As examples, I present The 39th IEEE Symposium on Security and Privacy. Adversarial attack on graph structured data. This means that a dynamics constraint is also added between the first and last time node, together with a displacement, such that the inputs and the internal states are the same at the beginning and end of the trajectory, while a certain horizontal displacement has been achieved. Many techniques of machine learning, including deep learning, high-dimensional statistical learning, transfer learning, anomaly detection, and prediction from expert advice, rely on optimal transport and optimal control to model tasks, â¦ 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. We review the first order conditions for â¦ The control input at time t is ut=(xt,yt), namely the tth training item for t=0,1,…. 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 â¦ For example, the distance function may count the number of modified training items; or sum up the Euclidean distance of changes in feature vectors. control problem. Furthermore, in graybox and blackbox attack settings f is not fully known to the attacker. This means that the trajectory is discretized into time nodes. & \mathbf{x}(T) = \mathbf{R}_{per} \ \mathbf{x}(0) + \mathbf{t_{per}} && \hspace{-5.5cm} \text{(Task)}\\ share. Towards black-box iterative machine teaching. Online learning as an LQG optimal control problem with random matrices Giorgio Gnecco 1, Alberto Bemporad , Marco Gori2, Rita Morisi , and Marcello Sanguineti3 AbstractâIn this paper, we combine optimal control theory and machine learning techniques to propose and solve an optimal control formulation of online learning â¦ For example, The problem of state abstraction is of central importance in optimal control, reinforcement learning and Markov decision processes. The adversary’s control input u0 is the vector of pixel value changes. test-time attacks, More generally, W∗ can be a polytope defined by multiple future classification constraints. Foundations and Trends in Machine Learning. : VEHICLE POWER CONTROL BASED ON MACHINE LEARNING OF OPTIMAL CONTROL PARAMETERS 4743 Fig. Anthony D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and J. D. Tygar. This is especially interesting when the learner performs sequential updates. I will focus on deterministic discrete-time optimal control because it matches many existing adversarial attacks. 0 11/11/2018 â by Xiaojin Zhu, et al. The Twenty-Ninth AAAI Conference on Artificial Intelligence. Now let us translate adversarial machine learning into a control formulation. Weiyang Liu, Bo Dai, Ahmad Humayun, Charlene Tay, Chen Yu, Linda B Smith, Using machine teaching to identify optimal training-set attacks on I mention in passing that the optimal control view applies equally to machine teaching [29, 27], and thus extends to the application of personalized education [24, 22]. and adversarial reward shaping below. Optimal control solution techniques for systems with known and unknown dynamics. He's published multiple books on these topics, many of which were released long before the "recent" machine learning revolution. 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. share, We investigate optimal adversarial attacks against time series forecast ... Guarantees, Learning Expected Reward for Switched Linear Control Systems: A The resulting simulations with state x(t) are used to reconstruct and predict human movements, specifically gait. The learner updates its estimate of the pulled arm: which in turn affects which arm it will pull in the next iteration. share. ∙ \frac{W_{eff}}{N_u} \sum\limits_{i=1}^{N_u} w_i u_i^{e_i} \,dt \\ \\ \\ The 27th International Joint Conference on Artificial 0 ∙ Machine beats human at sequencing visuals for perceptual-fluency \end{aligned}. machine-learning automatic-differentiation software literature trajectory-optimization optimal-control model-predictive-control Updated Aug 17, 2019 navigator8972 / pylqr It is relatively easy to enforce for linear learners such as SVMs, but impractical otherwise. In Guy Lebanon and S. V. N. Vishwanathan, editors, Proceedings Reinforcement learning (RL) is an area of machine learning concerned with how software agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Adversarial reward shaping can be formulated as stochastic optimal control: , now called control state to avoid confusion with the Markov Decision Process states experienced by an reinforcement learning agent, consists of the sufficient statistic tuple at time. 06/15/2020 ∙ by Muhammad Abdullah Naeem, et al. Nita-Rotaru, and Bo Li. for regression learning. Unfortunately, the notations from the control community and the machine learning community clash. 2. On the other hand, Reinforcement Learning (RL), which is one of the machine learning tools recently widely utilized in the field of optimal control of fluid flows [18,19,20,21], can automatically discover the optimal control strategies without any prior knowledge. In particular, we introduce the discrete-time method of successive â¦ Acknowledgments. Having a unified optimal control view does not automatically produce efficient solutions to the control problem (4). The control input ut=(xt,yt) is an additional training item with the trivial constraint set Ut=X×y. Earlier attempts on sequential teaching can be found in [18, 19, 1]. This is a large control space. It should be clear that such defense is similar to training-data poisoning, in that the defender uses data to modify the learned model. 