\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 + by back-propagation. 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. 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. Goal: Introduce you to an impressive example of reinforcement learning (its biggest success). 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. This machine learning control (MLC) is motivated and detailed in Chapters 1 and 2. Weiyang Liu, Bo Dai, Ahmad Humayun, Charlene Tay, Chen Yu, Linda B Smith, In training-data poisoning the adversary can modify the training data. The control state is stochastic due to the stochastic reward rIt entering through (12). We use the fact that humans minimize energy expenditure in movements to find the optimal trajectory to perform a motion. 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. 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. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 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). & \mathbf{f}(\mathbf{x}(t),\mathbf{{\dot{x}}}(t),\mathbf{u}(t)) = \mathbf{0} && \hspace{-5.5cm} \text{(Dynamics)}\\ 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 … The adversary seeks to minimally perturb x into x′ such that the machine learning model classifies x and x′ differently. The function f defines the evolution of state under external control. 06/15/2020 ∙ by Muhammad Abdullah Naeem, et al. \underset{\mathbf{x}(t), \mathbf{u}(t), T}{\text{min}} ~~~~ share. ∙ 0 ∙ share . The 27th International Joint Conference on Artificial I will use the machine learning convention below. Earlier attempts on sequential teaching can be found in [18, 19, 1]. . ∙ That is. The adversary’s terminal cost is g1(x1)=I∞[h(x1)=h(x0)]. neuro-dynamic programming)? practice. 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]. There are telltale signs: adversarial attacks tend to be subtle and have peculiar non-i.i.d. Dynamic programming, Hamilton-Jacobi reachability, and direct and indirect methods for trajectory optimization. In the MaD lab, optimal control theory is applied to solve trajectory optimization problems of human motion. of the Eighteenth International Conference on Artificial Intelligence and 0 Some defense strategies can be viewed as optimal control, too. The adversary’s terminal cost g1(w1) measures the lack of intended harm. Optimal control What is control problem? test-time attacks, 11/11/2018 ∙ by Xiaojin Zhu, et al. However we don't control rotational speed of tires but only handle with the accelerator and brake … The Twenty-Ninth AAAI Conference on Artificial Intelligence. including test-item attacks, training-data poisoning, and adversarial reward Machine beats human at sequencing visuals for perceptual-fluency \text{subject to} ~~ 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. Note the machine learning model h is only used to define the hard constraint terminal cost; h itself is not modified. share, We investigate optimal adversarial attacks against time series forecast ... ∙ Wild patterns: Ten years after the rise of adversarial machine 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. In this article, I will explain reinforcement learning in relation to optimal control. The view encourages adversarial machine learning researcher to utilize It is relatively easy to enforce for linear learners such as SVMs, but impractical otherwise. ∙ An optimal control problem with discrete states and actions and probabilistic state transitions is called a Markov decision process (MDP). Adversarial training can be viewed as a heuristic to approximate the uncountable constraint (. 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. 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]). In Guy Lebanon and S. V. N. Vishwanathan, editors, Proceedings The adversary’s control input u0 is the vector of pixel value changes. The adversary has full knowledge of the dynamics f() if it knows the form (5), ℓ(), and the value of λ. Yang Fan, Fei Tian, Tao Qin, and Tie-Yan Liu. A periodicity constraint is used to simulate gait. share, In this paper, we consider an adversarial scenario where one agent seeks... Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning.. Reinforcement learning differs from supervised learning … One-step control has not been the focus of the control community and there may not be ample algorithmic solutions to borrow from. The adversary’s goal is to use minimal reward shaping to force the learner into performing specific wrong actions. 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. 05/08/2018 ∙ by Melkior Ornik, et al. 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 … With these definitions, the adversary’s one-step control problem (4) specializes to. Initially h0 can be the model trained on the original training data. These adversarial examples do not even need to be successful attacks. The Twenty-Ninth AAAI Conference on Artificial Intelligence structures – as control input might be. 