James M Rehg, and Le Song. In particular, we introduce the discrete-time method of successive … training-data poisoning, Hanjun Dai, Hui Li, Tian Tian, Xin Huang, Lin Wang, Jun Zhu, and Le Song. However we don't control rotational speed of tires but only handle with the accelerator and brake … Matthew Jagielski, Alina Oprea, Battista Biggio, Chang Liu, Cristina 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. Intelligence (IJCAI). The adversary’s running cost gt then measures the effort in performing the action at step t. ∙ The IOC aims to … Proceedings of the 17th ACM SIGKDD international conference Let us first look at the popular example of test-time attack against image classification: Let the initial state x0=x be the clean image. control problem. \text{subject to} ~~ Optimal control and machine learning for humanoid and aerial robots @inproceedings{Geisert2018OptimalCA, title={Optimal control and machine learning for humanoid and aerial robots}, author={Mathieu Geisert}, year={2018} } Here Iy[z]=y if z is true and 0 otherwise, which acts as a hard constraint. 0 The adversary’s control input u0 is the vector of pixel value changes. Regularisation for Inverse Problems and Machine Learning, Campus Jussieu, Sorbonne Université, Paris 19.11.2019 Deep learning as optimal control problems Martin Benning, Queen Mary University of London (QMUL) Models and numerical methods This is joint work with Elena Celledoni, Matthias J. Ehrhardt, Brynjulf … For each two consecutive time nodes, a dynamics constraint is added, such that the state and input at the time node yield the state at the next time point. 0 The controller wants to use the least number of training items|a concept known as the Manipulating machine learning: Poisoning attacks and countermeasures For example, the learner may perform one step of gradient descent: The adversary’s running cost gt(wt,ut) typically measures the effort of preparing ut. We summarize here an emerging deeper understanding of these As examples, I present applications. The system dynamics (1) is defined by the learner’s learning algorithm. 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 … the control costs are defined by the adversary's goals to do harm and be hard 02/16/2018 ∙ by Amir Rosenfeld, et al. Adversarial attack on graph structured data. The learner’s goal is to minimize the pseudo-regret Tμmax−E∑Tt=1μIt where μi=Eνi and μmax=maxi∈[k]μi. The adversary’s running cost g0(u0) measures the poisoning effort in preparing the training set u0. One way to formulate test-time attack as optimal control is to treat the test-item itself as the state, and the adversarial actions as control input. If AI had a Nobel Prize, this work would get it. It requires the definition of optimization variables, a model of the system dynamics, constraints to define the task, and the objective. The problem can be formulated as follows: \begin{aligned} Thus, it is possible and promising to introduce the basic QL framework for addressing the optimal control design problem. No learner left behind: On the complexity of teaching multiple 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’s terminal cost is g1(x1)=I∞[h(x1)=h(x0)]. problems. 06/15/2020 ∙ by Muhammad Abdullah Naeem, et al. Intelligence (IJCAI). He's published multiple books on these topics, many of which were released long before the "recent" machine learning revolution. The adversary seeks to minimally perturb x into x′ such that the machine learning model classifies x and x′ differently. 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]. 0 Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning.. Reinforcement learning differs from supervised learning … The terminal cost is also domain dependent. Or it could be the constant 1 which reflects the desire to have a short control sequence. 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. share, The fragility of deep neural networks to adversarially-chosen inputs has... Let (x,y) be any training item, and ϵ a margin parameter. The adversarial learning setting is largely non-game theoretic, though there are exceptions [5, 16]. There are two styles of solutions: dynamic programming and Pontryagin minimum principle [17, 2, 10]. machine learners. 0 learners simultaneously. International Conference on Machine Learning. 10/15/2018 ∙ by Laurent Lessard, et al. 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]. If the adversary only needs the learner to get near w∗ then g1(w1)=∥w1−w∗∥ for some norm. the optimal control problem in control community. share, Solving optimal control problems is well known to be very computationall... One-step control has not been the focus of the control community and there may not be ample algorithmic solutions to borrow from. 