With the increasing power of computers and the rapid development of self-learning methodologies such as machine learning and artificial intelligence, the problem of constructing an automatic Financial Trading Systems (FTFs) becomes an increasingly attractive research topic. An intuitive way of developing such a trading algorithm is to use Reinforcement Learning (RL) algorithms, which does not require model-building. In this paper, we dive into the RL algorithms and illustrate the definitions of the reward function, actions and policy functions in details, as well as introducing algorithms that could be applied to FTFs.
We show how an action-dependent baseline can be used by the policy gradient theorem using function approximation, originally presented with action-independent baselines by (Sutton et al. 2000).
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable functions, multiresolution analysis enables us to construct a wavelet system from which the basis functions are selected adaptively, resulting in a tree structure. Furthermore, we present the convergence rate of our multiscale approximation which does not depend on the regularity of basi…
University of NSW（新南威尔士大学）；NICTA（澳大利亚国家信息与通信技术研究院）；Medicare Australia（澳大利亚医疗保险局）；ANU（澳大利亚国立大学）；University College London（伦敦大学学院）
This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific ex…
Reinforcement learning is commonly used with function approximation. However, very few positive results are known about the convergence of function approximation based RL control algorithms. In this paper we show that TD(0) and Sarsa(0) with linear function approximation is convergent for a simple class of problems, where the system is linear and the costs are quadratic (the LQ control problem). Furthermore, we show that for systems with Gaussian noise and non-completely observable states (the LQG problem), the mentioned RL algorithms are still convergent, if they are combined with Kalman filt…
Using a martingale concentration inequality, concentration bounds `from time $n_0$ on' are derived for stochastic approximation algorithms with contractive maps and both martingale difference and Markov noises. These are applied to reinforcement learning algorithms, in particular to asynchronous Q-learning and TD(0).
Natural policy gradient methods are popular reinforcement learning methods that improve the stability of policy gradient methods by utilizing second-order approximations to precondition the gradient with the inverse of the Fisher-information matrix. However, to the best of the authors' knowledge, there has not been a study that has investigated the effects of different second-order approximations in a comprehensive and systematic manner. To address this, five different second-order approximations were studied and compared across multiple key metrics including performance, stability, sample eff…
This works handles the inverse reinforcement learning problem in high-dimensional state spaces, which relies on an efficient solution of model-based high-dimensional reinforcement learning problems. To solve the computationally expensive reinforcement learning problems, we propose a function approximation method to ensure that the Bellman Optimality Equation always holds, and then estimate a function based on the observed human actions for inverse reinforcement learning problems. The time complexity of the proposed method is linearly proportional to the cardinality of the action set, thus it c…
University of Florida（佛罗里达大学）；Carnegie Mellon University（卡内基梅隆大学）；Institute for Advanced Studies（高等研究院）；Microsoft Research（微软研究院）
We design a new provably efficient algorithm for episodic reinforcement learning with generalized linear function approximation. We analyze the algorithm under a new expressivity assumption that we call "optimistic closure," which is strictly weaker than assumptions from prior analyses for the linear setting. With optimistic closure, we prove that our algorithm enjoys a regret bound of $\tilde{O}(\sqrt{d^3 T})$ where $d$ is the dimensionality of the state-action features and $T$ is the number of episodes. This is the first statistically and computationally efficient algorithm for reinforcement…
Offline reinforcement learning, which aims at optimizing sequential decision-making strategies with historical data, has been extensively applied in real-life applications. State-Of-The-Art algorithms usually leverage powerful function approximators (e.g. neural networks) to alleviate the sample complexity hurdle for better empirical performances. Despite the successes, a more systematic understanding of the statistical complexity for function approximation remains lacking. Towards bridging the gap, we take a step by considering offline reinforcement learning with differentiable function class…
Motivated by broad applications in reinforcement learning and federated learning, we study local stochastic approximation over a network of agents, where their goal is to find the root of an operator composed of the local operators at the agents. Our focus is to characterize the finite-time performance of this method when the data at each agent are generated from Markov processes, and hence they are dependent. In particular, we provide the convergence rates of local stochastic approximation for both constant and time-varying step sizes. Our results show that these rates are within a logarithmi…
Reinforcement learning (RL) algorithms based on high-dimensional function approximation have achieved tremendous empirical success in large-scale problems with an enormous number of states. However, most analysis of such algorithms gives rise to error bounds that involve either the number of states or the number of features. This paper considers the situation where the function approximation is made either using the kernel method or the two-layer neural network model, in the context of a fitted Q-iteration algorithm with explicit regularization. We establish an $\tilde{O}(H^3|\mathcal {A}|^{\f…
