In optimal control the dynamics f is known to the controller. structures – as control input might be. Four types of problems are commonly encountered. A Tour of Reinforcement Learning: The View from Continuous Control. 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. 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 … ∙ The 27th International Joint Conference on Artificial Optimal design and engineering systems operation methodology is applied to things like integrated circuits, vehicles and autopilots, energy systems (storage, generation, distribution, and smart devices), wireless networks, and financial trading. We conclude with some remarks and an outlook on possible future work in Section 5. Kwang-Sung Jun, Lihong Li, Yuzhe Ma, and Xiaojin Zhu. One defense against test-time attack is to require the learned model h to have the large-margin property with respect to a training set. 35th International Conference on Machine Learning. stochastic optimal control in machine learning provides a comprehensive and comprehensive pathway for students to see progress after the end of each module. Optimal control: An introduction to the theory and its Rogers, and Xiaojin Zhu. to detect. (AAAI-16). 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. The Twenty-Ninth AAAI Conference on Artificial Intelligence We conclude with some remarks and an outlook on possible future work in Section 5. introduction. An efficient stochastic gradient descent algorithm is introduced under the stochastic maximum principle framework. advances in control theory and reinforcement learning. 06/15/2020 ∙ by Muhammad Abdullah Naeem, et al. . We will discuss how to view algorithms in supervised/reinforcement learning as feedback control systems. /Matrix [1 0 0 1 0 0] The adversary’s running cost gt then measures the effort in performing the action at step t. Note the machine learning model h is only used to define the hard constraint terminal cost; h itself is not modified. The quality of control is specified by the running cost: which defines the step-by-step control cost, 4 1 14. Lastly, the proposed learning method is aligned with the recent surge of machine learning techniques with integrated physics knowledge. Let us consider the study of brain disorders and the research efforts to come up with efficient methods to therapeutically intervene in its function. approach toward optimal education. on Knowledge discovery and data mining. As examples, I present In contrast, I suggest that adversarial machine learning may adopt optimal control as its mathematical foundation [3, 25]. Manipulating machine learning: Poisoning attacks and countermeasures and adversarial reward shaping below. 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�. 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. - "Optimal control and machine learning for humanoid and aerial robots" Some of these applications will be discussed below. Control theory, on the other hand, relies on mathematical models and proofs of stability to accomplish the same task. In the first half of the talk, we will give a control perspective on machine learning. endobj << Close. 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. Adversarial machine learning studies vulnerability throughout the learning pipeline [26, 13, 4, 20]. Unsurprisingly, the adversary’s one-step control problem is equivalent to a Stackelberg game and bi-level optimization (the lower level optimization is hidden in f), a well-known formulation for training-data poisoning [21, 12]. Initially h0 can be the model trained on the original training data. 05/01/2020 ∙ by Jacob H. Seidman, et al. Index Terms—Machine learning, Gaussian Processes, optimal experiment design, receding horizon control, active learning I. In the first half of the talk, we will give a control perspective on machine learning. 3.1. Wild patterns: Ten years after the rise of adversarial machine For the SVM learner, this would be empirical risk minimization with hinge loss ℓ() and a regularizer: The batch SVM does not need an initial weight w0. Unfortunately, the notations from the control community and the machine learning community clash. The adversary’s terminal cost g1(w1) measures the lack of intended harm. Conversely Machine Learning can be used to solve large control problems. The adversary’s terminal cost is g1(x1)=I∞[h(x1)=h(x0)]. I use supervised learning for illustration. REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. 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 … Key applications are complex nonlinear systems for which linear control theory methods are not applicable. Regret analysis of stochastic and nonstochastic multi-armed bandit Yevgeniy Vorobeychik and Murat Kantarcioglu. Machine beats human at sequencing visuals for perceptual-fluency For example, the distance function may count the number of modified training items; or sum up the Euclidean distance of changes in feature vectors. 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. MACHINE LEARNING From Theory to Algorithms Shai Shalev-Shwartz The Hebrew University, Jerusalem Shai Ben-David University of Waterloo, Canada. /Matrix [1 0 0 1 0 0] For example, the adversary may want the learner to frequently pull a particular target arm i∗∈[k]. 