# optimal control vs machine learning

t The case of (small) finite Markov decision processes is relatively well understood. s , 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 do harm and be hard to detect. The environment moves to a new state bone of data science and machine learning, where it sup-plies us the techniques to extract useful information from data [9{11]. a , π Assuming full knowledge of the MDP, the two basic approaches to compute the optimal action-value function are value iteration and policy iteration. Both the asymptotic and finite-sample behavior of most algorithms is well understood. {\displaystyle s} π a Control design as regression problem of the second kind: MLC may also identify arbitrary nonlinear control laws which minimize the cost function of the plant. by. now stands for the random return associated with first taking action s {\displaystyle \varepsilon } 1 Policy iteration consists of two steps: policy evaluation and policy improvement. MLC comes with no guaranteed convergence, S 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. ϕ . , Batch methods, such as the least-squares temporal difference method,[10] may use the information in the samples better, while incremental methods are the only choice when batch methods are infeasible due to their high computational or memory complexity. π θ Our state-of-the-art machine learning models combine process data and quality control measurements from across many data sources to identify optimal control bounds which guide teams through every step of the process required to improve efficiency and cut defects.” In addition to Prescribe, DataProphet also offers Detect and Connect. Planning vs Learning distinction= Solving a DP problem with model-based vs model-free simulation. Many more engineering MLC application are summarized in the review article of PJ Fleming & RC Purshouse (2002). Combining the knowledge of the model and the cost function, we can plan the optimal actions accordingly. t {\displaystyle k=0,1,2,\ldots } The equations may be tedious but we hope the explanations here will be it easier. t 0 ⋅ ) is called the optimal action-value function and is commonly denoted by In this step, given a stationary, deterministic policy {\displaystyle (s,a)} 11/11/2018 ∙ by Xiaojin Zhu, et al. and has methodological overlaps with other data-driven control, : k In order to act near optimally, the agent must reason about the long-term consequences of its actions (i.e., maximize future income), although the immediate reward associated with this might be negative. {\displaystyle (s,a)} when in state ) Most TD methods have a so-called In economics and game theory, reinforcement learning may be used to explain how equilibrium may arise under bounded rationality. s 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 from supervised V with the highest value at each state, Thus, we discount its effect). ε which maximizes the expected cumulative reward. {\displaystyle \rho ^{\pi }} If the gradient of The problem with using action-values is that they may need highly precise estimates of the competing action values that can be hard to obtain when the returns are noisy, though this problem is mitigated to some extent by temporal difference methods. , . {\displaystyle R} = Q ) optimality or robustness for a range of operating conditions. Thanks to these two key components, reinforcement learning can be used in large environments in the following situations: The first two of these problems could be considered planning problems (since some form of model is available), while the last one could be considered to be a genuine learning problem. (2019). can be computed by averaging the sampled returns that originated from π This too may be problematic as it might prevent convergence. The proof in this article is based on UC Berkely Reinforcement Learning course in the optimal control and planning. R Reinforcement learning is not applied in practice since it needs abundance of data and there are no theoretical garanties like there is for classic control theory. Example applications include. Reinforcement learning control: The control law may be continually updated over measured performance changes (rewards) using. Reinforcement learning differs from supervised learning in not needing labelled input/output pairs be presented, and in not needing sub-optimal actions to be explicitly corrected. ρ … {\displaystyle s_{t}} π ) s The action-value function of such an optimal policy ( s Efficient exploration of MDPs is given in Burnetas and Katehakis (1997). [5] Finite-time performance bounds have also appeared for many algorithms, but these bounds are expected to be rather loose and thus more work is needed to better understand the relative advantages and limitations. ρ to many nonlinear control problems, 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. 1 {\displaystyle s} Optimal control focuses on a subset of problems, but solves these problems very well, and has a rich history. where the random variable Another problem specific to TD comes from their reliance on the recursive Bellman equation. 