Policy evaluation with temporal differences: a survey and comparison

Policy evaluation is an essential step in most reinforcement learning approaches. It yields a value function, the quality assessment of states for a given policy, which can be used in a policy improvement step. Since the late 1980s, this research area has been dominated by temporal-difference (TD) methods due to their data-efficiency. However, core issues such as stability guarantees in the off-policy scenario, improved sample efficiency and probabilistic treatment of the uncertainty in the estimates have only been tackled recently, which has led to a large number of new approaches. This paper aims at making these new developments accessible in a concise overview, with foci on underlying cost functions, the off-policy scenario as well as on regularization in high dimensional feature spaces. By presenting the first extensive, systematic comparative evaluations comparing TD, LSTD, LSPE, FPKF, the residual- gradient algorithm, Bellman residual minimization, GTD, GTD2 and TDC, we shed light on the strengths and weaknesses of the methods. Moreover, we present alternative versions of LSTD and LSPE with drastically improved off-policy performance

Sparse Temporal Difference Learning using LASSO

International audienceWe consider the problem of on-line value function estimation in reinforcement learning. We concentrate on the function approximator to use. To try to break the curse of dimensionality, we focus on non parametric function approximators. We propose to fit the use of kernels into the temporal difference algorithms by using regression via the LASSO. We introduce the equi-gradient descent algorithm (EGD) which is a direct adaptation of the one recently introduced in the LARS algorithm family for solving the LASSO. We advocate our choice of the EGD as a judicious algorithm for these tasks. We present the EGD algorithm in details as well as some experimental results. We insist on the qualities of the EGD for reinforcement learning

Reinforcement learning in continuous state- and action-space

Reinforcement learning in the continuous state-space poses the problem of the inability to store the values of all state-action pairs in a lookup table, due to both storage limitations and the inability to visit all states sufficiently often to learn the correct values. This can be overcome with the use of function approximation techniques with generalisation capability, such as artificial neural networks, to store the value function. When this is applied we can select the optimal action by comparing the values of each possible action; however, when the action-space is continuous this is not possible. In this thesis we investigate methods to select the optimal action when artificial neural networks are used to approximate the value function, through the application of numerical optimization techniques. Although it has been stated in the literature that gradient-ascent methods can be applied to the action selection [47], it is also stated that solving this problem would be infeasible, and therefore, is claimed that it is necessary to utilise a second artificial neural network to approximate the policy function [21, 55]. The major contributions of this thesis include the investigation of the applicability of action selection by numerical optimization methods, including gradient-ascent along with other derivative-based and derivative-free numerical optimization methods,and the proposal of two novel algorithms which are based on the application of two alternative action selection methods: NM-SARSA [40] and NelderMead-SARSA. We empirically compare the proposed methods to state-of-the-art methods from the literature on three continuous state- and action-space control benchmark problems from the literature: minimum-time full swing-up of the Acrobot; Cart-Pole balancing problem; and a double pole variant. We also present novel results from the application of the existing direct policy search method genetic programming to the Acrobot benchmark problem [12, 14]

Distributed Optimisation in Wireless Sensor Networks: A Hierarchical Learning Approachs

Ph.DDOCTOR OF PHILOSOPH

Value Function Estimation in Optimal Control via Takagi-Sugeno Models and Linear Programming