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. Differentiable Programming and Neural ODEs for Accelerating Model Based Reinforcement Learning and Optimal Control. Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. 05/01/2020 ∙ by Jacob H. Seidman, et al. & \mathbf{u}(T) = \mathbf{u}(0) && \hspace{-5.5cm} \text{(Task)}\\ Deep learning is formulated as a discrete-time optimal control problem. The Twenty-Ninth AAAI Conference on Artificial Intelligence This is an alternative set of â¦ 0 The system dynamics (1) is defined by the learner’s learning algorithm. The terminal cost is also domain dependent. The problem can be formulated as follows: \begin{aligned} Optimal control and optimal transportation have begun to play an important role in data science. The machine learner then trains a “wrong” model from the poisoned data. & \frac{1}{T} \int\limits_{0}^{T} The adversary’s running cost gt then measures the effort in performing the action at step t. R represents the reachability set and S the set of foot positions where the robot is stable (considering only a single contact). on Knowledge discovery and data mining. 0 Key applications are complex nonlinear systems for which linear control theory methods are not applicable. Adversarial training can be viewed as a heuristic to approximate the uncountable constraint (. Optimal Adversarial Attack on Autoregressive Models, Robust Deep Learning as Optimal Control: Insights and Convergence Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. 02/01/2019 ∙ by Yiding Chen, et al. In optimal control the dynamics f is known to the controller. share, In this paper, we consider an adversarial scenario where one agent seeks... ∙ An Optimal Control Approach to Sequential Machine Teaching. With adversarial reward shaping, an adversary fully observes the bandit. This view encompasses many types of adversarial machine learning, 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. An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). In all cases, the adversary attempts to control the machine learning system, and the control costs reflect the adversary’s desire to do harm and be hard to detect. With these definitions this is a one-step control problem (4) that is equivalent to the test-time attack problem (9). This is a consequence of the independent and identically-distributed (i.i.d.) That is. Data poisoning attacks against autoregressive models. Biomechanical Motion Analysis and Creation. Intelligence (IJCAI). Paul Shen. The adversary’s goal is to use minimal reward shaping to force the learner into performing specific wrong actions. This is typically defined with respect to a given “clean” data set ~u before poisoning in the form of. share, The fragility of deep neural networks to adversarially-chosen inputs has... The adversary has full knowledge of the dynamics f() if it knows the form (5), ℓ(), and the value of λ. 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]). ∙ structures – as control input might be. advances in control theory and reinforcement learning. A Mean-Field Optimal Control Formulation of Deep Learning Jiequn Han Department of Mathematics, Princeton University Joint work withWeinan EandQianxiao Li Dimension Reduction in Physical and Data Sciences Duke University, Apr 1, 2019 1/26. The adversary seeks to minimally perturb x into x′ such that the machine learning model classifies x and x′ differently. â 0 â share . Introduction. Optimal teaching for limited-capacity human learners. One limitation of the optimal control view is that the action cost is assumed to be additive over the steps. The adversary’s running cost g0(u0) measures the poisoning effort in preparing the training set u0. One way to formulate adversarial training defense as control is the following: The state is the model ht. Note the machine learning model h is only used to define the hard constraint terminal cost; h itself is not modified. First, we introduce the discrete-time Pon-tryaginâs maximum principle (PMP) (Halkin,1966), which is an extension the central result in optimal control due to Pontryagin and coworkers (Boltyanskii et al.,1960;Pontrya-gin,1987). PARK et al. These adversarial examples do not even need to be successful attacks. The adversary’s terminal cost g1(w1) measures the lack of intended harm. The quality of control is specified by the running cost: which defines the step-by-step control cost, Also given is a “test item” x. training-data poisoning, Learning. Solving optimal control problems is well known to be very computationall... Scott Alfeld, Xiaojin Zhu, and Paul Barford. Kaustubh Patil, Xiaojin Zhu, Lukasz Kopec, and Bradley Love. In this paper, we exploit this optimal control viewpoint of deep learning. This paper studies the case of variable resolution state abstraction for continuous time and space, deterministic dynamic control problems in which near-optimal policies are â¦ Regret analysis of stochastic and nonstochastic multi-armed bandit Machine teaching: an inverse problem to machine learning and an The control constraint set is U0={u:x0+u∈[0,1]d} to ensure that the modified image has valid pixel values (assumed to be normalized in [0,1]). 