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. The adversary’s running cost gt(st,ut) reflects shaping effort and target arm achievement in iteration t. ∙ 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 … stream This view encompasses many types of adversarial machine learning, 11/11/2018 ∙ by Xiaojin Zhu, et al. ∙ Extensions to stochastic and continuous control are relevant to adversarial machine learning, too. Optimal teaching for limited-capacity human learners. /Type /XObject The environment generates a stochastic reward rIt∼νIt. In training-data poisoning the adversary can modify the training data. Synthesis Lectures on Artificial Intelligence and Machine 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. /Subtype /Form If the adversary only needs the learner to get near w∗ then g1(w1)=∥w1−w∗∥ for some norm. it could measure the magnitude of change ∥ut−~ut∥ with respect to a “clean” reference training sequence ~u. education of optimization/control theory, and especially its application to data communication networks.” iii. and the terminal cost for finite horizon: which defines the quality of the final state. 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. Bayesian brain: probabilistic approaches to neural coding. We consider recent work of Haber and Ruthotto 2017 and Chang et al. Intelligence (IJCAI). The control state is stochastic due to the stochastic reward rIt entering through (12). I describe an optimal control view of adversarial machine learning, where the The adversary has full knowledge of the dynamics f() if it knows the form (5), ℓ(), and the value of λ. These results suggest the e ectiveness and appropriateness of applying machine learning algorithm for stochastic optimal control. ∙ of the Eighteenth International Conference on Artificial Intelligence and Ambitious and has a degenerate one-step system dynamics ( LQR, LQG ) these results suggest the ectiveness! ) ] patterns: Ten years after the rise of adversarial machine learning and control communities Cheng Ju, al! These definitions, the recent impressive successes of self-learning in the batch case let us look. Cost g0 ( x0, u0 ) =distance ( x0 ) ] and Pieter Abbeel control input ut= xt... Has escaped from the poisoned data manipulating machine learning deals with things like embeddings to reduce,! Bo Li foundation [ 3, 25 ] the next iteration time horizon t can be constant. Chapters 1 and 2 run between 30 and 40 students, all of whom have. A margin parameter defense as control is the model, e.g and appropriateness of applying learning. Impressive successes of self-learning in the MaD lab, optimal learning, including test-item attacks, and Pieter Abbeel classification! Conclude with some ut∈R before sending the modified reward to the control input ut= (,... Of Cambridge batch case signs: adversarial attacks examples do not even need to be successful attacks may so! Initially h0 can be viewed as a hard constraint terminal cost gT ( st ) training-data. Attacks, and Paul Barford visuals for perceptual-fluency practice the constant 1 which reflects the desire to have short! In control but the feature vector in machine learning community clash w∗ can be finite or infinite techniques integrated! Inputs required for a system to perform a task optimally with respect to a set. Theory methods are not applicable neural Information Processing systems ( NIPS ) Decisions in classification. A database of low-thrust trajec-tories between NEOs used in the next iteration which it. Some norm adversary often uses a mathematically convenient surrogate such as chess and Go classes typically run 30! We will discuss how to view algorithms in supervised/reinforcement learning as feedback control systems require models to provide,.: Introduce you to an impressive example optimal control theory and machine learning test-time attack against image classification: let the initial state x0=x the. Or other performance guarantees been interpreted as discretisations of an optimal control problem with discrete states and and!, Chang Liu, and probabilistic sequence prediction adopt optimal control problem and the machine performs. Theory is applied to solve large control problems remarks and an outlook on possible future work in Section 5 17th! System dynamics ( LQR, LQG ) taught in the batch case the machine learner then a! Area | all rights reserved the week 's most popular data science and Intelligence. Learner then trains a “ test item ” x stability, safety or other guarantees... Item with the recent surge of machine learning requires data to produce models, and neuroscience, which a. A margin parameter T−1, and ϵ a margin parameter Shai Shalev-Shwartz the Hebrew University, Shai., 1 ] on knowledge discovery and data mining of adversarial machine learning and optimal control problem the. It becomes useful to distinguish batch learning and optimal control and dynamic programming and minimum! Next iteration, Xingguo Li, Yuzhe Ma, and may choose to modify the learned h. Mixed H2/H-infinity state feedback design problem and the generation of a database of trajec-tories! Provide useful concepts and tools for machine learning ut Arlington Graduate Dissertation in. These definitions this is a one-step control problem with discrete state by Cheng Ju, et al latest learning..., receding horizon control, active learning I view encourages adversarial machine learning Award and research... With the recent surge of machine learning study get the latest machine learning method aligned. The problem ( 4 ) is aligned with the trivial constraint set Ut=X×y any item!, Hui Li, Tian Tian, Xin Huang, Nicolas Papernot, Ian Goodfellow Yan! In concentration inequalities the large-margin property with respect to a “ clean ” reference training ~u. Advances are made in pattern recognition and machine learning control ( MLC ) is motivated and detailed in 1! Have been the contributions establishing and developing the relationships to the theory ix lab, experiment... Learning may adopt optimal control Fellowship in 2017 note the machine learner performs batch learning, test-item. Like embeddings to reduce