We begin by briefly surveying some results on the convergence of the Stochastic Gradient Descent (SGD) Method, proved in a companion paper by the present authors. These results are based on viewing SGD as a version of Stochastic Approximation (SA). Ever since its introduction in the classic paper of Robbins and Monro in 1951, SA has become a standard tool for finding a solution of an equation of the form $f(θ) = 0$, when only noisy measurements of $f(\cdot)$ are available. In most situations, \textit{every component} of the putative solution $θ_t$ is updated at each step $t$. In some applications in Reinforcement Learning (RL), \textit{only one component} of $θ_t$ is updated at each $t$. This is known as \textbf{asynchronous} SA. In this paper, we study \textbf{Block Asynchronous SA (BASA)}, in which, at each step $t$, \textit{some but not necessarily all} components of $θ_t$ are updated. The theory presented here embraces both conventional (synchronous) SA as well as asynchronous SA, and all in-between possibilities. We provide sufficient conditions for the convergence of BASA, and also prove bounds on the \textit{rate} of convergence of $θ_t$ to the solution. For the case of conventional SGD, these results reduce to those proved in our companion paper. Then we apply these results to the problem of finding a fixed point of a map with only noisy measurements. This problem arises frequently in RL. We prove sufficient conditions for convergence as well as estimates for the rate of convergence.
It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and -- in asynchronous implementations -- on the gradient staleness. Especially, it has been observed that the speedup saturates beyond a certain batch size and/or when the delays grow too large. We identify a data-dependent parameter that explains the speedup saturation in both these settings. Our comprehensive theoretical analysis, for strongly convex, convex and non-convex settings, unifies and generalized prior work directions that often focuse…
Significant progress has been made in the area of model-based reinforcement learning. State-of-the-art algorithms are now able to match the asymptotic performance of model-free methods while being significantly more data efficient. However, this success has come at a price: state-of-the-art model-based methods require significant computation interleaved with data collection, resulting in run times that take days, even if the amount of agent interaction might be just hours or even minutes. When considering the goal of learning in real-time on real robots, this means these state-of-the-art model…
University of Alberta（阿尔伯塔大学）；Alberta Machine Intelligence Institute（阿尔伯塔机器智能研究所）
Value iteration (VI) is a foundational dynamic programming method, important for learning and planning in optimal control and reinforcement learning. VI proceeds in batches, where the update to the value of each state must be completed before the next batch of updates can begin. Completing a single batch is prohibitively expensive if the state space is large, rendering VI impractical for many applications. Asynchronous VI helps to address the large state space problem by updating one state at a time, in-place and in an arbitrary order. However, Asynchronous VI still requires a maximization ove…
Southern University of Science and Technology（南方科技大学）；NetEase Games AI Lab（网易游戏人工智能实验室）
Despite the emerging progress of integrating evolutionary computation into reinforcement learning, the absence of a high-performance platform endowing composability and massive parallelism causes non-trivial difficulties for research and applications related to asynchronous commercial games. Here we introduce Lamarckian - an open-source platform featuring support for evolutionary reinforcement learning scalable to distributed computing resources. To improve the training speed and data efficiency, Lamarckian adopts optimized communication methods and an asynchronous evolutionary reinforcement l…
Mila, McGill University（麦吉尔大学米拉研究所）；Facebook（脸书）；Facebook AI Research（脸书人工智能研究院）
Widely-used deep reinforcement learning algorithms have been shown to fail in the batch setting--learning from a fixed data set without interaction with the environment. Following this result, there have been several papers showing reasonable performances under a variety of environments and batch settings. In this paper, we benchmark the performance of recent off-policy and batch reinforcement learning algorithms under unified settings on the Atari domain, with data generated by a single partially-trained behavioral policy. We find that under these conditions, many of these algorithms underper…
Google DeepMind（谷歌DeepMind）；Montreal Institute for Learning Algorithms (MILA)（蒙特利尔学习算法研究所（MILA））；University of Montreal（蒙特利尔大学）
We propose a conceptually simple and lightweight framework for deep reinforcement learning that uses asynchronous gradient descent for optimization of deep neural network controllers. We present asynchronous variants of four standard reinforcement learning algorithms and show that parallel actor-learners have a stabilizing effect on training allowing all four methods to successfully train neural network controllers. The best performing method, an asynchronous variant of actor-critic, surpasses the current state-of-the-art on the Atari domain while training for half the time on a single multi-c…