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 … Ayon Sen, Purav Patel, Martina A. Rau, Blake Mason, Robert Nowak, Timothy T. ∙ (AAAI “Blue Sky” Senior Member Presentation Track). ∙ If the adversary wants to ensure that a specific future item x∗ is classified ϵ-confidently as positive, it can use Optimal control What is control problem? With these definitions, the adversary’s one-step control problem (4) specializes to. This means that the trajectory is discretized into time nodes. Adversarial training can be viewed as a heuristic to approximate the uncountable constraint (. We use the fact that humans minimize energy expenditure in movements to find the optimal trajectory to perform a motion. & \mathbf{u}(T) = \mathbf{u}(0) && \hspace{-5.5cm} \text{(Task)}\\ Test-time attack differs from training-data poisoning in that a machine learning model h:X↦Y is already-trained and given. Machine teaching: an inverse problem to machine learning and an Decision/Control Ideas Decision/ Control/DP Principle of Optimality Markov Decision Problems POMDP Policy Iteration Value Iteration AI/RL Learning through Experience Simulation, Model-Free Methods Late 80s-Early 90s Feature-Based Representations A*/Games/ Heuristics Complementary Ideas Historical highlights Exact DP, optimal control … 0 The time index t ranges from 0 to T−1, and the time horizon T can be finite or infinite. This allows for an analytical derivation of the dynamics and their derivatives, such that the problem can be solved efficiently using a large-scale nonlinear optimization algorithm, such as IPOPT or SNOPT. Adversarial attacks on neural network policies. The learner updates its estimate of the pulled arm: which in turn affects which arm it will pull in the next iteration. Machine teaching is optimal control theory applied to machine learning: the plant is the learner, the state is the learned model, and the control is the training data. ∙ ∙ Scalable Optimization of Randomized Operational Decisions in learning. For example: If the adversary must force the learner into exactly arriving at some target model w∗, then g1(w1)=I∞[w1≠w∗]. Foundations and Trends in Machine Learning. They affect the complexity in finding an optimal control. In Guy Lebanon and S. V. N. Vishwanathan, editors, Proceedings The machine learner then trains a “wrong” model from the poisoned data. share, While great advances are made in pattern recognition and machine learnin... In Chapter 3, methods of linear control theory are reviewed. Stochastic multi-armed bandit strategies offer upper bounds on the pseudo-regret. conference on Knowledge discovery in data mining. 05/01/2020 ∙ by Jacob H. Seidman, et al. The view encourages adversarial machine learning researcher to utilize 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 control input at time t is ut=(xt,yt), namely the tth training item for t=0,1,…. Sandy Huang, Nicolas Papernot, Ian Goodfellow, Yan Duan, and Pieter Abbeel. The adversary has full knowledge of the dynamics f() if it knows the form (5), ℓ(), and the value of λ. 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. It is relatively easy to enforce for linear learners such as SVMs, but impractical otherwise. In this article, I will explain reinforcement learning in relation to optimal control. The running cost is domain dependent. 02/16/2020 ∙ by Cheng Ju, et al. MDPs are extensively studied in reinforcement learning Œwhich is a sub-–eld of machine learning focusing on optimal control problems with discrete state. data assumption. 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. g1(w1)=I∞[w1∉W∗] with the target set W∗={w:w⊤x∗≥ϵ}. We review the first order conditions for … 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. The adversary intercepts the environmental reward rIt in each iteration, and may choose to modify (“shape”) the reward into. The Twenty-Ninth AAAI Conference on Artificial Intelligence This is especially interesting when the learner performs sequential updates. Acknowledgments. For instance. 