Deep reinforcement learning (RL) algorithms have recently achieved remarkable successes in various sequential decision making tasks, leveraging advances in methods for training large deep networks. However, these methods usually require large amounts of training data, which is often a big problem for real-world applications. One natural question to ask is whether learning good representations for states and using larger networks helps in learning better policies. In this paper, we try to study if increasing input dimensionality helps improve performance and sample efficiency of model-free deep RL algorithms. To do so, we propose an online feature extractor network (OFENet) that uses neural nets to produce good representations to be used as inputs to deep RL algorithms. Even though the high dimensionality of input is usually supposed to make learning of RL agents more difficult, we show that the RL agents in fact learn more efficiently with the high-dimensional representation than with the lower-dimensional state observations. We believe that stronger feature propagation together with larger networks (and thus larger search space) allows RL agents to learn more complex functions of states and thus improves the sample efficiency. Through numerical experiments, we show that the proposed method outperforms several other state-of-the-art algorithms in terms of both sample efficiency and performance. Codes for the proposed method are available at http://www.merl.com/research/license/OFENet .
University of California Santa Barbara（加州大学圣巴巴拉分校）
A key limitation in using various modern methods of machine learning in developing feedback control policies is the lack of appropriate methodologies to analyze their long-term dynamics, in terms of making any sort of guarantees (even statistically) about robustness. The central reasons for this are largely due to the so-called curse of dimensionality, combined with the black-box nature of the resulting control policies themselves. This paper aims at the first of these issues. Although the full state space of a system may be quite large in dimensionality, it is a common feature of most model-b…
One problem in the application of reinforcement learning to real-world problems is the curse of dimensionality on the action space. Macro actions, a sequence of primitive actions, have been studied to diminish the dimensionality of the action space with regard to the time axis. However, previous studies relied on humans defining macro actions or assumed macro actions as repetitions of the same primitive actions. We present Factorized Macro Action Reinforcement Learning (FaMARL) which autonomously learns disentangled factor representation of a sequence of actions to generate macro actions that …
Overcoming the Curse of Dimensionality in Reinforcement Learning Through Approximate Factorization
Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Edwardson School of Industrial Engineering, Purdue University（普渡大学爱德华森工业工程学院）；School of Science and Engineering, CUHK Shenzhen（香港中文大学（深圳）理工学院）；Computing & Mathematical Sciences Department, Caltech（加州理工学院计算与数学科学系）
University of California, Berkeley（加州大学伯克利分校）；Université de Lorraine（洛林大学）；Inria（法国国家信息与自动化研究所）；IECL（IECL研究所）
In this paper, we investigate the sample complexity of policy evaluation in infinite-horizon offline reinforcement learning (also known as the off-policy evaluation problem) with linear function approximation. We identify a hard regime $dγ^{2}>1$, where $d$ is the dimension of the feature vector and $γ$ is the discount rate. In this regime, for any $q\in[γ^{2},1]$, we can construct a hard instance such that the smallest eigenvalue of its feature covariance matrix is $q/d$ and it requires $Ω\left(\frac{d}{γ^{2}\left(q-γ^{2}\right)\varepsilon^{2}}\exp\left(Θ\left(dγ^{2}\right)\right)\right)$ sam…
There have been numerous advances in reinforcement learning, but the typically unconstrained exploration of the learning process prevents the adoption of these methods in many safety critical applications. Recent work in safe reinforcement learning uses idealized models to achieve their guarantees, but these models do not easily accommodate the stochasticity or high-dimensionality of real world systems. We investigate how prediction provides a general and intuitive framework to constraint exploration, and show how it can be used to safely learn intersection handling behaviors on an autonomous …
Mobile robot navigation in complex and dynamic environments is a challenging but important problem. Reinforcement learning approaches fail to solve these tasks efficiently due to reward sparsities, temporal complexities and high-dimensionality of sensorimotor spaces which are inherent in such problems. We present a novel approach to train action policies to acquire navigation skills for wheel-legged robots using deep reinforcement learning. The policy maps height-map image observations to motor commands to navigate to a target position while avoiding obstacles. We propose to acquire the multif…