[ES] La presente Tesis emplea técnicas de programación dinámica y aprendizaje por refuerzo para el control de sistemas no lineales en espacios discretos y continuos. Inicialmente se realiza una revisión de los conceptos básicos de programación dinámica y aprendizaje por refuerzo para sistemas con un número finito de estados. Se analiza la extensión de estas técnicas mediante el uso de funciones de aproximación que permiten ampliar su aplicabilidad a sistemas con un gran número de estados o sistemas continuos. Las contribuciones de la Tesis son: -Se presenta una metodología que combina identificación y ajuste de la función Q, que incluye la identificación de un modelo Takagi-Sugeno, el cálculo de controladores subóptimos a partir de desigualdades matriciales lineales y el consiguiente ajuste basado en datos de la función Q a través de una optimización monotónica. -Se propone una metodología para el aprendizaje de controladores utilizando programación dinámica aproximada a través de programación lineal. La metodología hace que ADP-LP funcione en aplicaciones prácticas de control con estados y acciones continuos. La metodología propuesta estima una cota inferior y superior de la función de valor óptima a través de aproximadores funcionales. Se establecen pautas para los datos y la regularización de regresores con el fin de obtener resultados satisfactorios evitando soluciones no acotadas o mal condicionadas. -Se plantea una metodología bajo el enfoque de programación lineal aplicada a programación dinámica aproximada para obtener una mejor aproximación de la función de valor óptima en una determinada región del espacio de estados. La metodología propone aprender gradualmente una política utilizando datos disponibles sólo en la región de exploración. La exploración incrementa progresivamente la región de aprendizaje hasta obtener una política convergida.[CA] La present Tesi empra tècniques de programació dinàmica i aprenentatge per reforç per al control de sistemes no lineals en espais discrets i continus. Inicialment es realitza una revisió dels conceptes bàsics de programació dinàmica i aprenentatge per reforç per a sistemes amb un nombre finit d'estats. S'analitza l'extensió d'aquestes tècniques mitjançant l'ús de funcions d'aproximació que permeten ampliar la seua aplicabilitat a sistemes amb un gran nombre d'estats o sistemes continus. Les contribucions de la Tesi són: -Es presenta una metodologia que combina identificació i ajust de la funció Q, que inclou la identificació d'un model Takagi-Sugeno, el càlcul de controladors subòptims a partir de desigualtats matricials lineals i el consegüent ajust basat en dades de la funció Q a través d'una optimització monotónica. -Es proposa una metodologia per a l'aprenentatge de controladors utilitzant programació dinàmica aproximada a través de programació lineal. La metodologia fa que ADP-LP funcione en aplicacions pràctiques de control amb estats i accions continus. La metodologia proposada estima una cota inferior i superior de la funció de valor òptima a través de aproximadores funcionals. S'estableixen pautes per a les dades i la regularització de regresores amb la finalitat d'obtenir resultats satisfactoris evitant solucions no fitades o mal condicionades. -Es planteja una metodologia sota l'enfocament de programació lineal aplicada a programació dinàmica aproximada per a obtenir una millor aproximació de la funció de valor òptima en una determinada regió de l'espai d'estats. La metodologia proposa aprendre gradualment una política utilitzant dades disponibles només a la regió d'exploració. L'exploració incrementa progressivament la regió d'aprenentatge fins a obtenir una política convergida.[EN] The present Thesis employs dynamic programming and reinforcement learning techniques in order to obtain optimal policies for controlling nonlinear systems with discrete and continuous states and actions. Initially, a review of the basic concepts of dynamic programming and reinforcement learning is carried out for systems with a finite number of states. After that, the extension of these techniques to systems with a large number of states or continuous state systems is analysed using approximation functions. The contributions of the Thesis are: -A combined identification/Q-function fitting methodology, which involves identification of a Takagi-Sugeno model, computation of (sub)optimal controllers from Linear Matrix Inequalities, and the subsequent data-based fitting of Q-function via monotonic optimisation. -A methodology for learning controllers using approximate dynamic programming via linear programming is presented. The methodology makes that ADP-LP approach can work in practical control applications with continuous state and input spaces. The proposed methodology estimates a lower bound and upper bound of the optimal value function through functional approximators. Guidelines are provided for data and regressor regularisation in order to obtain satisfactory results avoiding unbounded or ill-conditioned solutions. -A methodology of approximate dynamic programming via linear programming in order to obtain a better approximation of the optimal value function in a specific region of state space. The methodology proposes to gradually learn a policy using data available only in the exploration region. The exploration progressively increases the learning region until a converged policy is obtained.This work was supported by the National Department of Higher Education, Science, Technology and Innovation of Ecuador (SENESCYT), and the Spanish ministry of Economy and European Union, grant DPI2016-81002-R (AEI/FEDER,UE). The author also received the grant for a predoctoral stay, Programa de Becas Iberoamérica- Santander Investigación 2018, of the Santander Bank.Díaz Iza, HP. (2020). Value Function Estimation in Optimal Control via Takagi-Sugeno Models and Linear Programming [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/139135TESI

