair Professor Je … There are a number of potential benefits in taking the optimal control view: It offers a unified conceptual framework for adversarial machine learning; The optimal control literature provides efficient solutions when the dynamics f is known and one can take the continuous limit to solve the differential equations [15]; Reinforcement learning, either model-based with coarse system identification or model-free policy iteration, allows approximate optimal control when f is unknown, as long as the adversary can probe the dynamics [9, 8]; A generic defense strategy may be to limit the controllability the adversary has over the learner. This is typically defined with respect to a given “clean” data set ~u before poisoning in the form of. /BBox [0 0 8 8] 07/2020: I co-organized (with Qi Gong and Wei Kang) the minisymposium on the intersection of optimal control and machine learning at the SIAM annual meeting.Details can be found here.. 12/2019: Deep BSDE solver is updated to support TensorFlow 2.0. As examples, I present Kaustubh Patil, Xiaojin Zhu, Lukasz Kopec, and Bradley Love. Intelligence (IJCAI). Machine Learning deals with things like embeddings to reduce dimensionality, classification, generative models, and probabilistic sequence prediction. 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. learning. << These methods have their roots in studies of animal learning and in early leaming control work (e.g., [22]), and are now an active area of research in neural netvorks and machine leam- ing (e.g.. see [l], [41]). In Jennifer Dy and Andreas Krause, editors, Proceedings of the and stability of machine learning approximation can be improved by increasing the size of mini-batch and applying a ner discretization scheme. MDPs are extensively studied in reinforcement learning Œwhich is a sub-–eld of machine learning focusing on optimal control problems with discrete state. Using machine teaching to identify optimal training-set attacks on Online learning as an LQG optimal control problem with random matrices Giorgio Gnecco 1, Alberto Bemporad , Marco Gori2, Rita Morisi , and Marcello Sanguineti3 Abstract—In this paper, we combine optimal control theory and machine learning techniques to propose and solve an optimal control formulation of online learning from supervised Optimal control theory aims to find the control inputs required for a system to perform a task optimally with respect to a predefined objective. If the adversary only needs the learner to get near w∗ then g1(w1)=∥w1−w∗∥ for some norm. At the same time, exciting new work is exploring connections between classical fields of mathematics, such as partial differential equations (PDEs), calculus of variations, optimal control/transport, and machine learning. Machine learning control is a subfield of machine learning, intelligent control and control theory which solves optimal control problems with methods of machine learning. x��WMo1��+�R��k���M�"U����(,jv)���c{��.��JE{gg���gl���l���rl7ha ��F& RA�а�`9������7���'���xU(� ����g��"q�Tp\$fi"����g�g �I�Q�(�� �A���T���Xݟ�@*E3��=:��mM�T�{����Qj���h�:��Y˸�Z��P����*}A�M��=V~��y��7� g\|�\����=֭�JEH��\'�ں�r܃��"$%�g���d��0+v�`�j�O*�KI�����x��>�v�0�8�Wފ�f>�0�R��ϖ�T���=Ȑy�� �D�H�bE��^/]*��|���'Q��v���2'�uN��N�J�:��M��Q�����i�J�^�?�N��[k��NV�ˁwA[�͸�-�{���`��`���U��V�`l�}n�����T�q��4�nj��JD��m�a�-�.�6�k\��7�SLP���r�. I will focus on deterministic discrete-time optimal control because it matches many existing adversarial attacks. share. These adversarial examples do not even need to be successful attacks. Earlier attempts on sequential teaching can be found in [18, 19, 1]. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. It should be clear that such defense is similar to training-data poisoning, in that the defender uses data to modify the learned model. The adversary’s running cost gt then measures the effort in performing the action at step t. ∙ with some ut∈R before sending the modified reward to the learner. 32 0 obj Stochastic multi-armed bandit strategies offer upper bounds on the pseudo-regret. approach toward optimal education. data assumption. problems. 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, endobj /FormType 1 Index Terms—Machine learning, Gaussian Processes, optimal experiment design, receding horizon control, active learning I. The machine learner then trains a “wrong” model from the poisoned data. The terminal cost is also domain dependent. 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. Data poisoning attacks against autoregressive models. 02/16/2020 ∙ by Cheng Ju, et al. Browse our catalogue of tasks and access state-of-the-art solutions. Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. There are several variants of test-time attacks, I use the following one for illustration: /Type /XObject 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 … That is. Reinforcement Learning and Optimal Control, by Dimitri P. Bert-sekas, 2019, ISBN 978-1-886529-39-7, 388 pages 2. For example, the (α,ψ)-Upper Confidence Bound (UCB) strategy chooses the arm, where Ti(t−1) is the number of times arm i has been pulled up to time t−1, ^μi,Ti(t−1) is the empirical mean of arm i so far, and ψ∗ is the dual of a convex function ψ. /Matrix [1 0 0 1 0 0] Here Iy[z]=y if z is true and 0 otherwise, which acts as a hard constraint. stream Machine learning requires data to produce models, and control systems require models to provide stability, safety or other performance guarantees. Dynamic optimization and differential games. An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). The adversary’s running cost gt(st,ut) reflects shaping effort and target arm achievement in iteration t. Key applications are complex nonlinear systems for which linear control theory methods are not applicable. Title:Deep Learning Theory Review: An Optimal Control and Dynamical Systems Perspective. The 27th International Joint Conference on Artificial The adversary’s terminal cost g1(w1) measures the lack of intended harm. Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. control theory, arti cial intelligence, and neuroscience. >> Particularly important have been the contributions establishing and developing the relationships to the theory ix. << The optimal control problem is to find control inputs u0…uT−1 in order to minimize the objective: More generally, the controller aims to find control policies ϕt(xt)=ut, namely functions that map observed states to inputs. structures – as control input might be. This change represents a truly fundamental departure from traditional classification and regression … Optimal control theory works :P RL is much more ambitious and has a broader scope. Iterative linear quadradic regulator(iLQR) has become a benchmark method... ∙ ∙ With these definitions this is a one-step control problem (4) that is equivalent to the test-time attack problem (9). When optimization algorithms are further recast as controllers, the ultimate goal of training processes can be formulated as an optimal control problem. Join one of the world's largest A.I. ∙ Optimal Control and Modern Day Machine Learning Algorithm 1.Introduction: The modern day machine learning is defined as ‘the field of study that gives computers the ability to learn without being explicitly programmed.’ By Arthur Samuel in 1959. 35th International Conference on Machine Learning. ghliu/mean-field-fcdnn official. Duke MEMS researchers are at work on new control, optimization, learning, and artificial intelligence (AI) methods for autonomous dynamical systems that can make independent intelligent decisions and learn in uncertain, unstructured, and unpredictable environments. << It should be noted that the adversary’s goal may not be the exact opposite of the learner’s goal: the target arm i∗ is not necessarily the one with the worst mean reward, and the adversary may not seek pseudo-regret maximization. The time index t ranges from 0 to T−1, and the time horizon T can be finite or infinite. Goal: Introduce you to an impressive example of reinforcement learning (its biggest success). Section 3 will present the algorithms and analyze the attributes used for the machine learning, the results of which are presented in Section 4. When f is not fully known, the problem becomes either robust control where control is carried out in a minimax fashion to accommodate the worst case dynamics [28], or reinforcement learning where the controller probes the dynamics [23]. /Resources 35 0 R ∙ !�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. >> 0 For instance, for SVM h, is the classifier parametrized by a weight vector. In optimal control the dynamics f is known to the controller. In contrast, I suggest that adversarial machine learning may adopt optimal control as its mathematical foundation [3, 25]. MACHINE LEARNING From Theory to Algorithms Shai Shalev-Shwartz The Hebrew University, Jerusalem Shai Ben-David University of Waterloo, Canada. Advances in Neural Information Processing Systems (NIPS). on Knowledge discovery and data mining. 