This paper introduces a new method for inverse reinforcement learning in large-scale and high-dimensional state spaces. To avoid solving the computationally expensive reinforcement learning problems in reward learning, we propose a function approximation method to ensure that the Bellman Optimality Equation always holds, and then estimate a function to maximize the likelihood of the observed motion. The time complexity of the proposed method is linearly proportional to the cardinality of the action set, thus it can handle large state spaces efficiently. We test the proposed method in a simulat…
We study reinforcement learning (RL) with linear function approximation. Existing algorithms for this problem only have high-probability regret and/or Probably Approximately Correct (PAC) sample complexity guarantees, which cannot guarantee the convergence to the optimal policy. In this paper, in order to overcome the limitation of existing algorithms, we propose a new algorithm called FLUTE, which enjoys uniform-PAC convergence to the optimal policy with high probability. The uniform-PAC guarantee is the strongest possible guarantee for reinforcement learning in the literature, which can dire…
Reinforcement learning in cooperative multi-agent settings has recently advanced significantly in its scope, with applications in cooperative estimation for advertising, dynamic treatment regimes, distributed control, and federated learning. In this paper, we discuss the problem of cooperative multi-agent RL with function approximation, where a group of agents communicates with each other to jointly solve an episodic MDP. We demonstrate that via careful message-passing and cooperative value iteration, it is possible to achieve near-optimal no-regret learning even with a fixed constant communic…
This paper gives specific divergence examples of value-iteration for several major Reinforcement Learning and Adaptive Dynamic Programming algorithms, when using a function approximator for the value function. These divergence examples differ from previous divergence examples in the literature, in that they are applicable for a greedy policy, i.e. in a "value iteration" scenario. Perhaps surprisingly, with a greedy policy, it is also possible to get divergence for the algorithms TD(1) and Sarsa(1). In addition to these divergences, we also achieve divergence for the Adaptive Dynamic Programmin…
In this paper, we provide two new stable online algorithms for the problem of prediction in reinforcement learning, \emph{i.e.}, estimating the value function of a model-free Markov reward process using the linear function approximation architecture and with memory and computation costs scaling quadratically in the size of the feature set. The algorithms employ the multi-timescale stochastic approximation variant of the very popular cross entropy (CE) optimization method which is a model based search method to find the global optimum of a real-valued function. A proof of convergence of the alg…
University of New South Wales（新南威尔士大学）；University of Amsterdam（阿姆斯特丹大学）
We present Nonparametric Approximation of Inter-Trace returns (NAIT), a Reinforcement Learning algorithm for discrete action, pixel-based environments that is both highly sample and computation efficient. NAIT is a lazy-learning approach with an update that is equivalent to episodic Monte-Carlo on episode completion, but that allows the stable incorporation of rewards while an episode is ongoing. We make use of a fixed domain-agnostic representation, simple distance based exploration and a proximity graph-based lookup to facilitate extremely fast execution. We empirically evaluate NAIT on both…
ATR Computational Neuroscience Laboratories（ATR计算神经科学实验室）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）
In recent years, neural networks have enjoyed a renaissance as function approximators in reinforcement learning. Two decades after Tesauro's TD-Gammon achieved near top-level human performance in backgammon, the deep reinforcement learning algorithm DQN achieved human-level performance in many Atari 2600 games. The purpose of this study is twofold. First, we propose two activation functions for neural network function approximation in reinforcement learning: the sigmoid-weighted linear unit (SiLU) and its derivative function (dSiLU). The activation of the SiLU is computed by the sigmoid functi…
Google Inc.（谷歌公司）；Microsoft Research, Redmond（微软研究院（雷德蒙德））；University of Illinois at Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）；Tencent AI Lab, Bellevue（腾讯人工智能实验室（贝尔维尤））
When function approximation is used, solving the Bellman optimality equation with stability guarantees has remained a major open problem in reinforcement learning for decades. The fundamental difficulty is that the Bellman operator may become an expansion in general, resulting in oscillating and even divergent behavior of popular algorithms like Q-learning. In this paper, we revisit the Bellman equation, and reformulate it into a novel primal-dual optimization problem using Nesterov's smoothing technique and the Legendre-Fenchel transformation. We then develop a new algorithm, called Smoothed …
Virginia Polytechnic Institute and State University（弗吉尼亚理工学院暨州立大学）
This paper presents research in progress investigating the viability and adaptation of reinforcement learning using deep neural network based function approximation for the task of radio control and signal detection in the wireless domain. We demonstrate a successful initial method for radio control which allows naive learning of search without the need for expert features, heuristics, or search strategies. We also introduce Kerlym, an open Keras based reinforcement learning agent collection for OpenAI's Gym.