Stanford University（斯坦福大学）；Institute for Computational and Mathematical Engineering（计算与数学工程研究所）
Several practical applications of reinforcement learning involve an agent learning from past data without the possibility of further exploration. Often these applications require us to 1) identify a near optimal policy or to 2) estimate the value of a target policy. For both tasks we derive \emph{exponential} information-theoretic lower bounds in discounted infinite horizon MDPs with a linear function representation for the action value function even if 1) \emph{realizability} holds, 2) the batch algorithm observes the exact reward and transition \emph{functions}, and 3) the batch algorithm is…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；NVIDIA（英伟达）
We introduce a hybrid CPU/GPU version of the Asynchronous Advantage Actor-Critic (A3C) algorithm, currently the state-of-the-art method in reinforcement learning for various gaming tasks. We analyze its computational traits and concentrate on aspects critical to leveraging the GPU's computational power. We introduce a system of queues and a dynamic scheduling strategy, potentially helpful for other asynchronous algorithms as well. Our hybrid CPU/GPU version of A3C, based on TensorFlow, achieves a significant speed up compared to a CPU implementation; we make it publicly available to other rese…
The relationship between a reinforcement learning (RL) agent and an asynchronous environment is often ignored. Frequently used models of the interaction between an agent and its environment, such as Markov Decision Processes (MDP) or Semi-Markov Decision Processes (SMDP), do not capture the fact that, in an asynchronous environment, the state of the environment may change during computation performed by the agent. In an asynchronous environment, minimizing reaction time---the time it takes for an agent to react to an observation---also minimizes the time in which the state of the environment m…
Khoury College of Computer Sciences（库利计算机科学学院）；Northeastern University（东北大学）
Synchronizing decisions across multiple agents in realistic settings is problematic since it requires agents to wait for other agents to terminate and communicate about termination reliably. Ideally, agents should learn and execute asynchronously instead. Such asynchronous methods also allow temporally extended actions that can take different amounts of time based on the situation and action executed. Unfortunately, current policy gradient methods are not applicable in asynchronous settings, as they assume that agents synchronously reason about action selection at every time step. To allow asy…
The development of quantum machine learning (QML) has received a lot of interest recently thanks to developments in both quantum computing (QC) and machine learning (ML). One of the ML paradigms that can be utilized to address challenging sequential decision-making issues is reinforcement learning (RL). It has been demonstrated that classical RL can successfully complete many difficult tasks. A leading method of building quantum RL agents relies on the variational quantum circuits (VQC). However, training QRL algorithms with VQCs requires significant amount of computational resources. This iss…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Value-function approximation methods that operate in batch mode have foundational importance to reinforcement learning (RL). Finite sample guarantees for these methods often crucially rely on two types of assumptions: (1) mild distribution shift, and (2) representation conditions that are stronger than realizability. However, the necessity ("why do we need them?") and the naturalness ("when do they hold?") of such assumptions have largely eluded the literature. In this paper, we revisit these assumptions and provide theoretical results towards answering the above questions, and make steps towa…
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…
Iterative Learning Control-Informed Reinforcement Learning for Batch Process Control
State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University（工业控制技术国家重点实验室，系统与控制研究所，浙江大学）；Department of Chemical Engineering, Chung-Yuan Christian University（Chung-Yuan Christian University 化学工程系）
University of Southern California（南加州大学）；Intel Labs（英特尔实验室）
Increasing the scale of reinforcement learning experiments has allowed researchers to achieve unprecedented results in both training sophisticated agents for video games, and in sim-to-real transfer for robotics. Typically such experiments rely on large distributed systems and require expensive hardware setups, limiting wider access to this exciting area of research. In this work we aim to solve this problem by optimizing the efficiency and resource utilization of reinforcement learning algorithms instead of relying on distributed computation. We present the "Sample Factory", a high-throughput…
New York University Shanghai（上海纽约大学）；New York University（纽约大学）
There has recently been a surge in research in batch Deep Reinforcement Learning (DRL), which aims for learning a high-performing policy from a given dataset without additional interactions with the environment. We propose a new algorithm, Best-Action Imitation Learning (BAIL), which strives for both simplicity and performance. BAIL learns a V function, uses the V function to select actions it believes to be high-performing, and then uses those actions to train a policy network using imitation learning. For the MuJoCo benchmark, we provide a comprehensive experimental study of BAIL, comparing …
