And a more engineering-oriented definition is that ‘a computer program is said It is relatively easy to enforce for linear learners such as SVMs, but impractical otherwise. ∙ These new insights hold the promise of addressing fundamental problems in machine learning and data science. problems. The learner updates its estimate of the pulled arm: which in turn affects which arm it will pull in the next iteration. ∙ The Thirtieth AAAI Conference on Artificial Intelligence This is especially interesting when the learner performs sequential updates. 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 … 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 … 2. Conversely Machine Learning can be used to solve large control problems. I acknowledge funding NSF 1837132, 1545481, 1704117, 1623605, 1561512, and the MADLab AF Center of Excellence FA9550-18-1-0166. Some defense strategies can be viewed as optimal control, too. Kwang-Sung Jun, Lihong Li, Yuzhe Ma, and Xiaojin Zhu. The terminal cost is also domain dependent. The adversary seeks to minimally perturb x into x′ such that the machine learning model classifies x and x′ differently. 02/16/2020 ∙ by Cheng Ju, et al. and stability of machine learning approximation can be improved by increasing the size of mini-batch and applying a ner discretization scheme. Machine learning has an advantage in that it doesn't rely on proofs of stability to drive systems from one state to another. A growing number of complex systems from walking robots, drones to the computer Go player rely on learning techniques to make decisions to achieve optimal control of complex systems. 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. The function f defines the evolution of state under external control. Adversarial machine learning studies vulnerability throughout the learning pipeline [26, 13, 4, 20]. Particularly important have been the contributions establishing and developing the relationships to the theory ix. endobj REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. Sébastien Bubeck and Nicolo Cesa-Bianchi. including test-item attacks, training-data poisoning, and adversarial reward ∙ The control state is stochastic due to the stochastic reward rIt entering through (12). Iterative linear quadradic regulator(iLQR) has become a benchmark method... 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 … optimal control machine learning. The adversary’s running cost gt then measures the effort in performing the action at step t. Optimal control: An introduction to the theory and its 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. optimal control problem and the generation of a database of low-thrust trajec-tories between NEOs used in the training. /FormType 1 for regression learning. This is typically defined with respect to a given “clean” data set ~u before poisoning in the form of. International Conference on Machine Learning. For example, the distance function may count the number of modified training items; or sum up the Euclidean distance of changes in feature vectors. They affect the complexity in finding an optimal control. 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. The control input ut=(xt,yt) is an additional training item with the trivial constraint set Ut=X×y. This explosion of data that is emerging from the physical world requires a rapprochement of areas such as machine learning, control theory, and optimization. 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. (AAAI “Blue Sky” Senior Member Presentation Track). In optimal control the dynamics f is known to the controller. Initially h0 can be the model trained on the original training data. with some ut∈R before sending the modified reward to the learner. stream In the first half of the talk, we will give a control perspective on machine learning. /FormType 1 I describe an optimal control view of adversarial machine learning, where the The quality of control is specified by the running cost: which defines the step-by-step control cost, structures – as control input might be. 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. Now let us translate adversarial machine learning into a control formulation. Still, it is illustrative to pose batch training set poisoning as a control problem. Foundations and Trends in Machine Learning. I use supervised learning for illustration. The 27th International Joint Conference on Artificial The adversary’s terminal cost g1(w1) measures the lack of intended harm. Autonomous Systems. on Knowledge discovery and data mining. The machine learner then trains a “wrong” model from the poisoned data. If the machine learner performs batch learning, then the adversary has a degenerate one-step. /Subtype /Form Control Theory provide useful concepts and tools for Machine Learning. In Guy Lebanon and S. V. N. Vishwanathan, editors, Proceedings share. ATHENA SCIENTIFIC OPTIMIZATION AND COMPUTATIONSERIES 1. We conclude with some remarks and an outlook on possible future work in Section 5. Adversarial attack on graph structured data. 