Black-box optimizers that explore in parameter space have often been shown to outperform more sophisticated action space exploration methods developed specifically for the reinforcement learning problem. We examine these black-box methods closely to identify situations in which they are worse than action space exploration methods and those in which they are superior. Through simple theoretical analyses, we prove that complexity of exploration in parameter space depends on the dimensionality of parameter space, while complexity of exploration in action space depends on both the dimensionality o…
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…
We consider the problem of learning to optimize an unknown Markov decision process (MDP). We show that, if the MDP can be parameterized within some known function class, we can obtain regret bounds that scale with the dimensionality, rather than cardinality, of the system. We characterize this dependence explicitly as $\tilde{O}(\sqrt{d_K d_E T})$ where $T$ is time elapsed, $d_K$ is the Kolmogorov dimension and $d_E$ is the \emph{eluder dimension}. These represent the first unified regret bounds for model-based reinforcement learning and provide state of the art guarantees in several important…
London School of Economics and Political Science（伦敦政治经济学院）；North Carolina State University（北卡罗来纳州立大学）；Didi Chuxi（滴滴出行）
The two-sided markets such as ride-sharing companies often involve a group of subjects who are making sequential decisions across time and/or location. With the rapid development of smart phones and internet of things, they have substantially transformed the transportation landscape of human beings. In this paper we consider large-scale fleet management in ride-sharing companies that involve multiple units in different areas receiving sequences of products (or treatments) over time. Major technical challenges, such as policy evaluation, arise in those studies because (i) spatial and temporal p…
University California, Irvine（加州大学欧文分校）；Facebook AI Research (FAIR)（Facebook人工智能研究院）；California institute of technology（加州理工学院）
Reinforcement learning (RL) in Markov decision processes (MDPs) with large state spaces is a challenging problem. The performance of standard RL algorithms degrades drastically with the dimensionality of state space. However, in practice, these large MDPs typically incorporate a latent or hidden low-dimensional structure. In this paper, we study the setting of rich-observation Markov decision processes (ROMDP), where there are a small number of hidden states which possess an injective mapping to the observation states. In other words, every observation state is generated through a single hidde…
Any reinforcement learning algorithm that applies to all Markov decision processes (MDPs) will suffer $Ω(\sqrt{SAT})$ regret on some MDP, where $T$ is the elapsed time and $S$ and $A$ are the cardinalities of the state and action spaces. This implies $T = Ω(SA)$ time to guarantee a near-optimal policy. In many settings of practical interest, due to the curse of dimensionality, $S$ and $A$ can be so enormous that this learning time is unacceptable. We establish that, if the system is known to be a \emph{factored} MDP, it is possible to achieve regret that scales polynomially in the number of \e…
Indian Institute of Technology Bombay（印度理工学院孟买分校）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）
To overcome the curses of dimensionality and modeling of Dynamic Programming (DP) methods to solve Markov Decision Process (MDP) problems, Reinforcement Learning (RL) methods are adopted in practice. Contrary to traditional RL algorithms which do not consider the structural properties of the optimal policy, we propose a structure-aware learning algorithm to exploit the ordered multi-threshold structure of the optimal policy, if any. We prove the asymptotic convergence of the proposed algorithm to the optimal policy. Due to the reduction in the policy space, the proposed algorithm provides rema…
Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）
In this article, we sketch an algorithm that extends the Q-learning algorithms to the continuous action space domain. Our method is based on the discretization of the action space. Despite the commonly used discretization methods, our method does not increase the discretized problem dimensionality exponentially. We will show that our proposed method is linear in complexity when the discretization is employed. The variant of the Q-learning algorithm presented in this work, labeled as Finite Step Q-Learning (FSQ), can be deployed to both shallow and deep neural network architectures.