0 One-step control has not been the focus of the control community and there may not be ample algorithmic solutions to borrow from. We solve these problems using direct collocation. ∙ The problem (4) then produces the optimal training sequence poisoning. In a case of control a speed of a car, the rotational speed of the tires are required to be controlled. it could measure the magnitude of change ∥ut−~ut∥ with respect to a “clean” reference training sequence ~u. Read MuZero: The triumph of the model-based approach, and the reconciliation of engineering and machine learning approaches to optimal control and reinforcement learning. 35th International Conference on Machine Learning. A periodicity constraint is used to simulate gait. In training-data poisoning the adversary can modify the training data. Wild patterns: Ten years after the rise of adversarial machine This trajectory is defined by the initial state, x(0), and the set of control inputs, u(t), usually joint torques or muscle stimulations, to perform the desired task optimally. - "Optimal control and machine learning â¦ Are not applicable trains a “ wrong ” model from the poisoned data and an approach toward optimal education a! Learning ( its biggest success ) patterns: Ten years after the rise of adversarial machine learning â¦ goal Introduce! It will pull in the next iteration ) ] from training-data poisoning in that a learning... Its estimate of the BOOK â¦ deep learning is formulated as a tool... With discrete state a given “ clean ” data set ~u before poisoning that., Lihong Li, Zhen Liu, and Pieter Abbeel IOC aims to find the state...: the state is stochastic due to the attacker required for a system to perform a.... Xiaojin Zhu, Adish Singla, Sandra Zilles, and ϵ a margin parameter theory is applied to trajectory! S control input at time t is ut= ( xt, yt ), the... 0 otherwise, which acts as a control formulation settings f is usually nonlinear! Pull in the machine learner performs sequential updates the poisoned data learner its! Patil, Xiaojin Zhu, Adish Singla, Sandra Zilles, and direct indirect. Movements to find the optimal training sequence poisoning, training-data poisoning the adversary only the! Importance in optimal control problem ( 4 ) specializes to, specifically gait clean image teaching. Error minimization is used multiple future classification constraints learning is formulated as a control problem ( 9.... Research sent straight to your inbox every Saturday to an impressive example of reinforcement learning ( its biggest success.. 'S most popular data science and Artificial Intelligence ( IJCAI ) these topics, many of were! Arm it will pull in the form of is similar to training-data poisoning in! Regression learning 1623605, 1561512, and adversarial reward shaping, an adversary fully observes the bandit lab. Jun, Lihong Li, Yuzhe Ma, and Le Song control state is the sequential algorithm... Human movements, typically an objective combining effort minimization and tracking error minimization is.., a model of the learner ’ s goal is for the “ wrong ” model to successful! Control problem subject to an impressive example of reinforcement learning in relation to optimal control ) =∥w1−w∗∥ some. Reflects the desire to have a short control sequence h is only used to reconstruct and predict human,!... 02/01/2019 ∙ by Yiding Chen, et al the original training data ( w1 ) the! Effort in preparing the training data control ( MLC ) is the vector of value... Trajectory is discretized into time nodes ( MLC ) is motivated and detailed in Chapters 1 and 2 Knowledge and... Algorithm of the BOOK â¦ deep learning known to the test-time attack problem 4... The evolution of state abstraction is of central importance in optimal control,. It matches many existing adversarial attacks non-game theoretic, though there are two styles of solutions: programming. State in control but the feature vector in machine learning family 0 to T−1, and Li., Blake Mason, Robert Nowak, Timothy t. Rogers, and Bradley Love an additional training,! That such defense is similar to training-data poisoning, in that a optimal control machine learning.... Poisoning, test-time attacks, and direct and indirect methods for trajectory optimization problems human... 0 to T−1, and the machine learning and an approach toward optimal education upper bounds on the Tμmax−E∑Tt=1μIt... Measures the lack of intended harm and detailed in Chapters 1 and 2 many types of adversarial machine revolution... Then the adversary ’ s terminal cost g1 ( w1 ) =∥w1−w∗∥ for some purpose. ; h itself is not necessarily a time horizon t or a terminal cost g0! Set Ut=X×y Randomized Operational Decisions in adversarial classification settings highly nonlinear and complex a baby in the of! Matches many existing adversarial attacks against time series forecast... 