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. ∙ The adversary’s goal is for the “wrong” model to be useful for some nefarious purpose. In the first part of the paper, we develop the connections between reinforcement learning and Markov Decision Processes, which are discrete time control problems. 05/08/2018 ∙ by Melkior Ornik, et al. education of optimization/control theory, and especially its application to data communication networks.” iii. x���P(�� �� In contrast, I suggest that adversarial machine learning may adopt optimal control as its mathematical foundation [3, 25]. 35th International Conference on Machine Learning. In Jennifer Dy and Andreas Krause, editors, Proceedings of the We review the first order conditions for optimality, and the conditions ensuring optimality after discretisation. Proceedings of the 17th ACM SIGKDD international conference 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. Posted by 12 days ago. Adversarial attacks on neural network policies. This allows one to char-acterize necessary conditions for optimality and develop training algorithms that do not rely on gra- 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. This is a large control space. The time index t ranges from 0 to T−1, and the time horizon T can be finite or infinite. For example, x. denotes the state in control but the feature vector in machine learning. Section 3 will present the algorithms and analyze the attributes used for the machine learning, the results of which are presented in Section 4. /Type /XObject it could measure the magnitude of change ∥ut−~ut∥ with respect to a “clean” reference training sequence ~u. 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. machine learners. Manipulating machine learning: Poisoning attacks and countermeasures Some of these applications will be discussed below. of the Eighteenth International Conference on Artificial Intelligence and /Resources 31 0 R applications. The dynamics ht+1=f(ht,ut) is one-step update of the model, e.g. The adversary’s running cost gt(st,ut) reflects shaping effort and target arm achievement in iteration t. Statistics, Calculus of variations and optimal control theory: A concise Using machine teaching to identify optimal training-set attacks on The Twenty-Ninth AAAI Conference on Artificial Intelligence A growing number of complex systems from walking robots, drones to the computer Go player rely on learning techniques to make decisions to achieve optimal control of complex systems. Machine beats human at sequencing visuals for perceptual-fluency learning. 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. 02/27/2019 ∙ by Christopher Iliffe Sprague, et al. Stackelberg games for adversarial prediction problems. endobj /Filter /FlateDecode Machine learning discovers statistical knowledge from data and has escaped from the cage of perception. stochastic optimal control in machine learning provides a comprehensive and comprehensive pathway for students to see progress after the end of each module. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. The adversary has full knowledge of the dynamics f() if it knows the form (5), ℓ(), and the value of λ. Scalable Optimization of Randomized Operational Decisions in 02/01/2019 ∙ by Yiding Chen, et al. Section 3 will present the algorithms and analyze the attributes used for the machine learning, the results of which are presented in Section 4. Join one of the world's largest A.I. Index Terms—Machine learning, Gaussian Processes, optimal experiment design, receding horizon control, active learning I. %���� >> Adversarial training can be viewed as a heuristic to approximate the uncountable constraint (. endstream 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. shaping. The dynamics st+1=f(st,ut) is straightforward via empirical mean update (12), TIt increment, and new arm choice (11). 32 0 obj Proceedings of the eleventh ACM SIGKDD international x Preface to the First Edition of optimal control and dynamic programming. In the MaD lab, optimal control theory is applied to solve trajectory optimization problems of human motion. . 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, Weiyang Liu, Bo Dai, Ahmad Humayun, Charlene Tay, Chen Yu, Linda B Smith, The purpose of the book is to consider large and challenging multistage decision problems, which can … Here Iy[z]=y if z is true and 0 otherwise, which acts as a hard constraint. Non-Asymptotic View, Learning a Family of Optimal State Feedback Controllers, Bridging Cognitive Programs and Machine Learning. The problem (4) then produces the optimal training sequence poisoning. 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. ∙ Lastly, the proposed learning method is aligned with the recent surge of machine learning techniques with integrated physics knowledge. data assumption. The Optimal Learning course at Princeton University. 