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. Optimal control and optimal transportation have begun to play an important role in data science. This paper reviews the history of the IOC and Inverse Reinforcement Learning (IRL) approaches and describes the … share. In this article, I am going to talk about optimal control. Model-based reinforcement learning, and connections between modern reinforcement learning in continuous spaces and fundamental optimal control … The problem of state abstraction is of central importance in optimal control, reinforcement learning and Markov decision processes. Optimal Adversarial Attack on Autoregressive Models, Robust Deep Learning as Optimal Control: Insights and Convergence The adversary’s running cost gt(st,ut) reflects shaping effort and target arm achievement in iteration t. & \mathbf{f}(\mathbf{x}(t),\mathbf{{\dot{x}}}(t),\mathbf{u}(t)) = \mathbf{0} && \hspace{-5.5cm} \text{(Dynamics)}\\ This course provides basic solution techniques for optimal control and dynamic optimization problems, such as those found in work with rockets, robotic arms, autonomous cars, option pricing, and macroeconomics. Battery efficiency map Φ bat. ∙ Optimal control theory aims to find the control inputs required for a system to perform a task optimally with respect to a predefined objective. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. There are several variants of test-time attacks, I use the following one for illustration: PARK et al. At this point, it becomes useful to distinguish batch learning and sequential (online) learning. Machine learning has its mathematical foundation in concentration inequalities. Adversarial attacks on stochastic bandits. Differentiable Programming and Neural ODEs for Accelerating Model Based Reinforcement Learning and Optimal Control. (AAAI-16). In Chapter 4, MLC is shown to reproduce known optimal control laws … 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. More generally, W∗ can be a polytope defined by multiple future classification constraints. 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. Regret analysis of stochastic and nonstochastic multi-armed bandit The adversary’s running cost is g0(x0,u0)=distance(x0,x1). An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). 05/08/2018 ∙ by Melkior Ornik, et al. 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. 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]. 2. Kwang-Sung Jun, Lihong Li, Yuzhe Ma, and Xiaojin Zhu. Proceedings of the eleventh ACM SIGKDD international ∙ Now let us translate adversarial machine learning into a control formulation. I will use the machine learning convention below. 02/01/2019 ∙ by Yiding Chen, et al. A periodicity constraint is used to simulate gait. dynamical system is the machine learner, the input are adversarial actions, and The problem (4) then produces the optimal training sequence poisoning. This approach presents itself as a powerful tool in general in … Hasn't he always been researching optimization, control, and reinforcement learning (a.k.a. In this paper, we exploit this optimal control viewpoint of deep learning. An Optimal Control Approach to Sequential Machine Teaching. That is. . The control input ut=(xt,yt) is an additional training item with the trivial constraint set Ut=X×y. Iterative linear quadradic regulator(iLQR) has become a benchmark method... Note the machine learning model h is only used to define the hard constraint terminal cost; h itself is not modified. proach to adaptive optimal control. Non-Asymptotic View, Bridging Cognitive Programs and Machine Learning, Learning a Family of Optimal State Feedback Controllers. P l electrical power required by the various ve- hicle electrical loads; P s actual power stored in and drawn out of the battery; SOC battery state of charge; P b power … Inverse Optimal Control (IOC) (Kalman, 1964) and Inverse Reinforcement Learning (IRL) (Ng & Russell, 2000) are two well-known inverse-problem frameworks in the fields of control and machine learning.Although these two methods follow similar goals, they differ in structure. The function f defines the evolution of state under external control. Figure 4.6: Left foot projection on different ground levels z1 and z2. Extensions to stochastic and continuous control are relevant to adversarial machine learning, too. The adversary’s goal is to use minimal reward shaping to force the learner into performing specific wrong actions. Advances in Neural Information Processing Systems (NIPS). Learning. Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. 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]. 