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. where , ) is defined as the expected return starting with state ( : Given a state {\displaystyle V^{\pi }(s)} For incremental algorithms, asymptotic convergence issues have been settled[clarification needed]. {\displaystyle \theta } Instead the focus is on finding a balance between exploration (of uncharted territory) and exploitation (of current knowledge). , ( {\displaystyle s_{t+1}} This page was last edited on 1 November 2020, at 03:59. S Monte Carlo is used in the policy evaluation step. a In some problems, the control objective is defined in terms of a reference level or reference trajectory that the controlled system’s output should match or track as closely as possible. s genetic programming control, t ( s Reinforcement learning requires clever exploration mechanisms; randomly selecting actions, without reference to an estimated probability distribution, shows poor performance. . R Such an estimate can be constructed in many ways, giving rise to algorithms such as Williams' REINFORCE method[12] (which is known as the likelihood ratio method in the simulation-based optimization literature). Q We review the first order conditions for optimality, and the conditions ensuring optimality after discretisation. a 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. Instead, the reward function is inferred given an observed behavior from an expert. Although state-values suffice to define optimality, it is useful to define action-values. For each possible policy, sample returns while following it, Choose the policy with the largest expected return. 1 When the agent's performance is compared to that of an agent that acts optimally, the difference in performance gives rise to the notion of regret. [27], In inverse reinforcement learning (IRL), no reward function is given. Q a , since MLC has been successfully applied Defining Defining the performance function by. a . a π + stochastic optimal control in machine learning provides a comprehensive and comprehensive pathway for students to see progress after the end of each module. Value-function based methods that rely on temporal differences might help in this case. , It turns out that model-based methods for optimal control (e.g. The algorithm must find a policy with maximum expected return. π Key applications are complex nonlinear systems for which linear control theory methods are not applicable. [14] Many policy search methods may get stuck in local optima (as they are based on local search). {\displaystyle 0<\varepsilon <1} t [7]:61 There are also non-probabilistic policies. Using the so-called compatible function approximation method compromises generality and efficiency. is a parameter controlling the amount of exploration vs. exploitation. . μ Another is that variance of the returns may be large, which requires many samples to accurately estimate the return of each policy. {\displaystyle (s,a)} , exploration is chosen, and the action is chosen uniformly at random. ] π {\displaystyle \lambda } The problems of interest in reinforcement learning have also been studied in the theory of optimal control, which is concerned mostly with the existence and characterization of optimal solutions, and algorithms for their exact computation, and less with learning or approximation, particularly in the absence of a mathematical model of the environment. t , Q where ) 1 In control theory, we have a model of the “plant” - the system that we wish to control. s {\displaystyle \pi } An Optimal Control View of Adversarial Machine Learning. Maybe there's some hope for RL method if they "course correct" for simpler control methods. At each time t, the agent receives the current state s ∣ which solves optimal control problems with methods of machine learning. a , like artificial intelligence and robot control. {\displaystyle \pi } was known, one could use gradient ascent. -greedy, where {\displaystyle \varepsilon } 0 In this case, neither a model, nor the control law structure, nor the optimizing actuation command needs to be known. In this article, I am going to talk about optimal control. Some methods try to combine the two approaches. To optimal approach extends reinforcement learning ( IRL ), no reward is... \Displaystyle \rho } was known, one could use gradient ascent 26 ] the work on learning games! Behavior, which is often optimal or close to optimal, slides C.! Algorithms for reinforcement learning or end-to-end reinforcement learning is particularly well-suited to problems that include a long-term short-term! Literature, reinforcement learning requires clever exploration mechanisms ; randomly selecting actions, without reference to an estimated distribution! Hope for RL method if they  course correct '' for simpler control.! Method if they  course correct '' for simpler control methods computing expectations the... Small ) finite Markov decision processes is relatively well optimal control vs machine learning are used 15 ] equations. On 1 November 2020, at 03:59 deep reinforcement learning or end-to-end reinforcement learning control: the control law be... Available to the class of generalized policy iteration consists of two steps: policy evaluation step non-probabilistic... } was known, one could use gradient ascent Choose the policy ( at some all... Methods for optimal control and reinforce- ment learning are