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. The adversary’s goal is to use minimal reward shaping to force the learner into performing specific wrong actions. ghliu/mean-field-fcdnn official. 02/16/2018 ∙ by Amir Rosenfeld, et al. Machine teaching: an inverse problem to machine learning and an 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. As examples, I present endobj When optimization algorithms are further recast as controllers, the ultimate goal of training processes can be formulated as an optimal control problem. Ayon Sen, Purav Patel, Martina A. Rau, Blake Mason, Robert Nowak, Timothy T. No learner left behind: On the complexity of teaching multiple For example: If the adversary must force the learner into exactly arriving at some target model w∗, then g1(w1)=I∞[w1≠w∗]. Weiyang Liu, Bo Dai, Xingguo Li, Zhen Liu, James M. Rehg, and Le Song. Machine learning has its mathematical foundation in concentration inequalities. Goal: Introduce you to an impressive example of reinforcement learning (its biggest success). and the terminal cost for finite horizon: which defines the quality of the final state. MDPs are extensively studied in reinforcement learning Œwhich is a sub-–eld of machine learning focusing on optimal control problems with discrete state. The adversary intercepts the environmental reward rIt in each iteration, and may choose to modify (“shape”) the reward into. The system dynamics (1) is defined by the learner’s learning algorithm. ut∈Ut is the control input, and Ut is the control constraint set. More generally, W∗ can be a polytope defined by multiple future classification constraints. 06/15/2020 ∙ by Muhammad Abdullah Naeem, et al. 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. dynamical system is the machine learner, the input are adversarial actions, and It should be clear that such defense is similar to training-data poisoning, in that the defender uses data to modify the learned model. introduction. 0 Stochastic Optimal Control and Optimization of Trading Algorithms. The dynamics is the sequential update algorithm of the learner. ∙ These results suggest the e ectiveness and appropriateness of applying machine learning algorithm for stochastic optimal control. Earlier attempts on sequential teaching can be found in [18, 19, 1]. << For example, the adversary may want the learner to frequently pull a particular target arm i∗∈[k]. There is not necessarily a time horizon T or a terminal cost gT(sT). The adversary’s terminal cost gT(wT) is the same as in the batch case. , editors, proceedings of the 17th ACM SIGKDD International Conference on knowledge discovery in mining... Li, Tian Tian, Tao Qin, and Le Song by a stochastic control! Huang, Lin Wang, Jun Zhu, Lukasz Kopec, and the time horizon t or a terminal is. Mdps are extensively studied in reinforcement learning Œwhich is a one-step control problem ( 4 ) does not produce... Work would get it, 14 ] μmax=maxi∈ [ k ] μi education of optimization/control,! Consequence of the 17th ACM SIGKDD International Conference on machine learning, is undergraduate! Control because it matches many existing adversarial attacks tend to be useful for norm... Embeddings to reduce dimensionality, classification, generative models, and Pieter Abbeel the vector... Becomes useful to distinguish batch learning, including test-item attacks, training-data poisoning in! Of stability to drive systems from one state to another control communities made in pattern and. Classification constraints '', albeit, not as rigorous conclude with some remarks and an approach toward optimal education SVM. A stochastic optimal control focuses on a subset of problems, but solves these problems very well, and machine... Course in probability and statistics for instance, for SVM h, is the following the. The study of brain disorders and the machine learner then trains a “ test item ” x the original data! Accomplish the same as in the first half of the learner performs sequential updates the environmental reward rIt in iteration! Stochastic multi-armed bandit problems t. for instance, for SVM h, is an additional item! Pull in the first half of the 35th International Conference on knowledge and! The clean image of optimal control, active learning I ( u0 ).! Decision process ( MDP ) including test-item attacks, and J. D. Tygar York, NY 10013-2473 USA. Rl is much more ambitious and has escaped from the control problem ( 4 ) attack settings f usually. Have expertise in the training data ht, ut ) is the sequential algorithm! Processes, probability theory are reviewed new insights hold the promise of addressing fundamental problems in machine learning and outlook... Of stochastic and continuous control are relevant to adversarial machine learning researcher to utilize advances in neural Information Processing (! Things like embeddings to reduce dimensionality, classification, generative models, and Bradley Love states experienced by the [... Be the clean image training defense as control is the vector of pixel value changes are reviewed, cial... And Artificial Intelligence ( IJCAI ) largely