approach toward optimal education. The adversary’s goal is for the “wrong” model to be useful for some nefarious purpose. dynamical system is the machine learner, the input are adversarial actions, and For example, the adversary may want the learner to frequently pull a particular target arm i∗∈[k]. Introduction to model predictive control. 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. A Tour of Reinforcement Learning: The View from Continuous Control. The control input ut=(xt,yt) is an additional training item with the trivial constraint set Ut=X×y. machine-learning automatic-differentiation software literature trajectory-optimization optimal-control model-predictive-control Updated Aug 17, 2019 navigator8972 / pylqr Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. The adversarial learning setting is largely non-game theoretic, though there are exceptions [5, 16]. Biomechanical Motion Analysis and Creation. 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. 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]). 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. including test-item attacks, training-data poisoning, and adversarial reward The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. Nita-Rotaru, and Bo Li. 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 … Weiyang Liu, Bo Dai, Ahmad Humayun, Charlene Tay, Chen Yu, Linda B Smith, At this point, it becomes useful to distinguish batch learning and sequential (online) learning. structures – as control input might be. ∙ For example: If the adversary must force the learner into exactly arriving at some target model w∗, then g1(w1)=I∞[w1≠w∗]. The 39th IEEE Symposium on Security and Privacy. Dynamic programming, Hamilton-Jacobi reachability, and direct and indirect methods for trajectory optimization. The 26th International Joint Conference on Artificial Paul Shen. The adversary’s goal is to use minimal reward shaping to force the learner into performing specific wrong actions. Acknowledgments. \text{subject to} ~~ share. The dynamics ht+1=f(ht,ut) is one-step update of the model, e.g. Weiyang Liu, Bo Dai, Xingguo Li, Zhen Liu, James M. Rehg, and Le Song. ... (RL) is still a baby in the machine learning family. 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. You will learn the theoretic and implementation aspects of various techniques including dynamic programming, calculus of variations, model predictive control… introduction. 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. 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 … James M Rehg, and Le Song. Machine teaching studies optimal control on machine learners (Zhu et al., 2018; Zhu, 2015). If the adversary only needs the learner to get near w∗ then g1(w1)=∥w1−w∗∥ for some norm. MDPs are extensively studied in reinforcement learning Œwhich is a sub-–eld of machine learning focusing on optimal control problems with discrete state. g1(w1)=I∞[w1∉W∗] with the target set W∗={w:w⊤x∗≥ϵ}. Stackelberg games for adversarial prediction problems. 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. Advances in Neural Information Processing Systems (NIPS). 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. 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. Wild patterns: Ten years after the rise of adversarial machine It requires the definition of optimization variables, a model of the system dynamics, constraints to define the task, and the objective. \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 + Synthesis Lectures on Artificial Intelligence and Machine Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. . Stochastic multi-armed bandit strategies offer upper bounds on the pseudo-regret. For example, the distance function may count the number of modified training items; or sum up the Euclidean distance of changes in feature vectors. Adversarial attacks on neural network policies. That is. We solve these problems using direct collocation. Having a unified optimal control view does not automatically produce efficient solutions to the control problem (4). One way to formulate adversarial training defense as control is the following: The state is the model ht. 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. In Chapter 4, MLC is shown to reproduce known optimal control laws … ∙ 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]). This is an alternative set of … and adversarial reward shaping below. training-data poisoning, International Conference on Machine Learning. This is especially interesting when the learner performs sequential updates. The Twenty-Ninth AAAI Conference on Artificial Intelligence In the MaD lab, optimal control theory is applied to solve trajectory optimization problems of human motion. There are several variants of test-time attacks, I use the following one for illustration: 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). 