Carnegie Mellon University（卡内基梅隆大学）；University of California, Los Angles（加利福尼亚大学洛杉矶分校）
Value function approximation has demonstrated phenomenal empirical success in reinforcement learning (RL). Nevertheless, despite a handful of recent progress on developing theory for RL with linear function approximation, the understanding of general function approximation schemes largely remains missing. In this paper, we establish a provably efficient RL algorithm with general value function approximation. We show that if the value functions admit an approximation with a function class $\mathcal{F}$, our algorithm achieves a regret bound of $\widetilde{O}(\mathrm{poly}(dH)\sqrt{T})$ where $d…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；C3.ai Digital Transformation Institute（C3.ai数字化转型研究院）
We provide performance guarantees for a variant of simulation-based policy iteration for controlling Markov decision processes that involves the use of stochastic approximation algorithms along with state-of-the-art techniques that are useful for very large MDPs, including lookahead, function approximation, and gradient descent. Specifically, we analyze two algorithms; the first algorithm involves a least squares approach where a new set of weights associated with feature vectors is obtained via least squares minimization at each iteration and the second algorithm involves a two-time-scale sto…
Full-sampling (e.g., Q-learning) and pure-expectation (e.g., Expected Sarsa) algorithms are efficient and frequently used techniques in reinforcement learning. Q$(σ,λ)$ is the first approach unifies them with eligibility trace through the sampling degree $σ$. However, it is limited to the tabular case, for large-scale learning, the Q$(σ,λ)$ is too expensive to require a huge volume of tables to accurately storage value functions. To address above problem, we propose a GQ$(σ,λ)$ that extends tabular Q$(σ,λ)$ with linear function approximation. We prove the convergence of GQ$(σ,λ)$. Empirical re…
Opportunistic spectrum access is one of the emerging techniques for maximizing throughput in congested bands and is enabled by predicting idle slots in spectrum. We propose a kernel-based reinforcement learning approach coupled with a novel budget-constrained sparsification technique that efficiently captures the environment to find the best channel access actions. This approach allows learning and planning over the intrinsic state-action space and extends well to large state spaces. We apply our methods to evaluate coexistence of a reinforcement learning-based radio with a multi-channel adver…
We propose a successive convex approximation based off-policy optimization (SCAOPO) algorithm to solve the general constrained reinforcement learning problem, which is formulated as a constrained Markov decision process (CMDP) in the context of average cost. The SCAOPO is based on solving a sequence of convex objective/feasibility optimization problems obtained by replacing the objective and constraint functions in the original problems with convex surrogate functions. At each iteration, the convex surrogate problem can be efficiently solved by Lagrange dual method even the policy is parameter…
Optimizing prices for energy demand response requires a flexible controller with ability to navigate complex environments. We propose a reinforcement learning controller with surprise minimizing modifications in its architecture. We suggest that surprise minimization can be used to improve learning speed, taking advantage of predictability in peoples' energy usage. Our architecture performs well in a simulation of energy demand response. We propose this modification to improve functionality and save in a large scale experiment.