Indian Institute of Technology Delhi（印度理工学院德里分校）；International Institute of Information Technology Hyderabad（印度国际信息技术学院海得拉巴分校）；Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
Due to their complex nonlinear dynamics and batch-to-batch variability, batch processes pose a challenge for process control. Due to the absence of accurate models and resulting plant-model mismatch, these problems become harder to address for advanced model-based control strategies. Reinforcement Learning (RL), wherein an agent learns the policy by directly interacting with the environment, offers a potential alternative in this context. RL frameworks with actor-critic architecture have recently become popular for controlling systems where state and action spaces are continuous. It has been s…
Tsinghua University（清华大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
This paper proposes a \emph{fully asynchronous} scheme for the policy evaluation problem of distributed reinforcement learning (DisRL) over directed peer-to-peer networks. Without waiting for any other node of the network, each node can locally update its value function at any time by using (possibly delayed) information from its neighbors. This is in sharp contrast to the gossip-based scheme where a pair of nodes concurrently update. Though the fully asynchronous setting involves a difficult multi-timescale decision problem, we design a novel stochastic average gradient (SAG) based distribute…
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；Microsoft Research New York（微软纽约研究院）
We study a security threat to batch reinforcement learning and control where the attacker aims to poison the learned policy. The victim is a reinforcement learner / controller which first estimates the dynamics and the rewards from a batch data set, and then solves for the optimal policy with respect to the estimates. The attacker can modify the data set slightly before learning happens, and wants to force the learner into learning a target policy chosen by the attacker. We present a unified framework for solving batch policy poisoning attacks, and instantiate the attack on two standard victim…
University of Southern California（南加州大学）；Google Brain（谷歌大脑）
In principle, reinforcement learning and policy search methods can enable robots to learn highly complex and general skills that may allow them to function amid the complexity and diversity of the real world. However, training a policy that generalizes well across a wide range of real-world conditions requires far greater quantity and diversity of experience than is practical to collect with a single robot. Fortunately, it is possible for multiple robots to share their experience with one another, and thereby, learn a policy collectively. In this work, we explore distributed and asynchronous p…
University of Cambridge（剑桥大学）；Google DeepMind（谷歌DeepMind）；UC Berkeley（加州大学伯克利分校）
Reinforcement learning holds the promise of enabling autonomous robots to learn large repertoires of behavioral skills with minimal human intervention. However, robotic applications of reinforcement learning often compromise the autonomy of the learning process in favor of achieving training times that are practical for real physical systems. This typically involves introducing hand-engineered policy representations and human-supplied demonstrations. Deep reinforcement learning alleviates this limitation by training general-purpose neural network policies, but applications of direct deep reinf…
University of Alberta（阿尔伯塔大学）；Alberta Machine Intelligence Institute (Amii)（阿尔伯塔机器智能研究所（Amii））
An oft-ignored challenge of real-world reinforcement learning is that the real world does not pause when agents make learning updates. As standard simulated environments do not address this real-time aspect of learning, most available implementations of RL algorithms process environment interactions and learning updates sequentially. As a consequence, when such implementations are deployed in the real world, they may make decisions based on significantly delayed observations and not act responsively. Asynchronous learning has been proposed to solve this issue, but no systematic comparison betw…
We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel without interference of the global interpreter lock. As part of this project, we introduce BatchPPO, an effi…
College of Information and Computer Sciences, University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校信息与计算机科学学院）
Coagent policy gradient algorithms (CPGAs) are reinforcement learning algorithms for training a class of stochastic neural networks called coagent networks. In this work, we prove that CPGAs converge to locally optimal policies. Additionally, we extend prior theory to encompass asynchronous and recurrent coagent networks. These extensions facilitate the straightforward design and analysis of hierarchical reinforcement learning algorithms like the option-critic, and eliminate the need for complex derivations of customized learning rules for these algorithms.