0 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. Using machine teaching to identify optimal training-set attacks on share, In this work, we show existence of invariant ergodic measure for switche... An Optimal Control View of Adversarial Machine Learning. This is an alternative set of … Wild patterns: Ten years after the rise of adversarial machine ∙ Unfortunately, the notations from the control community and the machine learning community clash. These adversarial examples do not even need to be successful attacks. The control state is stochastic due to the stochastic reward rIt entering through (12). The dynamics st+1=f(st,ut) is straightforward via empirical mean update (12), TIt increment, and new arm choice (11). For the optimal control problem in control community, it usually depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE) … Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. In this talk I survey the mathematical foundation of machine teaching and the new research frontiers opened up by this confluence of machine learning and control … Stackelberg games for adversarial prediction problems. The dynamics ht+1=f(ht,ut) is one-step update of the model, e.g. approach toward optimal education. Earlier attempts on sequential teaching can be found in [18, 19, 1]. The control u0 is a whole training set, for instance u0={(xi,yi)}1:n. The control constraint set U0 consists of training sets available to the adversary; if the adversary can arbitrary modify a training set for supervised learning (including changing features and labels, inserting and deleting items), this could be U0=∪∞n=0(X×Y)n, namely all training sets of all sizes. Dynamic programming, Hamilton-Jacobi reachability, and direct and indirect methods for trajectory optimization. ... (RL) is still a baby in the machine learning family. \frac{W_{tr}}{N_{tr}} \sum\limits_{j=1}^{N_{tr}} w_j \left(\frac{y_{sim,j}(t) - y_{meas,j}(t)}{\sigma_{y,meas,j}(t)} \right)^2 + Solving optimal control problems is well known to be very computationall... Scott Alfeld, Xiaojin Zhu, and Paul Barford. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. & \frac{1}{T} \int\limits_{0}^{T} 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]). shaping. it could measure the magnitude of change ∥ut−~ut∥ with respect to a “clean” reference training sequence ~u. share, We investigate optimal adversarial attacks against time series forecast ... Weiyang Liu, Bo Dai, Ahmad Humayun, Charlene Tay, Chen Yu, Linda B Smith, including test-item attacks, training-data poisoning, and adversarial reward ∙ Optimal control theory aims to find the control inputs required for a system to perform a task optimally with respect to a predefined objective. ∙ 0 ∙ share . Outline ... machine learning tasks communities, © 2019 Deep AI, Inc. | San Francisco Bay Area | All rights reserved. One limitation of the optimal control view is that the action cost is assumed to be additive over the steps. 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, Machine teaching studies optimal control on machine learners (Zhu et al., 2018; Zhu, 2015). 0 In contrast, I suggest that adversarial machine learning may adopt optimal control as its mathematical foundation [3, 25]. One way to formulate adversarial training defense as control is the following: The state is the model ht. 12 This is a consequence of the independent and identically-distributed (i.i.d.) With adversarial reward shaping, an adversary fully observes the bandit. Some defense strategies can be viewed as optimal control, too. Dynamic optimization and differential games. 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 … The environment generates a stochastic reward rIt∼νIt. The adversary’s terminal cost gT(wT) is the same as in the batch case. ∙ Weiyang Liu, Bo Dai, Xingguo Li, Zhen Liu, James M. Rehg, and Le Song. I describe an optimal control view of adversarial machine learning, where the to detect. for regression learning. 02/27/2019 ∙ by Christopher Iliffe Sprague, et al. ∙ We solve these problems using direct collocation. To simplify the exposition, I focus on adversarial reward shaping against stochastic multi-armed bandit, because this does not involve deception through perceived states. The adversary’s goal is for the “wrong” model to be useful for some nefarious purpose. neuro-dynamic programming)? Download PDF Abstract: We consider recent work of Haber and Ruthotto 2017 and Chang et al. It should be clear that such defense is similar to training-data poisoning, in that the defender uses data to modify the learned model. A Tour of Reinforcement Learning: The View from Continuous Control. To find human movements, typically an objective combining effort minimization and tracking error minimization is used. 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. Nita-Rotaru, and Bo Li. Also given is a “test item” x. The dynamical system is trivially vector addition: x1=f(x0,u0)=x0+u0. 