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 … 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. share, In this paper, we consider an adversarial scenario where one agent seeks... The terminal cost is also domain dependent. on Knowledge discovery and data mining. Solving optimal control problems is well known to be very computationall... Scott Alfeld, Xiaojin Zhu, and Paul Barford. The problem can be formulated as follows: \begin{aligned} Hasn't he always been researching optimization, control, and reinforcement learning (a.k.a. The adversary’s running cost gt then measures the effort in performing the action at step t. With these definitions, the adversary’s one-step control problem (4) specializes to. & \mathbf{x}_{L} \le \mathbf{x} \le \mathbf{x}_{U} && \hspace{-5.5cm} \text{(Bounds)}\\ We review the first order conditions for … - "Optimal control and machine learning … The adversary seeks to minimally perturb x into x′ such that the machine learning model classifies x and x′ differently. The control state is stochastic due to the stochastic reward rIt entering through (12). Rogers, and Xiaojin Zhu. I acknowledge funding NSF 1837132, 1545481, 1704117, 1623605, 1561512, and the MADLab AF Center of Excellence FA9550-18-1-0166. (AAAI-16). The adversary’s control input u0 is the vector of pixel value changes. More generally, W∗ can be a polytope defined by multiple future classification constraints. We summarize here an emerging deeper understanding of these One-step control has not been the focus of the control community and there may not be ample algorithmic solutions to borrow from. The Thirtieth AAAI Conference on Artificial Intelligence 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, … The dynamics st+1=f(st,ut) is straightforward via empirical mean update (12), TIt increment, and new arm choice (11). Proceedings of the eleventh ACM SIGKDD international 0 Ayon Sen, Purav Patel, Martina A. Rau, Blake Mason, Robert Nowak, Timothy T. Iterative linear quadradic regulator(iLQR) has become a benchmark method... 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, 35th International Conference on Machine Learning. The adversary’s terminal cost is g1(x1)=I∞[h(x1)=h(x0)]. We use the fact that humans minimize energy expenditure in movements to find the optimal trajectory to perform a motion. An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). Initially h0 can be the model trained on the original training data. The adversary’s running cost gt(st,ut) reflects shaping effort and target arm achievement in iteration t. ∙ 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. R represents the reachability set and S the set of foot positions where the robot is stable (considering only a single contact). & \mathbf{u}_{L} \le \mathbf{u} \le \mathbf{u}_{U} && \hspace{-5.5cm} \text{(Bounds)}\\ For instance, for SVM h, is the classifier parametrized by a weight vector. The 27th International Joint Conference on Artificial 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. In Guy Lebanon and S. V. N. Vishwanathan, editors, Proceedings He's published multiple books on these topics, many of which were released long before the "recent" machine learning revolution. Introduction. The adversary has full knowledge of the dynamics f() if it knows the form (5), ℓ(), and the value of λ. Now let us translate adversarial machine learning into a control formulation. ∙ share, Solving optimal control problems is well known to be very computationall... 0 Optimal teaching for limited-capacity human learners. 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 … Intelligence (IJCAI). 10/15/2018 ∙ by Laurent Lessard, et al. It is relatively easy to enforce for linear learners such as SVMs, but impractical otherwise. 2. Unfortunately, the notations from the control community and the machine learning community clash. ∙ 0 ∙ share . 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]. In this article, I will explain reinforcement learning in relation to optimal control. The learner updates its estimate of the pulled arm: which in turn affects which arm it will pull in the next iteration. This approach presents itself as a powerful tool in general in … I describe an optimal control view of adversarial machine learning, where the the control costs are defined by the adversary's goals to do harm and be hard share, In this work, we show existence of invariant ergodic measure for switche... Anthony D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and J. D. Tygar. ∙ 0 ∙ share . 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. Adversarial attack on graph structured data. 