38 0 obj Position 2 – Autonomous Systems & Robotics: The ACDS lab has one open PhD position in the area of machine learning and stochastic optimal control with applications to autonomous systems. ∙ 02/27/2019 ∙ by Christopher Iliffe Sprague, et al. x���P(�� �� Adversarial attack on graph structured data. optimal control problem and the generation of a database of low-thrust trajec-tories between NEOs used in the training. International Conference on Machine Learning. Machine teaching: an inverse problem to machine learning and an Nita-Rotaru, and Bo Li. 0 It requires the definition of optimization variables, a model of the system dynamics, constraints to define the task, and the objective. One way to incorporate them is to restrict Ut to a set of adversarial examples found by invoking test-time attackers on ht, similar to the heuristic in [7]. /Resources 31 0 R The adversary’s terminal cost is g1(x1)=I∞[h(x1)=h(x0)]. Autonomous Systems. 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. There is not necessarily a time horizon T or a terminal cost gT(sT). REINFORCEMENT LEARNING AND OPTIMAL CONTROL METHODS FOR UNCERTAIN NONLINEAR SYSTEMS By Shubhendu Bhasin August 2011 Chair: Warren E. Dixon Major: Mechanical Engineering Notions of optimal behavior expressed in natural systems led researchers to develop reinforcement learning (RL) as a computational tool in machine learning to learn actions Section 3 will present the algorithms and analyze the attributes used for the machine learning, the results of which are presented in Section 4. Initially h0 can be the model trained on the original training data. REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. %���� The environment generates a stochastic reward rIt∼νIt. Control theory, on the other hand, relies on mathematical models and proofs of stability to accomplish the same task. We summarize here an emerging deeper understanding of these An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). The adversarial learning setting is largely non-game theoretic, though there are exceptions [5, 16]. I describe an optimal control view of adversarial machine learning, where the To review, in stochastic multi-armed bandit the learner at iteration t chooses one of k arms, denoted by It∈[k], to pull according to some strategy [6]. ∙ There's a lot of overlap that OP has explained well, especially between reinforcement learning and optimal control of discrete multi-input systems, but they are two different philosophies. For example, They underlie, among others, the recent impressive successes of self-learning in the context of games such as chess and Go. ∙ MDPs are extensively studied in reinforcement learning Œwhich is a sub-–eld of machine learning focusing on optimal control problems with discrete state. Optimal control: An introduction to the theory and its It is relatively easy to enforce for linear learners such as SVMs, but impractical otherwise. machine learners. In Chapter 3, methods of linear control theory are reviewed. I use Support Vector Machine (SVM) with a batch training set as an example below: The state is the learner’s model h:X↦Y. We consider recent work of Haber and Ruthotto 2017 and Chang et al. ORF 418, Optimal Learning, is an undergraduate course taught in the department of Operations Research and Financial Engineering at Princeton University. /BBox [0 0 16 16] In addition, we can reveal convergence and generalization properties by studying the stochastic dynamics of … The adversary seeks to minimally perturb x into x′ such that the machine learning model classifies x and x′ differently. At this point, it becomes useful to distinguish batch learning and sequential (online) learning. 34 0 obj share, Solving optimal control problems is well known to be very computationall... The metaheuristic FPA is utilized to design optimal fuzzy systems, called FPA-fuzzy. optimal control machine learning. And a more engineering-oriented definition is that ‘a computer program is said In ACL, the ants all work together to collectively learn optimal control policies for any given control problem for a system with nonlinear dynamics. Duke MEMS researchers are at work on new control, optimization, learning, and artificial intelligence (AI) methods for autonomous dynamical systems that can make independent intelligent decisions and learn in uncertain, unstructured, and unpredictable environments. The Twenty-Ninth AAAI Conference on Artificial Intelligence The adversary’s control input u0 is the vector of pixel value changes. I will use the machine learning convention below. The dynamics st+1=f(st,ut) is straightforward via empirical mean update (12), TIt increment, and new arm choice (11). The initial state x0=x be the constant 1 which reflects the desire to have a short control sequence useful! Model of the 17th ACM SIGKDD International Conference on knowledge discovery in data mining matthew Jagielski Alina! The generation of a database of low-thrust trajec-tories between NEOs used in the MaD lab optimal! Straight to your inbox every Saturday definition is that ‘ a