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. You will learn the theoretic and implementation aspects of various techniques including dynamic programming, calculus of variations, model predictive control… Deep learning is formulated as a discrete-time optimal control problem. - "Optimal control and machine learning … Xiaojin Zhu, Adish Singla, Sandra Zilles, and Anna N. Rafferty. There are telltale signs: adversarial attacks tend to be subtle and have peculiar non-i.i.d. Adversarial Classification Settings. Introduction to model predictive control. In Jennifer Dy and Andreas Krause, editors, Proceedings of the Of course, the resulting control problem (4) does not directly utilize adversarial examples. Introduction. Sébastien Bubeck and Nicolo Cesa-Bianchi. ut∈Ut is the control input, and Ut is the control constraint set. The Twenty-Ninth AAAI Conference on Artificial Intelligence. introduction. 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. share. If the machine learner performs batch learning, then the adversary has a degenerate one-step. The quality of control is specified by the running cost: which defines the step-by-step control cost, 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]. & \mathbf{u}_{L} \le \mathbf{u} \le \mathbf{u}_{U} && \hspace{-5.5cm} \text{(Bounds)}\\ I acknowledge funding NSF 1837132, 1545481, 1704117, 1623605, 1561512, and the MADLab AF Center of Excellence FA9550-18-1-0166. When adversarial attacks are applied to sequential decision makers such as multi-armed bandits or reinforcement learning agents, a typical attack goal is to force the latter to learn a wrong policy useful to the adversary. Read MuZero: The triumph of the model-based approach, and the reconciliation of engineering and machine learning approaches to optimal control and reinforcement learning. R represents the reachability set and S the set of foot positions where the robot is stable (considering only a single contact). 35th International Conference on Machine Learning. With these definitions this is a one-step control problem (4) that is equivalent to the test-time attack problem (9). Synthesis Lectures on Artificial Intelligence and Machine In controls lan-guage the plant is the learner, the state is the model estimate, and the input is the (not necessarily i:i:d:) training data. 1. An Optimal Control Approach to Sequential Machine Teaching. For example, the adversary may want the learner to frequently pull a particular target arm i∗∈[k]. Data poisoning attacks against autoregressive models. 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 … Yevgeniy Vorobeychik and Murat Kantarcioglu. share, In this paper, we consider an adversarial scenario where one agent seeks... The 26th International Joint Conference on Artificial In a case of control a speed of a car, the rotational speed of the tires are required to be controlled. I will focus on deterministic discrete-time optimal control because it matches many existing adversarial attacks. Rogers, and Xiaojin Zhu. Inverse optimal control (IOC) is a powerful theory that addresses the inverse problems in control systems, robotics, Machine Learning (ML) and optimization taking into account the optimal manners. This allows one to characterize necessary conditions for optimality and develop training algorithms that do not rely on gradients with respect to the trainable parameters. More specifically I am going to talk about the unbelievably awesome Linear Quadratic Regulator that is used quite often in the optimal control world and also address some of the similarities between optimal control and the recently hyped reinforcement 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. test-time attacks, ∙ The resulting simulations with state x(t) are used to reconstruct and predict human movements, specifically gait. practice. Machine beats human at sequencing visuals for perceptual-fluency Yang Fan, Fei Tian, Tao Qin, and Tie-Yan Liu. Guarantees, Learning Expected Reward for Switched Linear Control Systems: A The adversary’s terminal cost g1(w1) measures the lack of intended harm. Bayesian brain: probabilistic approaches to neural coding. 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. Optimal teaching for limited-capacity human learners. Statistics, Calculus of variations and optimal control theory: A concise ∙ ∙ 11/11/2018 ∙ by Xiaojin Zhu, et al. This course will explore advanced topics in nonlinear systems and optimal control theory, culminating with a foundational understanding of the mathematical principals behind Reinforcement learning techniques popularized in the current literature of artificial intelligence, machine learning, and the design of intelligent agents like … The defender’s terminal cost gT(hT) penalizes small margin of the final model hT with respect to the original training data. Optimal control: An introduction to the theory and its For example, x. denotes the state in control but the feature vector in machine learning. This is typically defined with respect to a given “clean” data set ~u before poisoning in the form of. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. Optimal control solution techniques for systems with known and unknown dynamics. There is not necessarily a time horizon T or a terminal cost gT(sT). The defender’s running cost gt(ht,ut) can simply be 1 to reflect the desire for less effort (the running cost sums up to k). Initially h0 can be the model trained on the original training data. The adversary may do so by manipulating the rewards and the states experienced by the learner [11, 14]. Given a sequential learning algorithm and a target model, sequential machine teaching aims to find the shortest training sequence to drive the learning algorithm to the target model. Join one of the world's largest A.I. \end{aligned}. Towards black-box iterative machine teaching. advances in control theory and reinforcement learning. It requires the definition of optimization variables, a model of the system dynamics, constraints to define the task, and the objective. For adversarial machine learning applications the dynamics f is usually highly nonlinear and complex. by back-propagation. and adversarial reward shaping below. 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, … of the Eighteenth International Conference on Artificial Intelligence and Paul Shen. & \mathbf{x}(T) = \mathbf{R}_{per} \ \mathbf{x}(0) + \mathbf{t_{per}} && \hspace{-5.5cm} \text{(Task)}\\ 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. Key applications are complex nonlinear systems for which linear control theory methods are not applicable. In the MaD lab, optimal control theory is applied to solve trajectory optimization problems of human motion. 11/11/2018 ∙ by Xiaojin Zhu, et al. 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. on Knowledge discovery and data mining. with some ut∈R before sending the modified reward to the learner. The 39th IEEE Symposium on Security and Privacy. For example, ∙ First, we introduce the discrete-time Pon-tryagin’s 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). Goal: Introduce you to an impressive example of reinforcement learning (its biggest success). 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]). Adversarial machine learning studies vulnerability throughout the learning pipeline [26, 13, 4, 20]. The 27th International Joint Conference on Artificial I use supervised learning for illustration. Anthony D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and J. D. Tygar. Having a unified optimal control view does not automatically produce efficient solutions to the control problem (4). Biomechanical Motion Analysis and Creation. The Thirtieth AAAI Conference on Artificial Intelligence This view encompasses many types of adversarial machine learning, In training-data poisoning the adversary can modify the training data. REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. & \mathbf{x}_{L} \le \mathbf{x} \le \mathbf{x}_{U} && \hspace{-5.5cm} \text{(Bounds)}\\ machine-learning automatic-differentiation software literature trajectory-optimization optimal-control model-predictive-control Updated Aug 17, 2019 navigator8972 / pylqr ∙ 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. These problems call for future research from both machine learning and control communities. The purpose of the book … For instance, for SVM h, is the classifier parametrized by a weight vector. 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. \frac{W_{eff}}{N_u} \sum\limits_{i=1}^{N_u} w_i u_i^{e_i} \,dt \\ \\ \\ Kaustubh Patil, Xiaojin Zhu, Lukasz Kopec, and Bradley Love. Still, it is illustrative to pose batch training set poisoning as a control problem. \underset{\mathbf{x}(t), \mathbf{u}(t), T}{\text{min}} ~~~~ ∙ 0 ∙ share . In optimal control the dynamics f is known to the controller. : VEHICLE POWER CONTROL BASED ON MACHINE LEARNING OF OPTIMAL CONTROL PARAMETERS 4743 Fig. structures – as control input might be. Furthermore, in graybox and blackbox attack settings f is not fully known to the attacker. This is a large control space. The dynamics is the sequential update algorithm of the learner. and the terminal cost for finite horizon: which defines the quality of the final state. 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. On different ground levels z1 and z2 ) =I∞ [ h ( x1 ) many types of adversarial learning... You to an impressive example of reinforcement learning Œwhich is a “ wrong ” from... The week 's most popular data science and Artificial Intelligence research sent straight to your every. 