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). For the optimal control problem in control community, it usually depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE) … Foundations and Trends in Machine Learning. There are two styles of solutions: dynamic programming and Pontryagin minimum principle [17, 2, 10]. PARK et al. Data poisoning attacks against autoregressive models. Adversarial training can be viewed as a heuristic to approximate the uncountable constraint (. neuro-dynamic programming)? This is typically defined with respect to a given “clean” data set ~u before poisoning in the form of. proach to adaptive optimal control. advances in control theory and reinforcement learning. Scalable Optimization of Randomized Operational Decisions in and the terminal cost for finite horizon: which defines the quality of the final state. REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. The learner’s goal is to minimize the pseudo-regret Tμmax−E∑Tt=1μIt where μi=Eνi and μmax=maxi∈[k]μi. The quality of control is specified by the running cost: which defines the step-by-step control cost, (AAAI “Blue Sky” Senior Member Presentation Track). share, We investigate optimal adversarial attacks against time series forecast ... Battery efficiency map Φ bat. The dynamics is the sequential update algorithm of the learner. One limitation of the optimal control view is that the action cost is assumed to be additive over the steps. control problem. 0 I will use the machine learning convention below. The time index t ranges from 0 to T−1, and the time horizon T can be finite or infinite. to detect. Non-Asymptotic View, Bridging Cognitive Programs and Machine Learning, Learning a Family of Optimal State Feedback Controllers. Figure 4.6: Left foot projection on different ground levels z1 and z2. The adversary’s terminal cost gT(wT) is the same as in the batch case. & \frac{1}{T} \int\limits_{0}^{T} With these definitions this is a one-step control problem (4) that is equivalent to the test-time attack problem (9). Optimal control and optimal transportation have begun to play an important role in data science. An Optimal Control View of Adversarial Machine Learning. In training-data poisoning the adversary can modify the training data. 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. The adversary may do so by manipulating the rewards and the states experienced by the learner [11, 14]. There are telltale signs: adversarial attacks tend to be subtle and have peculiar non-i.i.d. 11/11/2018 ∙ by Xiaojin Zhu, et al. Differentiable Programming and Neural ODEs for Accelerating Model Based Reinforcement Learning and Optimal Control. Thus, it is possible and promising to introduce the basic QL framework for addressing the optimal control design problem. For example, Towards black-box iterative machine teaching. applications. Guarantees, Learning Expected Reward for Switched Linear Control Systems: A Kaustubh Patil, Xiaojin Zhu, Lukasz Kopec, and Bradley Love. communities, © 2019 Deep AI, Inc. | San Francisco Bay Area | All rights reserved. share, The fragility of deep neural networks to adversarially-chosen inputs has... 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]. test-time attacks, In this paper, we exploit this optimal control viewpoint of deep learning. No learner left behind: On the complexity of teaching multiple Optimal control: An introduction to the theory and its Earlier attempts on sequential teaching can be found in [18, 19, 1]. There is not necessarily a time horizon T or a terminal cost gT(sT). The problem (4) then produces the optimal training sequence poisoning. The optimal control problem is to find control inputs u0…uT−1 in order to minimize the objective: More generally, the controller aims to find control policies ϕt(xt)=ut, namely functions that map observed states to inputs. It should be noted that the adversary’s goal may not be the exact opposite of the learner’s goal: the target arm i∗ is not necessarily the one with the worst mean reward, and the adversary may not seek pseudo-regret maximization. ∙ 02/27/2019 ∙ by Christopher Iliffe Sprague, et al. 1. Adversarial machine learning studies vulnerability throughout the learning pipeline [26, 13, 4, 20]. The function f defines the evolution of state under external control. & \mathbf{f}(\mathbf{x}(t),\mathbf{{\dot{x}}}(t),\mathbf{u}(t)) = \mathbf{0} && \hspace{-5.5cm} \text{(Dynamics)}\\ Here Iy[z]=y if z is true and 0 otherwise, which acts as a hard constraint. I use supervised learning for illustration. 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. for regression learning. Of course, the resulting control problem (4) does not directly utilize adversarial examples. the optimal control problem in control community. The view encourages adversarial machine learning researcher to utilize The defender’s terminal cost gT(hT) penalizes small margin of the final model hT with respect to the original training data. Optimal control theory aims to find the control inputs required for a system to perform a task optimally with respect to a predefined objective. In particular, we introduce the discrete-time method of successive … ∙ The IOC aims to … Optimal control solution techniques for systems with known and unknown dynamics. machine learners. Xiaojin Zhu, Adish Singla, Sandra Zilles, and Anna N. Rafferty. 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]. Extensions to stochastic and continuous control are relevant to adversarial machine learning, too. 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.