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. Read MuZero: The triumph of the model-based approach, and the reconciliation of engineering and machine learning approaches to optimal control and reinforcement learning. share, While great advances are made in pattern recognition and machine learnin... ∙ Figure 4.6: Left foot projection on different ground levels z1 and z2. Bayesian brain: probabilistic approaches to neural coding. 35th International Conference on Machine Learning. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. 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 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. Kaustubh Patil, Xiaojin Zhu, Lukasz Kopec, and Bradley Love. 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 ∙ I describe an optimal control view of adversarial machine learning, where the Paul Shen. 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. and adversarial reward shaping below. Earlier attempts on sequential teaching can be found in [18, 19, 1]. The adversary’s goal is for the “wrong” model to be useful for some nefarious purpose. Yevgeniy Vorobeychik and Murat Kantarcioglu. 2. 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. Nita-Rotaru, and Bo Li. In this article, I will explain reinforcement learning in relation to optimal control. Wild patterns: Ten years after the rise of adversarial machine To simplify the exposition, I focus on adversarial reward shaping against stochastic multi-armed bandit, because this does not involve deception through perceived states. Hanjun Dai, Hui Li, Tian Tian, Xin Huang, Lin Wang, Jun Zhu, and Le Song. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. communities, © 2019 Deep AI, Inc. | San Francisco Bay Area | All rights reserved. Thus, it is possible and promising to introduce the basic QL framework for addressing the optimal control design problem. 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 … Let (x,y) be any training item, and ϵ a margin parameter. 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. International Conference on Machine Learning. Machine teaching: an inverse problem to machine learning and an 0 The adversary’s goal is to use minimal reward shaping to force the learner into performing specific wrong actions. Stackelberg games for adversarial prediction problems. Test-time attack differs from training-data poisoning in that a machine learning model h:X↦Y is already-trained and given. Also given is a “test item” x. 11/11/2018 ∙ by Xiaojin Zhu, et al. Statistics, Calculus of variations and optimal control theory: A concise 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. The dynamics st+1=f(st,ut) is straightforward via empirical mean update (12), TIt increment, and new arm choice (11). Acknowledgments. 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 … Differentiable Programming and Neural ODEs for Accelerating Model Based Reinforcement Learning and Optimal Control. They affect the complexity in finding an optimal control. 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. The view encourages adversarial machine learning researcher to utilize Sandy Huang, Nicolas Papernot, Ian Goodfellow, Yan Duan, and Pieter Abbeel. Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning.. Reinforcement learning differs from supervised learning … Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. 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. Extensions to stochastic and continuous control are relevant to adversarial machine learning, too. 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. Proceedings of the eleventh ACM SIGKDD international The system dynamics (1) is defined by the learner’s learning algorithm. Introduction to model predictive control. PARK et al. Intelligence (IJCAI). \underset{\mathbf{x}(t), \mathbf{u}(t), T}{\text{min}} ~~~~ 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. ∙ 0 ∙ share . There are two styles of solutions: dynamic programming and Pontryagin minimum principle [17, 2, 10]. 06/15/2020 ∙ by Muhammad Abdullah Naeem, et al. 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, … 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 … 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. Biomechanical Motion Analysis and Creation. This approach presents itself as a powerful tool in general in … with some ut∈R before sending the modified reward to the learner. \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 + If AI had a Nobel Prize, this work would get it. 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]. The 26th International Joint Conference on Artificial It is relatively easy to enforce for linear learners such as SVMs, but impractical otherwise. Battery efficiency map Φ bat. by back-propagation. I will use the machine learning convention below. The learner’s goal is to minimize the pseudo-regret Tμmax−E∑Tt=1μIt where μi=Eνi and μmax=maxi∈[k]μi. An Optimal Control Approach to Sequential Machine Teaching. Learning. 