Motivated by the wide adoption of reinforcement learning (RL) in real-world personalized services, where users' sensitive and private information needs to be protected, we study regret minimization in finite-horizon Markov decision processes (MDPs) under the constraints of differential privacy (DP). Compared to existing private RL algorithms that work only on tabular finite-state, finite-actions MDPs, we take the first step towards privacy-preserving learning in MDPs with large state and action spaces. Specifically, we consider MDPs with linear function approximation (in particular linear mixt…
Autonomous navigation has recently gained great interest in the field of reinforcement learning. However, little attention was given to the time optimal velocity control problem, i.e. controlling a vehicle such that it travels at the maximal speed without becoming dynamically unstable (roll-over or sliding). Time optimal velocity control can be solved numerically using existing methods that are based on optimal control and vehicle dynamics. In this paper, we use deep reinforcement learning to generate the time optimal velocity control. Furthermore, we use the numerical solution to further impr…
Tel Aviv University（特拉维夫大学）；Google Research（谷歌研究院）
We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions.We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses.Our algorithm obtains an $\widetilde O(K^{6/7})$ regret bound, improving signifi…
Conduent Labs India（康杜恩特印度实验室）；University of Illinois Chicago（伊利诺伊大学芝加哥分校）
In this paper we explore methods to exploit symmetries for ensuring sample efficiency in reinforcement learning (RL), this problem deserves ever increasing attention with the recent advances in the use of deep networks for complex RL tasks which require large amount of training data. We introduce a novel method to detect symmetries using reward trails observed during episodic experience and prove its completeness. We also provide a framework to incorporate the discovered symmetries for functional approximation. Finally we show that the use of potential based reward shaping is especially effect…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We prove performance guarantees of two algorithms for approximating $Q^\star$ in batch reinforcement learning. Compared to classical iterative methods such as Fitted Q-Iteration---whose performance loss incurs quadratic dependence on horizon---these methods estimate (some forms of) the Bellman error and enjoy linear-in-horizon error propagation, a property established for the first time for algorithms that rely solely on batch data and output stationary policies. One of the algorithms uses a novel and explicit importance-weighting correction to overcome the infamous "double sampling" difficult…
Continuous reinforcement learning such as DDPG and A3C are widely used in robot control and autonomous driving. However, both methods have theoretical weaknesses. While DDPG cannot control noises in the control process, A3C does not satisfy the continuity conditions under the Gaussian policy. To address these concerns, we propose a new continues reinforcement learning method based on stochastic differential equations and we call it Incremental Reinforcement Learning (IRL). This method not only guarantees the continuity of actions within any time interval, but controls the variance of actions i…
University of Toronto（多伦多大学）；New York University（纽约大学）；Vector Institute（向量研究所）
In this work, we propose to apply trust region optimization to deep reinforcement learning using a recently proposed Kronecker-factored approximation to the curvature. We extend the framework of natural policy gradient and propose to optimize both the actor and the critic using Kronecker-factored approximate curvature (K-FAC) with trust region; hence we call our method Actor Critic using Kronecker-Factored Trust Region (ACKTR). To the best of our knowledge, this is the first scalable trust region natural gradient method for actor-critic methods. It is also a method that learns non-trivial task…
In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or requirements such as verifiable safety guarantees, it may not be feasible to actually use such high-performing DNNs in practice. Many techniques have been developed in recent years to compress or distill complex DNNs into smaller, faster or more understandable models and controllers. This work seeks to identify reduced models that not only preserve a desired performanc…
Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited. One exception is Rowland et al. (2018)'s analysis of the C51 algorithm in terms of the Cramér distance, but their results only apply to the tabular setting and ignore C51's use of a softmax to produce normalized distributions. In this paper we adapt the Cramér distance to deal with arbitrary vectors. From it we derive a new distributional algorithm which is fully Cramér-based and can be combined to linear function approximation, with formal guarantees in …
Boston University（波士顿大学）；The University of Sydney（悉尼大学）
We consider the regret minimization problem in reinforcement learning (RL) in the episodic setting. In many real-world RL environments, the state and action spaces are continuous or very large. Existing approaches establish regret guarantees by either a low-dimensional representation of the stochastic transition model or an approximation of the $Q$-functions. However, the understanding of function approximation schemes for state-value functions largely remains missing. In this paper, we propose an online model-based RL algorithm, namely the CME-RL, that learns representations of transition dis…
Technion - Israel Institute of Technology（以色列理工学院）
We consider the problem of reinforcement learning using function approximation, where the approximating basis can change dynamically while interacting with the environment. A motivation for such an approach is maximizing the value function fitness to the problem faced. Three errors are considered: approximation square error, Bellman residual, and projected Bellman residual. Algorithms under the actor-critic framework are presented, and shown to converge. The advantage of such an adaptive basis is demonstrated in simulations.
National University of Ireland, Galway（爱尔兰国立大学戈尔韦分校）
Recent advances in combining deep neural network architectures with reinforcement learning techniques have shown promising potential results in solving complex control problems with high dimensional state and action spaces. Inspired by these successes, in this paper, we build two kinds of reinforcement learning algorithms: deep policy-gradient and value-function based agents which can predict the best possible traffic signal for a traffic intersection. At each time step, these adaptive traffic light control agents receive a snapshot of the current state of a graphical traffic simulator and pro…
The performance of a reinforcement learning (RL) system depends on the computational architecture used to approximate a value function. Deep learning methods provide both optimization techniques and architectures for approximating nonlinear functions from noisy, high-dimensional observations. However, prevailing optimization techniques are not designed for strictly-incremental online updates. Nor are standard architectures designed for observations with an a priori unknown structure: for example, light sensors randomly dispersed in space. This paper proposes an online RL prediction algorithm w…