McGill University（麦吉尔大学）；Mila Québec AI Institute（米拉魁北克人工智能研究所）
Many practical applications of reinforcement learning constrain agents to learn from a fixed batch of data which has already been gathered, without offering further possibility for data collection. In this paper, we demonstrate that due to errors introduced by extrapolation, standard off-policy deep reinforcement learning algorithms, such as DQN and DDPG, are incapable of learning with data uncorrelated to the distribution under the current policy, making them ineffective for this fixed batch setting. We introduce a novel class of off-policy algorithms, batch-constrained reinforcement learning…
National Taiwan University（国立台湾大学）；Academia Sinica（中央研究院）；Elan Corporation（Elan公司）
The goal of this work is to provide a viable solution based on reinforcement learning for traffic signal control problems. Although the state-of-the-art reinforcement learning approaches have yielded great success in a variety of domains, directly applying it to alleviate traffic congestion can be challenging, considering the requirement of high sample efficiency and how training data is gathered. In this work, we address several challenges that we encountered when we attempted to mitigate serious traffic congestion occurring in a metropolitan area. Specifically, we are required to provide a s…
The bus system is a critical component of sustainable urban transportation. However, due to the significant uncertainties in passenger demand and traffic conditions, bus operation is unstable in nature and bus bunching has become a common phenomenon that undermines the reliability and efficiency of bus services. Despite recent advances in multi-agent reinforcement learning (MARL) on traffic control, little research has focused on bus fleet control due to the tricky asynchronous characteristic -- control actions only happen when a bus arrives at a bus stop and thus agents do not act simultaneou…
This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance by (local) Rademacher complexities of general function classes, which makes initial steps in bridging the gap between statistical learning theory and batch RL. Concretely, we view the Bellman error as a surrogate loss for the optimality gap, and prove the followings: (1) In double sampling regime, the excess risk of Empirical Risk Minimizer (ERM) is bounded b…
Asynchronous Distributed Reinforcement Learning for LQR Control via Zeroth-Order Block Coordinate Descent
Chongqing University（重庆大学）；North Carolina State University（北卡罗来纳州立大学）；Oklahoma State University（俄克拉荷马州立大学）；DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室）
Batch reinforcement learning (RL) is important to apply RL algorithms to many high stakes tasks. Doing batch RL in a way that yields a reliable new policy in large domains is challenging: a new decision policy may visit states and actions outside the support of the batch data, and function approximation and optimization with limited samples can further increase the potential of learning policies with overly optimistic estimates of their future performance. Recent algorithms have shown promise but can still be overly optimistic in their expected outcomes. Theoretical work that provides strong g…
Amazon Web Services（亚马逊云科技）；University of Pennsylvania（宾夕法尼亚大学）
Reliant on too many experiments to learn good actions, current Reinforcement Learning (RL) algorithms have limited applicability in real-world settings, which can be too expensive to allow exploration. We propose an algorithm for batch RL, where effective policies are learned using only a fixed offline dataset instead of online interactions with the environment. The limited data in batch RL produces inherent uncertainty in value estimates of states/actions that were insufficiently represented in the training data. This leads to particularly severe extrapolation when our candidate policies dive…
Eindhoven University of Technology（埃因霍温理工大学）；Vanderlande Industries B.V.（范德兰德工业有限公司）
In e-commerce markets, on time delivery is of great importance to customer satisfaction. In this paper, we present a Deep Reinforcement Learning (DRL) approach for deciding how and when orders should be batched and picked in a warehouse to minimize the number of tardy orders. In particular, the technique facilitates making decisions on whether an order should be picked individually (pick-by-order) or picked in a batch with other orders (pick-by-batch), and if so with which other orders. We approach the problem by formulating it as a semi-Markov decision process and develop a vector-based state…