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 … Xiaojin Zhu, Adish Singla, Sandra Zilles, and Anna N. Rafferty. applications. 0 ∙ 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. . ∙ 02/01/2019 ∙ by Yiding Chen, et al. 10/15/2018 ∙ by Laurent Lessard, et al. \frac{W_{eff}}{N_u} \sum\limits_{i=1}^{N_u} w_i u_i^{e_i} \,dt \\ \\ \\ 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. 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]). advances in control theory and reinforcement learning. Join one of the world's largest A.I. share. Optimal control and optimal transportation have begun to play an important role in data science. Yang Fan, Fei Tian, Tao Qin, and Tie-Yan Liu. 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. At this point, it becomes useful to distinguish batch learning and sequential (online) learning. In Guy Lebanon and S. V. N. Vishwanathan, editors, Proceedings it could measure the magnitude of change ∥ut−~ut∥ with respect to a “clean” reference training sequence ~u. The controller wants to use the least number of training items|a concept known as the 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 … machine-learning automatic-differentiation software literature trajectory-optimization optimal-control model-predictive-control Updated Aug 17, 2019 navigator8972 / pylqr There is not necessarily a time horizon T or a terminal cost gT(sT). Anthony D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and J. D. Tygar. This is an alternative set of … In particular, we introduce the discrete-time method of successive … The problem of state abstraction is of central importance in optimal control, reinforcement learning and Markov decision processes. Machine learning has its mathematical foundation in concentration inequalities. shaping. 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. The running cost is domain dependent. The adversary has full knowledge of the dynamics f() if it knows the form (5), ℓ(), and the value of λ. Furthermore, in graybox and blackbox attack settings f is not fully known to the attacker. One limitation of the optimal control view is that the action cost is assumed to be additive over the steps. share, In this work, we show existence of invariant ergodic measure for switche... Proceedings of the 17th ACM SIGKDD international conference The adversary’s running cost g0(u0) measures the poisoning effort in preparing the training set u0. For example, x. denotes the state in control but the feature vector in machine learning. The control input at time t is ut=(xt,yt), namely the tth training item for t=0,1,…. ∙ James M Rehg, and Le Song. The control input ut=(xt,yt) is an additional training item with the trivial constraint set Ut=X×y. You will learn the theoretic and implementation aspects of various techniques including dynamic programming, calculus of variations, model predictive control… ∙ The dynamics is the sequential update algorithm of the learner. The 27th International Joint Conference on Artificial Rogers, and Xiaojin Zhu. With these definitions, the adversary’s one-step control problem (4) specializes to. In this paper, we exploit this optimal control viewpoint of deep learning. 0 This is typically defined with respect to a given “clean” data set ~u before poisoning in the form of. Machine beats human at sequencing visuals for perceptual-fluency The terminal cost is also domain dependent. For example, the distance function may count the number of modified training items; or sum up the Euclidean distance of changes in feature vectors. If the machine learner performs batch learning, then the adversary has a degenerate one-step. In Chapter 4, MLC is shown to reproduce known optimal control laws … Outline ... machine learning tasks Adversarial attack on graph structured data. Goal: Introduce you to an impressive example of reinforcement learning (its biggest success). Adversarial attacks on stochastic bandits. There are several variants of test-time attacks, I use the following one for illustration: Deep learning is formulated as a discrete-time optimal control problem. g1(w1)=I∞[w1∉W∗] with the target set W∗={w:w⊤x∗≥ϵ}. (AAAI “Blue Sky” Senior Member Presentation Track). In this article, I am going to talk about optimal control. 05/08/2018 ∙ by Melkior Ornik, et al. There are a number of potential benefits in taking the optimal control view: It offers a unified conceptual framework for adversarial machine learning; The optimal control literature provides efficient solutions when the dynamics f is known and one can take the continuous limit to solve the differential equations [15]; Reinforcement learning, either model-based with coarse system identification or model-free policy iteration, allows approximate optimal control when f is unknown, as long as the adversary can probe the dynamics [9, 8]; A generic defense strategy may be to limit the controllability the adversary has over the learner. This paper reviews the history of the IOC and Inverse Reinforcement Learning (IRL) approaches and describes the … conference on Knowledge discovery in data mining. The adversary’s terminal cost is g1(x1)=I∞[h(x1)=h(x0)]. ∙ The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. Adversarial attacks on neural network policies. The resulting simulations with state x(t) are used to reconstruct and predict human movements, specifically gait. control problem. 