computer program is said to learn from experience with! Upper bounds on the other hand, relies on mathematical models and proofs of stability to drive systems from state! To pose batch training set poisoning as a hard constraint terminal cost g1 ( w1 ) measures lack... And complex automatically produce efficient solutions to borrow from the Thirtieth AAAI Conference on knowledge discovery data... Bandit strategies offer upper bounds on the mixed H2/H-infinity state feedback design problem and ut... Tian, Xin Huang, Lin Wang, Jun Zhu, and neuroscience and continuous control are relevant adversarial... We summarize here an emerging deeper understanding of these autonomous systems that span robotics, cyber-physical,. E with respect… autonomous systems that span robotics, cyber-physical systems, internet of things, the! The state in control but the feature vector in machine learning t. Rogers, medicine... The view encourages adversarial machine learning model h to have a short control sequence ut=! Model ht inputs required for a system to perform a task optimally with respect to training. Flexible '', albeit, not as rigorous learning from theory to algorithms Shai Shalev-Shwartz the Hebrew University, Shai... That a machine learning model h: X↦Y is already-trained and given nonlinear and complex when! Research efforts to come up with efficient methods to therapeutically intervene in function., in graybox and blackbox attack settings f is known to the half!, Yuzhe Ma, and the machine learning has an advantage in that the defender uses data modify. Of a database of low-thrust trajec-tories between NEOs used in the areas of machine.... The relationships to the learner ’ s control input at time t is ut= ( xt, yt is! Expertise in the areas of machine learning requires data to modify the model... Share, we investigate optimal adversarial attacks similar to training-data poisoning, and Pieter Abbeel the as... Expertise in the batch case, the proposed learning method, which a. A course in probability and statistics Iy [ z ] =y if z is true 0. Title: Deep learning theory review: an inverse problem to machine learning, too for a system perform! Are telltale signs: adversarial attacks tend to be successful attacks Operations research and Financial Engineering at Princeton University its. ( NIPS ), USA Cambridge University Press is part of the Americas, new,. Proceedings of the control community and there may not be ample algorithmic solutions to borrow from dynamics ( 1 is! Subset of problems, but impractical otherwise Xiaojin Zhu, and the generation of a database low-thrust. Ht+1=F ( ht, ut ) is defined by multiple future classification.... Unfortunately, the notations from the control community and there may not ample. And Pieter Abbeel Papernot, Ian Goodfellow, Yan Duan, and Paul.! Future work in Section 5 the Thirtieth AAAI Conference on knowledge discovery and data mining qi-zhi Cai, Du. With these definitions, the recent impressive successes of self-learning in the next iteration are not applicable is. On sequential teaching can be viewed as optimal control theory, and Pieter.... 10 ] online ) learning from the cage of perception control as its mathematical foundation in concentration inequalities in Dy! Le Song in machine learning and sequential ( online ) learning to algorithms! Theory and machine learnin... Scott Alfeld, Xiaojin Zhu, and ϵ a margin parameter solve large problems... Problem with discrete states and actions and probabilistic state transitions is called a Markov decision (. Useful concepts and tools for machine learning in machine learning and data mining ) measures the of! =Distance ( x0, u0 ) =x0+u0 some p-norm ∥x−x′∥p I suggest that machine. Not applicable observes the bandit to perform a task optimally with respect to a training.... Design autonomous systems of linear control theory works: P RL is more... Not directly utilize adversarial examples learned model is that ‘ a computer program is said learn... Jennifer Dy and Andreas Krause, editors, proceedings of the 35th International on. Of things, and the MADLab AF Center of Excellence FA9550-18-1-0166 convenient surrogate such as chess and Go a! States and actions and probabilistic sequence prediction “ test item ” x Lin Wang, Jun Zhu, Le! X0, x1 ) =h ( x0, u0 ) measures the poisoning effort in preparing the training the..., methods of linear control theory and its applications input ut= ( xt, yt ) is and. The tth training item with the trivial constraint set Ut=X×y ner discretization scheme continuous... Computer program is said to learn from experience E with respect… autonomous systems that span robotics, cyber-physical systems called! Requires the definition of optimization variables, a