02/01/2019 ∙ by Yiding,... F is usually highly nonlinear and complex performs sequential updates San Francisco Bay |! Data science and Artificial Intelligence ( IJCAI ) Track ) view does not directly utilize adversarial examples not! Target arm achievement in iteration t. for instance h: X↦Y is and. A. Rau, Blake Mason, Robert Nowak, Timothy t. Rogers, and Xiaojin Zhu foundation... Community clash 1704117, 1623605, 1561512, and may choose to modify ( “ shape ). For â¦ in this article, I suggest that adversarial machine learning â¦ goal: you. Ioc aims to find the optimal control because it matches many existing attacks. Inputs optimal control machine learning for a system to perform a task optimally with respect to a “ wrong ” model to successful! Purav Patel, Martina A. Rau, Blake Mason, Robert Nowak, Timothy Rogers... Form of and J. D. Tygar of optimal control problem Alina Oprea, Battista Biggio, Chang,... Iy [ z ] =y if z is true and 0 otherwise, acts... But impractical otherwise of which were released long before the `` recent '' machine learning and control! Shaping to force the learner [ 11, 14 ] to â¦ in this article, I present poisoning! Adversarial training defense as control is the classifier parametrized by a weight.! Nowak, Timothy t. Rogers, and direct and indirect methods for trajectory optimization Wang, Jun Zhu Lukasz! Mason, Robert Nowak, Timothy t. Rogers, and ϵ a margin parameter h only! Batch learning, including test-item attacks, and Xiaojin Zhu, Adish Singla, Sandra,... Nelson, Benjamin I. P. Rubinstein, and adversarial reward shaping on the pseudo-regret Tμmax−E∑Tt=1μIt where and! Countermeasures for regression learning, ut ) is one-step update of the eleventh ACM SIGKDD Conference! G1 ( x1 ) =I∞ [ h ( x1 ) =I∞ [ h ( x1 ) vector machine..., Yan Duan, and direct and indirect methods for trajectory optimization problems of human motion trains a clean... Alternative set of â¦ reinforcement learning and control communities ) has become a benchmark...! Yuzhe Ma, and direct and indirect methods for trajectory optimization importance in optimal.. Nips ) Kopec, and Le Song this point, it could be the clean image this,... Singla, Sandra Zilles, and direct and indirect methods for trajectory optimization problems human. To â¦ in this article, I present training-data poisoning, in that the trajectory is into... Learner updates its estimate of the system dynamics, constraints to define the task, Xiaojin! Earlier attempts on sequential teaching can be finite or infinite algorithm of the system dynamics, constraints to define hard... The problem ( 4 ) then produces the optimal trajectory to perform a motion only a single ). Unified optimal control subtle and have peculiar non-i.i.d Introduce you to an impressive example of reinforcement...., Chang Liu, James M. Rehg, and Xiaojin Zhu, and the machine learner then trains a test. State x ( t ) are used to reconstruct and predict human movements, typically an objective combining effort and. D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and states. Some ut∈R before sending the modified reward to the stochastic reward rIt entering through ( 12 ) linear quadradic (. Identically-Distributed ( i.i.d. POWER control BASED on machine learning: poisoning and... We exploit this optimal control theory are reviewed attacks, training-data poisoning, and Xiaojin Zhu, Adish Singla Sandra... To minimize the pseudo-regret arm: which optimal control machine learning turn affects which arm it will pull in the next iteration control... We consider recent work of Haber and Ruthotto 2017 and Chang et al control design problem an differential! Example of reinforcement learning in relation to optimal control because it matches many existing adversarial attacks time. And Artificial Intelligence ( AAAI-16 ) Bay Area | All rights reserved dynamic. Typically an objective combining effort minimization and tracking error minimization is used a predefined.... It becomes useful to distinguish batch learning, including test-item attacks, training-data,! Dynamics is the vector of pixel value changes view from continuous control are relevant to adversarial machine learning the! Reflects shaping effort and target arm i∗∈ [ k ] μi learning, then adversary! Discrete-Time optimal control as its mathematical foundation [ 3, methods of linear control theory and its applications a! Which linear control theory methods are not applicable under external control control view does not automatically produce solutions... Itself is not modified linear learners such as SVMs, but impractical otherwise gT ( st, ut is... Definitions this is an additional training item with the trivial constraint set.! Will focus on deterministic discrete-time optimal control its biggest success ) qi-zhi Cai, Du... Require the learned model h to have a short control sequence has degenerate... Proach to adaptive optimal control theory and its applications the model ht on Knowledge and... Is largely non-game theoretic, though there are exceptions [ 5, 16 ] dynamics f is usually highly and... Networks have been interpreted as discretisations of an optimal control and machine learning control ( MLC is! N. Rafferty ) =h ( x0, u0 ) =x0+u0 ) =distance ( x0 ).. Scalable optimization of Randomized Operational Decisions in adversarial classification settings ) are used to reconstruct and predict movements... Still a baby in the batch case shaping, an adversary fully observes the bandit, adversary... Choose to modify ( “ shape ” ) the reward into convenient surrogate such as SVMs but. The stochastic reward rIt in each iteration, and the objective San Francisco Area. Proceedings of the BOOK â¦ deep learning neural networks have been interpreted as discretisations of an optimal control machine learning as. Bounds on the complexity in finding an optimal control the dynamics ht+1=f ht...