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 … However we don't control rotational speed of tires but only handle with the accelerator and brake … 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. 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 … One-step control has not been the focus of the control community and there may not be ample algorithmic solutions to borrow from. 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]. Advances in Neural Information Processing Systems (NIPS). Optimal control What is control problem? I will focus on deterministic discrete-time optimal control because it matches many existing adversarial attacks. The machine learner then trains a “wrong” model from the poisoned data. including test-item attacks, training-data poisoning, and adversarial reward 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. & \mathbf{f}(\mathbf{x}(t),\mathbf{{\dot{x}}}(t),\mathbf{u}(t)) = \mathbf{0} && \hspace{-5.5cm} \text{(Dynamics)}\\ The function f defines the evolution of state under external control. Adversarial Classification Settings. A Tour of Reinforcement Learning: The View from Continuous Control. It requires the definition of optimization variables, a model of the system dynamics, constraints to define the task, and the objective. 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, The adversarial learning setting is largely non-game theoretic, though there are exceptions [5, 16]. 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]. For example, The dynamics ht+1=f(ht,ut) is one-step update of the model, e.g. to detect. Optimal control solution techniques for systems with known and unknown dynamics. ∙ This is a large control space. ∙ That is. The adversary may do so by manipulating the rewards and the states experienced by the learner [11, 14]. 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. ... (RL) is still a baby in the machine learning family. For example, the adversary may want the learner to frequently pull a particular target arm i∗∈[k]. ∙ 0 ∙ share . Synthesis Lectures on Artificial Intelligence and Machine With adversarial reward shaping, an adversary fully observes the bandit. Here Iy[z]=y if z is true and 0 otherwise, which acts as a hard constraint. In optimal control the dynamics f is known to the controller. For instance. Matthew Jagielski, Alina Oprea, Battista Biggio, Chang Liu, Cristina The adversary’s terminal cost gT(wT) is the same as in the batch case. & \mathbf{u}_{L} \le \mathbf{u} \le \mathbf{u}_{U} && \hspace{-5.5cm} \text{(Bounds)}\\ More generally, W∗ can be a polytope defined by multiple future classification constraints. 05/01/2020 ∙ by Jacob H. Seidman, et al. I acknowledge funding NSF 1837132, 1545481, 1704117, 1623605, 1561512, and the MADLab AF Center of Excellence FA9550-18-1-0166. \end{aligned}. Adversarial training can be viewed as a heuristic to approximate the uncountable constraint (. I use supervised learning for illustration. 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. This is especially interesting when the learner performs sequential updates. Foundations and Trends in Machine 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. Machine teaching studies optimal control on machine learners (Zhu et al., 2018; Zhu, 2015). Non-Asymptotic View, Bridging Cognitive Programs and Machine Learning, Learning a Family of Optimal State Feedback Controllers. 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. These adversarial examples do not even need to be successful attacks. Optimal control theory aims to find the control inputs required for a system to perform a task optimally with respect to a predefined objective. the optimal control problem in control community. As examples, I present Introduction. 0 If the adversary wants to ensure that a specific future item x∗ is classified ϵ-confidently as positive, it can use 0 1. 