Advancing the Applicability of Reinforcement Learning to Autonomous Control

Mit dateneffizientem Reinforcement Learning (RL) konnten beeindruckendeErgebnisse erzielt werden, z.B. für die Regelung von Gasturbinen. In derPraxis erfordert die Anwendung von RL jedoch noch viel manuelle Arbeit, wasbisher RL für die autonome Regelung untauglich erscheinen ließ. Dievorliegende Arbeit adressiert einige der verbleibenden Probleme, insbesonderein Bezug auf die Zuverlässigkeit der Policy-Erstellung. Es werden zunächst RL-Probleme mit diskreten Zustands- und Aktionsräumenbetrachtet. Für solche Probleme wird häufig ein MDP aus Beobachtungengeschätzt, um dann auf Basis dieser MDP-Schätzung eine Policy abzuleiten. DieArbeit beschreibt, wie die Schätzer-Unsicherheit des MDP in diePolicy-Erstellung eingebracht werden kann, um mit diesem Wissen das Risikoeiner schlechten Policy aufgrund einer fehlerhaften MDP-Schätzung zuverringern. Außerdem wird so effiziente Exploration sowie Policy-Bewertungermöglicht. Anschließend wendet sich die Arbeit Problemen mit kontinuierlichenZustandsräumen zu und konzentriert sich auf auf RL-Verfahren, welche aufFitted Q-Iteration (FQI) basieren, insbesondere Neural Fitted Q-Iteration(NFQ). Zwar ist NFQ sehr dateneffizient, jedoch nicht so zuverlässig, wie fürdie autonome Regelung nötig wäre. Die Arbeit schlägt die Verwendung vonEnsembles vor, um die Zuverlässigkeit von NFQ zu erhöhen. Es werden eine Reihevon Möglichkeiten der Ensemble-Nutzung entworfen und evaluiert. Bei allenbetrachteten RL-Problemen sorgen Ensembles für eine zuverlässigere Erstellungguter Policies. Im nächsten Schritt werden Möglichkeiten der Policy-Bewertung beikontinuierlichen Zustandsräumen besprochen. Die Arbeit schlägt vor, FittedPolicy Evaluation (FPE), eine Variante von FQI für Policy Evaluation, mitanderen Regressionsverfahren und/oder anderen Datensätzen zu kombinieren, umein Maß für die Policy-Qualität zu erhalten. Experimente zeigen, dassExtra-Tree-FPE ein realistisches Qualitätsmaß für NFQ-generierte Policies liefernkann. Schließlich kombiniert die Arbeit Ensembles und Policy-Bewertung, um mit sichändernden RL-Problemen umzugehen. Der wesentliche Beitrag ist das EvolvingEnsemble, dessen Policy sich langsam ändert, indem alte, untaugliche Policiesentfernt und neue hinzugefügt werden. Es zeigt sich, dass das EvolvingEnsemble deutlich besser funktioniert als einfachere Ansätze.With data-efficient reinforcement learning (RL) methods impressive resultscould be achieved, e.g., in the context of gas turbine control. However, inpractice the application of RL still requires much human intervention, whichhinders the application of RL to autonomous control. This thesis addressessome of the remaining problems, particularly regarding the reliability of thepolicy generation process. The thesis first discusses RL problems with discrete state and action spaces.In that context, often an MDP is estimated from observations. It is describedhow to incorporate the estimators' uncertainties into the policy generationprocess. This information can then be used to reduce the risk of obtaining apoor policy due to flawed MDP estimates. Moreover, it is discussed how to usethe knowledge of uncertainty for efficient exploration and the assessment ofpolicy quality without requiring the policy's execution. The thesis then moves on to continuous state problems and focuses on methodsbased on fitted Q-iteration (FQI), particularly neural fitted Q-iteration(NFQ). Although NFQ has proven to be very data-efficient, it is not asreliable as required for autonomous control. The thesis proposes to useensembles to increase reliability. Several ways of ensemble usage in an NFQcontext are discussed and evaluated on a number of benchmark domains. It showsthat in all considered domains with ensembles good policies can be producedmore reliably. Next, policy assessment in continuous domains is discussed. The thesisproposes to use fitted policy evaluation (FPE), an adaptation of FQI to policyevaluation, combined with a different function approximator and/or differentdataset to obtain a measure for policy quality. Results of experiments showthat extra-tree FPE, applied to policies generated by NFQ, produces valuefunctions that can well be used to reason about the true policy quality. Finally, the thesis combines ensembles and policy assessment to derive methodsthat can deal with changing environments. The major contribution is theevolving ensemble. The policy of the evolving ensemble changes slowly as newpolicies are added and old policies removed. It turns out that the evolvingensemble approaches work considerably better than simpler approaches likesingle policies learned with recent observations or simple ensembles