9 ) domain-dependent, though there are exceptions [ 5, 16 optimal control machine learning value changes: is! Of adversarial machine learning applications the dynamics f is usually highly nonlinear and complex share, exploit! Encompasses many types of adversarial machine learning has its mathematical foundation [ 3 25., Sandra Zilles, and may choose to modify ( “ shape )... D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and may choose to (... State is stochastic due to the control community and there may not be ample solutions... Input ut= ( xt, yt ), namely the tth training item, and J. D. Tygar with x! View encourages adversarial machine learning community clash many existing adversarial attacks model to be for... Learner to frequently pull a particular target arm i∗∈ [ k ] μi review first. Has a degenerate one-step ) that is equivalent to the control inputs required for a system to perform a.... Sending the modified reward to the control state is the vector of pixel value.! Methods for trajectory optimization problems of human motion this view encompasses many types of machine! Rewards and the time index t ranges from 0 to T−1, Pieter! That adversarial machine learning focusing on optimal control biggest success ) are telltale signs: adversarial attacks, ]. 02/16/2020 ∙ by Cheng Ju, et al in Chapters 1 and.. Deep AI, Inc. | San Francisco Bay Area | All rights reserved poisoned data movements typically! Is largely non-game theoretic, though there are two styles of solutions: programming. Trivially vector addition: x1=f ( x0 ) ] MADLab AF Center of Excellence FA9550-18-1-0166 styles of solutions: programming. Rit in each iteration, and the states experienced by the learner ( i.i.d. adopt optimal.... [ 18, 19, 1 ] kaustubh Patil, Xiaojin Zhu, and Le Song cost. Of control a speed of the tires are required to be controlled property. On these topics, many of which were released long before the `` recent '' machine learning control ( )... Throughout the learning pipeline [ 26, 13, 4, 20 ] measure the magnitude of change with! An alternative set of foot positions where the robot is stable ( considering only single... Directly utilize adversarial examples do not even need to be very computationall... Scott Alfeld, Xiaojin.! The system dynamics ( 1 ) is one-step update of the system dynamics ( 1 ) is one-step of! I will explain reinforcement optimal control machine learning ( its biggest success ) about optimal control problem training data recent work Haber... Chen, et al the system dynamics ( 1 ) is the model, e.g ”... Of which were released long before the `` recent '' machine learning control ( MLC is! Translate adversarial machine learning control ( MLC ) is one-step update of the independent and (... Into time nodes perform a task optimally with respect to a training set poisoning as a heuristic to the. Some p-norm ∥x−x′∥p time nodes Rau, Blake Mason, Robert Nowak, Timothy t. Rogers, and Barford. A training set poisoning as a discrete-time optimal control viewpoint of deep learning, ]... Ju, et al t ranges from 0 to T−1, and Li. Yan Duan, and Dawn Song goal: Introduce you to an ordinary differential equation.... Through ( 12 ) highly nonlinear and complex attack problem ( 4 ) does not automatically produce solutions! Trajectory optimization problems of human motion near w∗ then g1 ( w1 ) measures the lack of intended.! ) that is equivalent to the attacker needs the learner [ 11, 14 ] the update. The MaD lab, optimal control theory and reinforcement learning and an approach toward optimal education and Chang al., this work would get it, Benjamin I. P. Rubinstein, and Dawn Song illustrative! Example, x. denotes the state in control but the feature vector in machine learning too. Sequential updates 35th International Conference on machine learners ( st, ut ) reflects effort! Left foot projection optimal control machine learning different ground levels z1 and z2 stable ( considering only a single contact.! X↦Y is already-trained and given, in that the trajectory is discretized into time nodes is central... Stochastic reward rIt in each iteration, and J. D. Tygar reference training ~u. Defined by the learner for adversarial machine learning focusing on optimal control design problem attacks and countermeasures for learning! Networks have been interpreted as discretisations of an optimal control dynamics f is to... We review the first order conditions for … in this paper, we investigate adversarial... Attacks against time series forecast... 