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} } ∙ The control input ut=(xt,yt) is an additional training item with the trivial constraint set Ut=X×y. 0 Differentiable Programming and Neural ODEs for Accelerating Model Based Reinforcement Learning and Optimal Control. Statistics, Calculus of variations and optimal control theory: A concise 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 … 0 Stochastic multi-armed bandit strategies offer upper bounds on the pseudo-regret. James M Rehg, and Le Song. The dynamical system is trivially vector addition: x1=f(x0,u0)=x0+u0. Furthermore, in graybox and blackbox attack settings f is not fully known to the attacker. control problem. 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. Anthony D. Joseph, Blaine Nelson, Benjamin I. P. Rubinstein, and J. D. Tygar. For the optimal control problem in control community, it usually depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE) … The Thirtieth AAAI Conference on Artificial Intelligence Paul Shen. The controller wants to use the least number of training items|a concept known as the 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. We summarize here an emerging deeper understanding of these Adversarial Classification Settings. : VEHICLE POWER CONTROL BASED ON MACHINE LEARNING OF OPTIMAL CONTROL PARAMETERS 4743 Fig. Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. One limitation of the optimal control view is that the action cost is assumed to be additive over the steps. Matthew Jagielski, Alina Oprea, Battista Biggio, Chang Liu, Cristina For example, x. denotes the state in control but the feature vector in machine learning. One way to formulate adversarial training defense as control is the following: The state is the model ht. Scalable Optimization of Randomized Operational Decisions in proach to adaptive optimal control. With these definitions this is a one-step control problem (4) that is equivalent to the test-time attack problem (9). \frac{W_{eff}}{N_u} \sum\limits_{i=1}^{N_u} w_i u_i^{e_i} \,dt \\ \\ \\ Adversarial attack on graph structured data. If AI had a Nobel Prize, this work would get it. Read MuZero: The triumph of the model-based approach, and the reconciliation of engineering and machine learning approaches to optimal control and reinforcement learning. ∙ 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 problem can be formulated as follows: \begin{aligned} It should be clear that such defense is similar to training-data poisoning, in that the defender uses data to modify the learned model. 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. ∙ ∙ Hanjun Dai, Hui Li, Tian Tian, Xin Huang, Lin Wang, Jun Zhu, and Le Song. 10/15/2018 ∙ by Laurent Lessard, et al. ut∈Ut is the control input, and Ut is the control constraint set. R represents the reachability set and S the set of foot positions where the robot is stable (considering only a single contact). There is not necessarily a time horizon T or a terminal cost gT(sT). 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. The dynamics ht+1=f(ht,ut) is one-step update of the model, e.g. Deep learning is formulated as a discrete-time optimal control problem. share. Proceedings of the 17th ACM SIGKDD international conference share, The fragility of deep neural networks to adversarially-chosen inputs has... The control input at time t is ut=(xt,yt), namely the tth training item for t=0,1,…. The dynamics st+1=f(st,ut) is straightforward via empirical mean update (12), TIt increment, and new arm choice (11). with some ut∈R before sending the modified reward to the learner. machine-learning automatic-differentiation software literature trajectory-optimization optimal-control model-predictive-control Updated Aug 17, 2019 navigator8972 / pylqr The problem of state abstraction is of central importance in optimal control, reinforcement learning and Markov decision processes. Solving optimal control problems is well known to be very computationall... Scott Alfeld, Xiaojin Zhu, and Paul Barford. g1(w1)=I∞[w1∉W∗] with the target set W∗={w:w⊤x∗≥ϵ}. Thus, it is possible and promising to introduce the basic QL framework for addressing the optimal control design problem. 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. Sandy Huang, Nicolas Papernot, Ian Goodfellow, Yan Duan, and Pieter Abbeel. applications. There are several variants of test-time attacks, I use the following one for illustration: The defender’s terminal cost gT(hT) penalizes small margin of the final model hT with respect to the original training data. Learning. The resulting simulations with state x(t) are used to reconstruct and predict human movements, specifically gait. Now let us translate adversarial machine learning into a control formulation.