Algorithmic Trading and Reinforcement Learning: Robust methodologies for AI in finance

The application of reinforcement learning (RL) to algorithmic trading is, in many ways, a perfect match. Trading is fundamentally a problem of making decisions under uncertainty, and reinforcement learning is a family of methods for solving such problems. Indeed, many researchers have explored this space and, for the most, validated RL, its ability to find effective solutions and its importance in studying the behaviour of agents in markets. In spite of this, many of the methods available today fail to meet expectations when evaluated in realistic environments. There are a number of reasons for this: partial observability, credit assignment and non-stationary dynamics. Unlike video games, the state and action spaces are often unstructured and unbounded, which poses challenges around knowledge representation and task invariance. As a final hurdle, traders also need RL to be able to handle risk-sensitive objectives with solid human interpretation to be used reliably in practice. All of these together make for an exceptionally challenging domain that poses fascinating questions about the efficacy of RL and the techniques one can use to address these issues. This dissertation makes several contributions towards two core themes that underlie the challenges mentioned above. The first, epistemic uncertainty, covers modelling challenges such as misspecification and robustness. The second relates to aleatoric risk and safety in the presence of intrinsic randomness. These will be studied in depth, for which we summarise, below, the key findings and insights developed during the course of the PhD. The first part of the thesis investigates the use of data and historical reconstruction as a platform for learning strategies in limit order book markets. The advantages and limitations of this class of model are explored and practical insights provided. It is demonstrated that these methods make minimal assumptions about the market's dynamics, but are restricted in terms of their ability to perform counterfactual simulations. Computational aspects of reconstruction are discussed, and a highly performant library provided for running experiments. The second chapter in this part of the thesis builds upon historical reconstruction by applying value-based RL methods to market making. We first propose an intuitive and effective reward function for both risk-neutral and risk-sensitive learning and justify it through variance analysis. Eligibility traces are shown to solve the credit assignment problem observed in past work, and a comparison of different state-of-the-art algorithms (each with different assumptions) is provided. We then propose a factored state representation which incorporates market microstructure and benefits from improved stability and asymptotic performance compared with benchmark algorithms from the literature. In the second part, we explore an alternative branch of modelling techniques based on explicit stochastic processes. Here, we focus on policy gradient methods, introducing a family of likelihoods functions that are effective in trading domains and studying their properties. Four key problem domains are introduced along with their solution concepts and baseline methods. In the second chapter of part two, we use adversarial reinforcement learning to derive epistemically robust strategies. The market making model of Avellaneda and Stoikov (2008) is recast as a zero-sum, two player game between the market maker, and the market. We study the theoretical properties of a one-shot projection, and empirically evaluate the dynamics of the full stochastic game. We show that the resulting algorithms are robust to discrepancies between train and test time price/execution dynamics, and that the resulting strategies dominate performance in all cases. The final results chapter addresses the intrinsic risk of trading and portfolio management by framing the problems explicitly as constrained Markov decision processes. A downside risk measure based on lower partial moments is proposed, and a tractable linear bound derived for application in temporal-difference learning. This proxy has a natural interpretation and favourable variance properties. An extension of previous work to use natural policy gradients is then explored. The value of these two techniques is demonstrated empirically for a multi-armed bandit and two trading scenarios. The results is a practical algorithm for learning downside risk-averse strategies