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). : VEHICLE POWER CONTROL BASED ON MACHINE LEARNING OF OPTIMAL CONTROL PARAMETERS 4743 Fig. Of course, the resulting control problem (4) does not directly utilize adversarial examples. If the adversary only needs the learner to get near w∗ then g1(w1)=∥w1−w∗∥ for some norm. For the optimal control problem in control community, it usually depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE) … He's published multiple books on these topics, many of which were released long before the "recent" machine learning revolution. In Chapter 3, methods of linear control theory are reviewed. The problem can be formulated as follows: \begin{aligned} 02/16/2020 ∙ by Cheng Ju, et al. Some defense strategies can be viewed as optimal control, too. No learner left behind: On the complexity of teaching multiple The environment generates a stochastic reward rIt∼νIt. These problems call for future research from both machine learning and control communities. Stochastic multi-armed bandit strategies offer upper bounds on the pseudo-regret. share. Now let us translate adversarial machine learning into a control formulation. 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. An Optimal Control Approach to Sequential Machine Teaching. neuro-dynamic programming)? To find human movements, typically an objective combining effort minimization and tracking error minimization is used. data assumption. ∙ for regression learning. ut∈Ut is the control input, and Ut is the control constraint set. 11/11/2018 ∙ by Xiaojin Zhu, et al. (AAAI-16). ∙ In the MaD lab, optimal control theory is applied to solve trajectory optimization problems of human motion. problems. Ayon Sen, Purav Patel, Martina A. Rau, Blake Mason, Robert Nowak, Timothy T. The 39th IEEE Symposium on Security and Privacy. Download PDF Abstract: We consider recent work of Haber and Ruthotto 2017 and Chang et al. In training-data poisoning the adversary can modify the training data. The adversary’s terminal cost g1(w1) measures the lack of intended harm. The Twenty-Ninth AAAI Conference on Artificial Intelligence Adversarial machine learning studies vulnerability throughout the learning pipeline [26, 13, 4, 20]. 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 … The quality of control is specified by the running cost: which defines the step-by-step control cost, We solve these problems using direct collocation. dynamical system is the machine learner, the input are adversarial actions, and 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} } Or it could be the constant 1 which reflects the desire to have a short control sequence. share, We investigate optimal adversarial attacks against time series forecast ... Iterative linear quadradic regulator(iLQR) has become a benchmark method... Towards black-box iterative machine teaching. An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). of the Eighteenth International Conference on Artificial Intelligence and The IOC aims to … introduction. MDPs are extensively studied in reinforcement learning Œwhich is a sub-–eld of machine learning focusing on optimal control problems with discrete state. Solving optimal control problems is well known to be very computationall... Scott Alfeld, Xiaojin Zhu, and Paul Barford. For adversarial machine learning applications the dynamics f is usually highly nonlinear and complex. Scalable Optimization of Randomized Operational Decisions in There are telltale signs: adversarial attacks tend to be subtle and have peculiar non-i.i.d. 12 02/27/2019 ∙ by Christopher Iliffe Sprague, et al. Key applications are complex nonlinear systems for which linear control theory methods are not applicable. We summarize here an emerging deeper understanding of these Optimal Adversarial Attack on Autoregressive Models, Robust Deep Learning as Optimal Control: Insights and Convergence With these definitions this is a one-step control problem (4) that is equivalent to the test-time attack problem (9). It should be clear that such defense is similar to training-data poisoning, in that the defender uses data to modify the learned model. 0 In a case of control a speed of a car, the rotational speed of the tires are required to be controlled. The Twenty-Ninth AAAI Conference on Artificial Intelligence. 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. 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]. The adversary seeks to minimally perturb x into x′ such that the machine learning model classifies x and x′ differently. 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 intercepts the environmental reward rIt in each iteration, and may choose to modify (“shape”) the reward into. & \frac{1}{T} \int\limits_{0}^{T} \text{subject to} ~~ ∙ share, Solving optimal control problems is well known to be very computationall... We use the fact that humans minimize energy expenditure in movements to find the optimal trajectory to perform a motion. learners simultaneously. 02/16/2018 ∙ by Amir Rosenfeld, et al. ∙ learning. Note the machine learning model h is only used to define the hard constraint terminal cost; h itself is not modified. training-data poisoning, machine learners. The adversary’s running cost gt(st,ut) reflects shaping effort and target arm achievement in iteration t. In Jennifer Dy and Andreas Krause, editors, Proceedings of the test-time attacks, Optimal control: An introduction to the theory and its Hasn't he always been researching optimization, control, and reinforcement learning (a.k.a. share, In this paper, we consider an adversarial scenario where one agent seeks... 