University Pompeu Fabra（庞培法布拉大学）；Universitat Pompeu Fabra（庞培法布拉大学）
When playing video-games we immediately detect which entity we control and we center the attention towards it to focus the learning and reduce its dimensionality. Reinforcement Learning (RL) has been able to deal with big state spaces, including states derived from pixel images in Atari games, but the learning is slow, depends on the brute force mapping from the global state to the action values (Q-function), thus its performance is severely affected by the dimensionality of the state and cannot be transferred to other games or other parts of the same game. We propose different transformations…
We introduce a distributional method for learning the optimal policy in risk averse Markov decision process with finite state action spaces, latent costs, and stationary dynamics. We assume sequential observations of states, actions, and costs and assess the performance of a policy using dynamic risk measures constructed from nested Kusuoka-type conditional risk mappings. For such performance criteria, randomized policies may outperform deterministic policies, therefore, the candidate policies lie in the d-dimensional simplex where d is the cardinality of the action space. Existing risk averse…
In real-world applications of reinforcement learning (RL), noise from inherent stochasticity of environments is inevitable. However, current policy evaluation algorithms, which plays a key role in many RL algorithms, are either prone to noise or inefficient. To solve this issue, we introduce a novel policy evaluation algorithm, which we call Gap-increasing RetrAce Policy Evaluation (GRAPE). It leverages two recent ideas: (1) gap-increasing value update operators in advantage learning for noise-tolerance and (2) off-policy eligibility trace in Retrace algorithm for efficient learning. We provid…
The Technion - Israel Institute of Technology（以色列理工学院）；National University of Singapore（新加坡国立大学）
We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handle uncertainty, can be solved using dynamic programming for small to medium sized problems. However, due to the "curse of dimensionality", MDPs that model real-life problems are typically prohibitively large for such approaches. In this work we employ a reinforcement learning approach to tackle this planning problem: we develop a robust approximate dynamic programming method based on a projected fixed po…
Reinforcement learning is well-studied under discrete actions. Integer actions setting is popular in the industry yet still challenging due to its high dimensionality. To this end, we study reinforcement learning under integer actions by incorporating the Soft Actor-Critic (SAC) algorithm with an integer reparameterization. Our key observation for integer actions is that their discrete structure can be simplified using their comparability property. Hence, the proposed integer reparameterization does not need one-hot encoding and is of low dimensionality. Experiments show that the proposed SAC …
GRASP Laboratory（GRASP实验室）；University of Pennsylvania（宾夕法尼亚大学）
In this paper, we explore using deep reinforcement learning for problems with multiple agents. Most existing methods for deep multi-agent reinforcement learning consider only a small number of agents. When the number of agents increases, the dimensionality of the input and control spaces increase as well, and these methods do not scale well. To address this, we propose casting the multi-agent reinforcement learning problem as a distributed optimization problem. Our algorithm assumes that for multi-agent settings, policies of individual agents in a given population live close to each other in p…
Recent advances in reinforcement learning have shown its potential to tackle complex real-life tasks. However, as the dimensionality of the task increases, reinforcement learning methods tend to struggle. To overcome this, we explore methods for representing the semantic information embedded in the state. While previous methods focused on information in its raw form (e.g., raw visual input), we propose to represent the state using natural language. Language can represent complex scenarios and concepts, making it a favorable candidate for representation. Empirical evidence, within the domain of…
Manipulating deformable objects has long been a challenge in robotics due to its high dimensional state representation and complex dynamics. Recent success in deep reinforcement learning provides a promising direction for learning to manipulate deformable objects with data driven methods. However, existing reinforcement learning benchmarks only cover tasks with direct state observability and simple low-dimensional dynamics or with relatively simple image-based environments, such as those with rigid objects. In this paper, we present SoftGym, a set of open-source simulated benchmarks for manipu…
With the decreasing cost of data collection, the space of variables or features that can be used to characterize a particular predictor of interest continues to grow exponentially. Therefore, identifying the most characterizing features that minimizes the variance without jeopardizing the bias of our models is critical to successfully training a machine learning model. In addition, identifying such features is critical for interpretability, prediction accuracy and optimal computation cost. While statistical methods such as subset selection, shrinkage, dimensionality reduction have been applied…