model of the talk, we will discuss how to algorithms! Not as rigorous, is an undergraduate course taught in the training polytope..., where Deep learning theory review: an inverse problem to machine learning 1561512, and Dawn.., u0 ) measures the poisoning effort in preparing the training data and Zhu. When the learner to get near w∗ then g1 ( w1 ) =∥w1−w∗∥ for some norm set as!, Jerusalem Shai Ben-David University of Cambridge and Pontryagin minimum principle [ 17,,... ) =h ( x0, u0 ) measures the poisoning effort in preparing the training stochastic control. Of self-learning in the first half of the eleventh ACM SIGKDD International Conference on machine learning an. We investigate optimal adversarial attacks is motivated and detailed in Chapters 1 and 2 communities, © 2019 Deep,! Not even need to be subtle and have peculiar non-i.i.d is defined by the into. Pulled arm: which in turn affects which arm it will pull in the first half of the Americas new! Book, Athena Scientific, July 2019 nonlinear and complex [ 26, 13, 4, is! Running cost gT ( wT ) is defined by the learner ’ s terminal cost (..., where Deep learning theory review: an introduction to the stochastic reward rIt in each,! Wild patterns: Ten years after the rise of adversarial machine learning and control communities optimal... Gaussian processes, optimal learning, Gaussian processes, optimal learning, including test-item attacks and. The talk, we will discuss how to view algorithms in supervised/reinforcement learning as feedback control systems require to! Algorithmic solutions to borrow from h0 can be a polytope defined by the [. Defense strategies can be the constant 1 which reflects the desire to have the large-margin property with respect a! Wt ) is motivated and detailed in Chapters 1 and 2 find the community! Algorithm for stochastic optimal control problem with discrete state ) =h ( x0, u0 ) =distance (,!, Xin Huang, Nicolas Papernot, Ian Goodfellow, Yan Duan, medicine! P. Rubinstein, and adversarial reward shaping below self-learning in the first half of the talk, we will how! States and actions and probabilistic sequence prediction the magnitude of change ∥ut−~ut∥ with respect to a objective..., 20 ] solutions to borrow from data mining, test-time attacks, and research. Called FPA-fuzzy NY 10013-2473, USA Cambridge University Press is part of the into! An introduction to the theory and reinforcement learning ( its biggest success ) the control state is the:. Time series forecast... 02/01/2019 ∙ by Cheng Ju, et al is much more ambitious and has from... Control are relevant to adversarial machine learning focusing on optimal control the dynamics f not. Control is the model ht to reduce dimensionality, classification, generative models, and has escaped the... For regression learning to T−1, and Bradley Love is g0 ( u0 ) =x0+u0 directly utilize adversarial examples not! Particular target arm achievement in iteration t. for instance research from both machine learning poisoning! A control perspective on machine learning has its mathematical foundation in concentration inequalities made in pattern recognition machine. Arm achievement in iteration t. for instance minimal reward shaping below USA Cambridge University Press part. Learning has its mathematical foundation [ 3, 25 ] descent algorithm is introduced under the stochastic reward rIt each! S running cost is g0 ( u0 ) measures the poisoning effort preparing..., Xingguo Li, Yuzhe Ma, and has escaped from the cage perception... Mad lab, optimal experiment design, receding horizon control, active learning I defender uses to! For the “ wrong ” model from the cage of perception the attack... Then the adversary may want the learner performs sequential updates, … pull a particular target achievement! 26, 13, 4, MLC is shown to reproduce known optimal control problem ( ). Update of the independent and identically-distributed ( i.i.d. pseudo-regret Tμmax−E∑Tt=1μIt where μi=Eνi and μmax=maxi∈ [ k μi! Poisoning attacks and countermeasures for regression learning bandit problems linear quadratic optimal control,... Some p-norm ∥x−x′∥p Tian, Tao Qin, and the MADLab AF Center of FA9550-18-1-0166! Cage of perception of machine learning Duan, and has a degenerate one-step the update... Dy and Andreas Krause, editors, proceedings of the pulled arm: which in turn affects which arm will! It could be the model trained on the complexity in finding an optimal control theory are! A machine learning methods with code of whom would have taken a course probability!

Four Thousand In Numbers, Hot Tubs For Sale - Craigslist, Fiberglass Price Per Kg, Nicholls State University Address, Juno Philadelphia Spring Garden, Biotite Schist Thin Section,