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. the control costs are defined by the adversary's goals to do harm and be hard 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. 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. 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. Optimal teaching for limited-capacity human learners. ∙ The adversary’s running cost is g0(x0,u0)=distance(x0,x1). Initially h0 can be the model trained on the original training data. Dynamic programming, Hamilton-Jacobi reachability, and direct and indirect methods for trajectory optimization. ∙ proach to adaptive optimal control. Weiyang Liu, Bo Dai, Ahmad Humayun, Charlene Tay, Chen Yu, Linda B Smith, REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. This view encompasses many types of adversarial machine learning, The dynamical system is trivially vector addition: x1=f(x0,u0)=x0+u0. The adversary’s control input u0 is the vector of pixel value changes. One way to formulate adversarial training defense as control is the following: The state is the model ht. Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. The problem (4) then produces the optimal training sequence poisoning. Weiyang Liu, Bo Dai, Xingguo Li, Zhen Liu, James M. Rehg, and Le Song. Regret analysis of stochastic and nonstochastic multi-armed bandit 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). The Thirtieth AAAI Conference on Artificial Intelligence This means that the trajectory is discretized into time nodes. Having a unified optimal control view does not automatically produce efficient solutions to the control problem (4). A periodicity constraint is used to simulate gait. The control state is stochastic due to the stochastic reward rIt entering through (12). Using machine teaching to identify optimal training-set attacks on 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 time index t ranges from 0 to T−1, and the time horizon T can be finite or infinite. Unfortunately, the notations from the control community and the machine learning community clash. Kwang-Sung Jun, Lihong Li, Yuzhe Ma, and Xiaojin Zhu. 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 … 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. 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]). The learner updates its estimate of the pulled arm: which in turn affects which arm it will pull in the next iteration. & \mathbf{u}(T) = \mathbf{u}(0) && \hspace{-5.5cm} \text{(Task)}\\ 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]. on Knowledge discovery and data mining. Manipulating machine learning: Poisoning attacks and countermeasures and the terminal cost for finite horizon: which defines the quality of the final state. The purpose of the book … Model-based reinforcement learning, and connections between modern reinforcement learning in continuous spaces and fundamental optimal control … 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. R represents the reachability set and S the set of foot positions where the robot is stable (considering only a single contact). & \mathbf{x}_{L} \le \mathbf{x} \le \mathbf{x}_{U} && \hspace{-5.5cm} \text{(Bounds)}\\ For instance, for SVM h, is the classifier parametrized by a weight vector. 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. & \mathbf{x}(T) = \mathbf{R}_{per} \ \mathbf{x}(0) + \mathbf{t_{per}} && \hspace{-5.5cm} \text{(Task)}\\ The defender’s terminal cost gT(hT) penalizes small margin of the final model hT with respect to the original training data. practice. 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. Still, it is illustrative to pose batch training set poisoning as a control problem. Guarantees, Learning Expected Reward for Switched Linear Control Systems: A An Optimal Control View of Adversarial Machine Learning. share, The fragility of deep neural networks to adversarially-chosen inputs has... - "Optimal control and machine learning … Intelligence (IJCAI). ∙ Sébastien Bubeck and Nicolo Cesa-Bianchi. structures – as control input might be. This is a consequence of the independent and identically-distributed (i.i.d.) We review the first order conditions for … In contrast, I suggest that adversarial machine learning may adopt optimal control as its mathematical foundation [3, 25]. Data poisoning attacks against autoregressive models. It requires the definition of optimization variables, a model of the system dynamics, constraints to define the task, and the objective. For example: If the adversary must force the learner into exactly arriving at some target model w∗, then g1(w1)=I∞[w1≠w∗]. approach toward optimal education. Dynamic optimization and differential games. 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 adversary’s running cost gt then measures the effort in performing the action at step t.