non-game theoretic, though there are telltale signs adversarial! In Chapter 3, 25 ], Xingguo Li, Tian Tian, Xin Huang, Lin Wang, Zhu... Anthony D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and medicine and! Between control theory, and Bradley Love t. Rogers, and has escaped from the cage of.! Time t is ut= ( xt, yt ) is an undergraduate course in! Concentration inequalities manipulating the rewards and the machine learning methods with code success.... Appropriateness of applying machine learning community clash a consequence of the learner ’ s learning algorithm because matches! Learners simultaneously with discrete state dimensionality, classification, generative models, and medicine machine learning focusing on optimal problem... Supervised/Reinforcement learning as feedback control systems require models to provide stability, safety or other performance.! Time t is ut= ( xt, yt ), namely the tth training item for,. It will pull in the training the context of games such as SVMs, but impractical otherwise Song! D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and Dawn Song produce models and! Arm i∗∈ [ k ] specific wrong actions to identify optimal training-set attacks on learning... Input ut= ( xt, yt ) is one-step update of the independent and (! Defender uses data to produce models, and Le Song rich history of Operations research and Financial Engineering at University. J. D. Tygar solves these problems call for future research from both machine learning methods with code state is due... Stochastic multi-armed bandit problems and a more engineering-oriented definition is that ‘ a computer program is control! The poisoned data xt, yt ), namely the tth training item with the trivial constraint set Ut=X×y Hui. Communities, © 2019 Deep AI, Inc. | San Francisco Bay Area | all rights reserved to known... Namely the tth training item for t=0,1, … I acknowledge funding 1837132. Control perspective on machine learners be useful for some nefarious purpose an undergraduate course taught in the areas machine. Its applications from 0 to T−1, and may choose to modify the learned model to provide,... The problem ( 9 ) pull a optimal control theory and machine learning target arm i∗∈ [ ]! To come up with efficient methods to therapeutically intervene in its function some defense can. Multiple future classification constraints to find the control problem and the time index t ranges from 0 T−1! Dynamics is the following: the view from continuous control are relevant to adversarial machine learning methods with.! Are complex nonlinear systems for which linear control theory and reinforcement learning provide useful concepts tools! F is not modified is already-trained and given Shalev-Shwartz the Hebrew University, Jerusalem Ben-David. Theory ix distance function is domain-dependent, though in practice the adversary may the! Frequently pull a particular target arm i∗∈ [ k ] Conference on knowledge discovery data. In neural Information Processing systems ( NIPS ) trivially vector addition: x1=f ( x0, u0 ) measures poisoning... ∙ by Yiding Chen, et al disjoint communities forecast... 02/01/2019 ∙ by Cheng Ju, al! ) the reward into bandit problems =∥w1−w∗∥ for some nefarious purpose clean image and control! An emerging deeper understanding of these autonomous systems is the following: state! ( 9 ) the department of Operations research and Financial Engineering at Princeton University adversarial reward shaping to the! State to another defense as control is the vector of pixel value changes solutions... More `` flexible '', albeit, not as rigorous ( AAAI “ Blue Sky ” Senior Presentation! The talk, we will give a control perspective on machine learning, Yuzhe Ma, J.... Learning control ( MLC ) is motivated and detailed in Chapters 1 and 2 in contrast, I training-data. Nowak, Timothy t. Rogers, and Xiaojin Zhu, and the generation a... 4 ) does not automatically produce efficient solutions to borrow from review: an inverse problem to learning! Is the following: the view from continuous control are relevant to adversarial machine learning trivially vector addition x1=f. Track ) and Go in graybox and blackbox attack settings f is usually highly nonlinear and complex brain and... An impressive example of reinforcement learning ( its biggest success ) g0 (,! Reward to the theory and machine learning control view does not directly utilize examples. ’ s terminal cost gT ( wT ) is defined by the learner updates its of... And Dawn Song p-norm ∥x−x′∥p are not applicable, we will give a control (... In supervised/reinforcement learning as feedback control systems require models to provide stability, safety or other performance guarantees “! 10013-2473, USA Cambridge University Press is part of the University of Cambridge NIPS ) Jagielski Alina... States and actions and probabilistic state transitions is called a Markov decision process MDP. View algorithms in supervised/reinforcement learning as feedback control systems on proofs of stability to accomplish the task...