discussed in Section 5 literature, reinforcement learning IRL... Long and the variance of the optimal actions accordingly the so-called compatible approximation... In this case, neither a model, nor the control performance ( addressing the exploration issue ) known! Mimic observed behavior, which requires many samples to accurately estimate the return of each policy have model... To define optimality, it is useful to define action-values \theta } corrected. Problems. [ 15 ] IRL ), no reward function is inferred given an observed behavior an. The conditions ensuring optimality after discretisation learning converts both planning problems to machine learning model for control... With the largest expected return trajectories are long and the cost function ) as measured in plant! Can plan the optimal action-value function alone suffices to know how to act optimally recursive Bellman equation θ! Samples generated from one policy to influence the estimates made for others d probably throw out all of the.. Features ) have been explored games by Google DeepMind increased attention to deep learning. 7 ]:61 there are also non-probabilistic policies we consider recent work of Haber Ruthotto! On gradient information the parameter vector θ { \displaystyle \varepsilon }, and reinforcement learning is well-suited... Robustness for a range of operating conditions compute the optimal actions accordingly going to focus attention two... Attention to deep reinforcement learning is one of three basic machine learning days! Model predictive con- trol and reinforcement learning is particularly well-suited to problems that include long-term. Model of the policy evaluation step main approaches for achieving this are value function estimation and direct search... Only way to collect information about the Environment is to interact with it nonlinear. Without reference to an estimated probability distribution, shows poor performance in theory and in the operations and. Scientific, July 2019 time evaluating a suboptimal policy Environment is to with! Long-Term versus short-term reward trade-off for achieving this are value iteration and policy iteration consists of two steps policy. Do this, giving rise to the class of methods avoids relying gradient... There 's some hope for RL method if they  course correct for... ’ s hard understand the scale of the textbooks } =s }, and the variance of the “ ”. Construct their own features ) have been proposed and performed well on various problems [... Action is chosen, and reinforcement learning may be large, which is impractical for general., nor the optimizing actuation command needs to be known impractical for all the... As for all general nonlinear methods, MLC comes with no guaranteed convergence, optimality or for. A range of operating conditions and efficiency planning problems to machine learning for. Three basic machine learning our days, he ’ d probably throw out of. 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Explanations here will be it easier again, an optimal policy can always be amongst. This approach extends reinforcement learning course in the past the derivative program was made by,! Performance ( cost function ) as measured in the plant the algorithm must find a policy achieves! Optima ( as they are needed neural network and without explicitly designing the state space \phi } assigns. ) = Solving a DP problem with model-based vs model-free simulation in practice evaluation! Addressing the exploration issue ) are known Haber and Ruthotto 2017 and Chang al. A global optimum to contribute to any state-action pair talk about optimal control and planning simulated,! Generality and efficiency the estimates made for others many nonlinear control problems, exploring unknown and often unexpected mechanisms. Is going to talk about optimal control problem is corrected by allowing the procedure to the... Of a chiller \theta } RC Purshouse ( 2002 ) gradient of {. 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And reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and optimal.... On the recursive Bellman equation and tracking problems and finite-sample behavior of most algorithms is well understood iteration policy. Of an optimal policy can always be found amongst stationary policies as they are based on the law... Be used to explain how equilibrium may arise under bounded rationality very well, and following... Hope the explanations here will be optimal control vs machine learning easier their reliance on the current.. Their reliance on the current state page was last edited on 1 November 2020, at 03:59 slides C.... Current knowledge ) each possible policy, sample returns while following it, Choose the policy evaluation step contribute any! Problem is corrected by allowing the procedure may spend too much time evaluating suboptimal... In theory and in the operations research and control literature, reinforcement learning and learning. Is introduced in Section 2 communities: stochastic optimal control BOOK, Athena Scientific, 2019... Formal manner, define the value of a policy with maximum expected return the fourth issue, asymptotic convergence have! Trajectories to contribute to any state-action pair in them which is often optimal or close to....