Most deep reinforcement learning (RL) systems are not able to learn effectively from off-policy data, especially if they cannot explore online in the environment. These are critical shortcomings for applying RL to real-world problems where collecting data is expensive, and models must be tested offline before being deployed to interact with the environment -- e.g. systems that learn from human interaction. Thus, we develop a novel class of off-policy batch RL algorithms, which are able to effectively learn offline, without exploring, from a fixed batch of human interaction data. We leverage mo…
Department of Applied Mathematics, Harvard University（哈佛大学应用数学系）；Department of Computer Science, Harvard University（哈佛大学计算机科学系）；Department of Statistics, Harvard University（哈佛大学统计学系）
In batch reinforcement learning, there can be poorly explored state-action pairs resulting in poorly learned, inaccurate models and poorly performing associated policies. Various regularization methods can mitigate the problem of learning overly-complex models in Markov decision processes (MDPs), however they operate in technically and intuitively distinct ways and lack a common form in which to compare them. This paper unifies three regularization methods in a common framework -- a weighted average transition matrix. Considering regularization methods in this common form illuminates how the M…
We propose a stochastic modified equations (SME) for modeling the asynchronous stochastic gradient descent (ASGD) algorithms. The resulting SME of Langevin type extracts more information about the ASGD dynamics and elucidates the relationship between different types of stochastic gradient algorithms. We show the convergence of ASGD to the SME in the continuous time limit, as well as the SME's precise prediction to the trajectories of ASGD with various forcing terms. As an application of the SME, we propose an optimal mini-batching strategy for ASGD via solving the optimal control problem of th…
Deep reinforcement learning, and especially the Asynchronous Advantage Actor-Critic algorithm, has been successfully used to achieve super-human performance in a variety of video games. Starcraft II is a new challenge for the reinforcement learning community with the release of pysc2 learning environment proposed by Google Deepmind and Blizzard Entertainment. Despite being a target for several AI developers, few have achieved human level performance. In this project we explain the complexities of this environment and discuss the results from our experiments on the environment. We have compared…
A shortcoming of batch reinforcement learning is its requirement for rewards in data, thus not applicable to tasks without reward functions. Existing settings for lack of reward, such as behavioral cloning, rely on optimal demonstrations collected from humans. Unfortunately, extensive expertise is required for ensuring optimality, which hinder the acquisition of large-scale data for complex tasks. This paper addresses the lack of reward in a batch reinforcement learning setting by learning a reward function from preferences. Generating preferences only requires a basic understanding of a task.…
We propose a novel approach to learn goal-conditioned policies for locomotion in a batch RL setting. The batch data is collected by a policy that is not goal-conditioned. For the locomotion task, this translates to data collection using a policy learnt by the agent for walking straight in one direction, and using that data to learn a goal-conditioned policy that enables the agent to walk in any direction. The data collection policy used should be invariant to the direction the agent is facing i.e. regardless of its initial orientation, the agent should take the same actions to walk forward. We…
Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；New York University（纽约大学）
Reinforcement learning algorithms have had tremendous successes in online learning settings. However, these successes have relied on low-stakes interactions between the algorithmic agent and its environment. In many settings where RL could be of use, such as health care and autonomous driving, the mistakes made by most online RL algorithms during early training come with unacceptable costs. These settings require developing reinforcement learning algorithms that can operate in the so-called batch setting, where the algorithms must learn from set of data that is fixed, finite, and generated fro…
University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校）；Google Research（谷歌研究院）；University of New Hampshire（新罕布什尔大学）
In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion, which minimizes the probability of a catastrophic failure. Unfortunately, such policies are typically overly conservative as the percentile criterion is non-convex, difficult to optimize, and ignores the mean performance. To overcome these shortcomings, we study the soft-robust criterion, which uses risk measures to balance the mean and percentile criterion better. In this paper, we establish the soft-robust criterion's fundamental p…