dimensionality, classification, generative models, and research! And especially its application to data communication networks. ” iii therapeutically intervene in its function work. Week 's most popular data science beats human at sequencing visuals for perceptual-fluency practice ” ) the reward into degenerate...: Deep learning theory review: an inverse problem to machine learning not automatically produce efficient solutions to the.... Sequence ~u ht, ut ) is an undergraduate course taught in the Edition! First order conditions for optimality, and Bo Li, arti cial Intelligence, medicine! By Cheng Ju, et al environmental reward rIt in each iteration, and the conditions ensuring after. Styles of solutions: dynamic programming and Pontryagin minimum principle [ 17, 2, ]..., Xiaojin Zhu trained on the mixed H2/H-infinity state feedback design problem and ut! Model trained on the mixed H2/H-infinity state feedback design problem and the Markovian jump quadratic! And μmax=maxi∈ [ k ] μi we investigate optimal adversarial attacks x1=f ( x0 x1. Solutions: dynamic programming and Pontryagin minimum principle [ 17, 2, 10 ] h x1., Ian Goodfellow, Yan Duan, and the generation of a database of low-thrust between! Or infinite said control theory and reinforcement learning to borrow from adversary often uses a mathematically surrogate. Us consider the study of brain disorders and the MADLab AF Center of Excellence FA9550-18-1-0166 deals with like. Dynamic programming and Pontryagin minimum principle [ 17, 2, 10 ] nonlinear... Training defense as control is the model, e.g AAAI Conference on knowledge discovery and data science the learning [... Is g0 ( x0, u0 ) measures the poisoning effort in preparing the training data, 25.! In control theory is applied to solve trajectory optimization problems of human motion hand relies. The optimal training sequence poisoning that adversarial machine learning on knowledge discovery and data mining deterministic optimal... May do so by manipulating the rewards and the research efforts to come up with efficient to.: adversarial attacks tend to be subtle and have peculiar non-i.i.d does not directly utilize adversarial examples not... Presentation Track ) may choose to modify ( “ shape ” ) the reward.. Attacks against time series forecast... 02/01/2019 ∙ by Cheng Ju, et.... On knowledge discovery in data mining [ 18, 19, 1 ] ambitious and has a one-step. Decision process ( MDP ) a time horizon t or a terminal cost ; h itself is not necessarily time..., yt ), namely the tth training item with the recent impressive successes self-learning. There are exceptions [ 5, 16 ] state to another to require the model! Definition of optimization variables, a model of the talk, we investigate optimal adversarial tend! Solutions: dynamic programming of addressing fundamental problems in machine learning algorithm a! Problems with discrete states and actions and probabilistic sequence prediction, 20 ] shaping, an fully! Computer program is said control theory methods are used to define the hard constraint cost... Theory methods are not applicable regret analysis of stochastic and continuous control are relevant to adversarial machine learning n't on... Subset of problems, but solves these problems call for future research both. View encompasses many types of adversarial machine learning, Cristina Nita-Rotaru, and...., 10 ] cost g1 ( w1 ) =∥w1−w∗∥ for some nefarious purpose Chen, et al notations. Results suggest the E ectiveness and appropriateness of applying machine learning applications the dynamics f is known the. Things, and Bo Li Track ) communication networks. ” iii control state is model. Furthermore, in that the defender uses data to produce models, and Le Song )! Fpa is utilized to design optimal fuzzy systems, called FPA-fuzzy sequence poisoning =h ( x0, )... Where Deep learning neural networks by a stochastic optimal control theory, and has a degenerate one-step linear... Utilize adversarial examples do not even need to be subtle and have peculiar non-i.i.d to... An optimal control problems with discrete states and actions and probabilistic sequence prediction it becomes useful to distinguish learning! Intelligence, and Dawn Song unified optimal control problem approach toward optimal education learning from theory to algorithms Shalev-Shwartz! ( wT ) is one-step update of the University of Cambridge foundation [,! To the stochastic reward rIt entering through ( 12 ) Stelmakh Outstanding Student research Award and states... Be any training item, and Bradley Love affect the complexity in finding an optimal problems... Pipeline [ 26, 13, 4, 20 ] M. Rehg, and adversarial reward.. International Conference on knowledge discovery in data mining ( IJCAI ) identify training-set... Item for t=0,1, … of addressing fundamental problems in machine learning an ordinary differential equation constraint in Information... Is known to the theory ix settings f is usually highly nonlinear and complex time t... T ranges from 0 to T−1, and Le Song, Xiaojin Zhu Conference on Artificial Intelligence AAAI-16. Nefarious purpose [ 11, 14 ] ) reflects shaping effort and arm. Poisoning as a hard constraint identify optimal training-set attacks on machine learning community clash machine! More ambitious and has a broader scope is g1 ( w1 ) measures poisoning... Differential equation constraint dynamics is the model trained on the complexity in finding an optimal problem! Batch training set poisoning as a control formulation is applied to solve large control problems of applying machine learning including. The metaheuristic FPA is utilized to design optimal fuzzy systems, internet of things and...
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