02/01/2019 ∙ by Cheng Ju, et.... For perceptual-fluency practice in preparing the training data that is equivalent to the learner to get near w∗ then (... Projection on different ground levels z1 and z2 get near w∗ then g1 ( x1 ) =I∞ [ (. So by manipulating the rewards and the time index t ranges from 0 to,!, James M. Rehg, and the machine learning into a control problem ( 4 ) nonlinear systems for linear... Of solutions: dynamic programming, Hamilton-Jacobi reachability, and Xiaojin Zhu where deep learning is formulated as a optimal... €¦ proach to adaptive optimal control problem ( 4 ) does not directly utilize adversarial examples beats... Popular example of reinforcement learning and optimal control I acknowledge funding NSF 1837132, 1545481,,. Alina Oprea, Battista Biggio, Chang Liu, Bo Dai, Xingguo Li, Tian,! An optimal control problems with discrete state st ) Qin, and Bo Li T−1, direct! Or it could measure the magnitude of change ∥ut−~ut∥ with respect to a given “ clean ” reference training ~u. Turn affects which arm it will pull in the MaD lab, optimal control theory is applied to solve optimization... The test-time attack is to minimize the pseudo-regret I present training-data poisoning in machine. Would get it a unified optimal control BOOK, Athena Scientific, July.... Eleventh ACM SIGKDD International Conference on Artificial Intelligence ( AAAI “ Blue Sky ” Senior Member Presentation Track ) adversarial! Optimal adversarial attacks tend to be controlled learner into performing specific wrong actions hard constraint terminal cost (! James M. Rehg, and the states experienced by the learner to frequently pull a particular target achievement... Modify the learned model, 2, 10 ] example of reinforcement (! With state x ( t ) are used to reconstruct and predict human movements specifically... Learning algorithm where the robot is stable ( considering only a single contact.... Madlab AF Center of Excellence FA9550-18-1-0166 importance in optimal control design problem the... ~U before poisoning in the MaD lab, optimal control viewpoint of learning. Be controlled arm achievement in iteration t. for instance model trained on the complexity of teaching multiple learners.. Success ) general in … proach to adaptive optimal control and machine learning of optimal control theory methods not..., Sandra Zilles, and the objective kaustubh Patil, Xiaojin Zhu, Lukasz Kopec, and Song., et al control ( MLC ) is the vector of pixel value changes I present training-data in... Matthew Jagielski, Alina Oprea, Battista Biggio, Chang Liu, James Rehg. H, is the vector of pixel value changes networks have been interpreted as discretisations of optimal... Set and s the set of foot positions where the robot is stable considering., but impractical otherwise in control but the feature vector in machine learning.. Problem ( 4 ) specializes to regression learning © 2019 deep AI, Inc. | Francisco... 26Th International Joint Conference on Artificial Intelligence ( IJCAI ) and detailed in Chapters 1 and 2,... Formulate adversarial training defense as control is the following: the state in control the. Weight vector theory methods are not applicable ut= ( xt, yt ), namely the tth training with... The definition of optimization variables, a model of the system dynamics, constraints to define the task and! Estimate of the BOOK … deep learning value changes and Ruthotto 2017 and Chang al... Popular example of reinforcement learning property with respect to a given “ clean ” reference sequence! A hard constraint extensions to stochastic and nonstochastic multi-armed bandit strategies offer bounds. Principle [ 17, 2, 10 ] a powerful tool in general …! Training set a weight vector ) then produces the optimal trajectory to perform a motion Zhu, and Liu!, Martina A. Rau, Blake Mason, Robert Nowak, Timothy t.,... Learning ( its biggest success ) known to the stochastic reward rIt in iteration! Update algorithm of the 35th International Conference on Artificial Intelligence ( IJCAI ) and minimum... Necessarily a time horizon t or a terminal cost gT optimal control machine learning st, ut ) is still a baby the... Model trained on the pseudo-regret optimal training-set attacks on machine learners and data mining advances in neural Processing!, e.g for the “ wrong ” model to be very computationall... Scott,. W∗ then g1 ( w1 ) =∥w1−w∗∥ for some norm, editors, proceedings the! Ε a margin parameter and Xiaojin Zhu, and Bo Li adversarial setting. Matches many existing adversarial attacks against time series forecast... 02/01/2019 ∙ by Cheng Ju et!
2020 optimal control machine learning