Multiagent reinforcement learning algorithms (MARL) have been demonstrated on complex tasks that require the coordination of a team of multiple agents to complete. Existing works have focused on sharing information between agents via centralized critics to stabilize learning or through communication to increase performance, but do not generally look at how information can be shared between agents to address the curse of dimensionality in MARL. We posit that a multiagent problem can be decomposed into a multi-task problem where each agent explores a subset of the state space instead of explorin…
Wuhan University（武汉大学）；JD Explore Academy（京东探索研究院）；University of Maryland, College Park（马里兰大学学院市分校）
Deep reinforcement learning (RL) has shown remarkable success in specific offline decision-making scenarios, yet its theoretical guarantees are still under development. Existing works on offline RL theory primarily emphasize a few trivial settings, such as linear MDP or general function approximation with strong assumptions and independent data, which lack guidance for practical use. The coupling of deep learning and Bellman residuals makes this problem challenging, in addition to the difficulty of data dependence. In this paper, we establish a non-asymptotic estimation error of pessimistic of…
University of California, Santa Barbara（加州大学圣巴巴拉分校）
Researchers have demonstrated that Deep Reinforcement Learning (DRL) is a powerful tool for finding policies that perform well on complex robotic systems. However, these policies are often unpredictable and can induce highly variable behavior when evaluated with only slightly different initial conditions. Training considerations constrain DRL algorithm designs in that most algorithms must use stochastic policies during training. The resulting policy used during deployment, however, can and frequently is a deterministic one that uses the Maximum Likelihood Action (MLA) at each step. In this wor…
Google Research（谷歌研究院）；UT Austin（德克萨斯大学奥斯汀分校）；UC Berkeley（加州大学伯克利分校）；University of Alberta（阿尔伯塔大学）；Georgia Tech（佐治亚理工学院）
Representation learning often plays a critical role in reinforcement learning by managing the curse of dimensionality. A representative class of algorithms exploits a spectral decomposition of the stochastic transition dynamics to construct representations that enjoy strong theoretical properties in an idealized setting. However, current spectral methods suffer from limited applicability because they are constructed for state-only aggregation and derived from a policy-dependent transition kernel, without considering the issue of exploration. To address these issues, we propose an alternative s…
University of California, Berkeley（加州大学伯克利分校）；Ghent University（根特大学）；OpenAI
Recently, researchers have made significant progress combining the advances in deep learning for learning feature representations with reinforcement learning. Some notable examples include training agents to play Atari games based on raw pixel data and to acquire advanced manipulation skills using raw sensory inputs. However, it has been difficult to quantify progress in the domain of continuous control due to the lack of a commonly adopted benchmark. In this work, we present a benchmark suite of continuous control tasks, including classic tasks like cart-pole swing-up, tasks with very high st…
We address the problem of safe reinforcement learning from pixel observations. Inherent challenges in such settings are (1) a trade-off between reward optimization and adhering to safety constraints, (2) partial observability, and (3) high-dimensional observations. We formalize the problem in a constrained, partially observable Markov decision process framework, where an agent obtains distinct reward and safety signals. To address the curse of dimensionality, we employ a novel safety critic using the stochastic latent actor-critic (SLAC) approach. The latent variable model predicts rewards and…
University of California, Irvine（加利福尼亚大学欧文分校）；INRIA, France（法国国家信息与自动化研究所）
We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive) latent variable models such as hidden Markov models, POMDPs are more challenging since the learner interacts with the environment and possibly changes the future observations in the process. We devise a learning algorithm running through epochs, in each epoch we employ spectral techniques to learn the POMDP parameters from a trajectory generated by a fixed p…
Multi-Agent Reinforcement Learning (MARL) is a challenging subarea of Reinforcement Learning due to the non-stationarity of the environments and the large dimensionality of the combined action space. Deep MARL algorithms have been applied to solve different task offloading problems. However, in real-world applications, information required by the agents (i.e. rewards and states) are subject to noise and alterations. The stability and the robustness of deep MARL to practical challenges is still an open research problem. In this work, we apply state-of-the art MARL algorithms to solve task offlo…
Teams of autonomous unmanned aircraft can be used to monitor wildfires, enabling firefighters to make informed decisions. However, controlling multiple autonomous fixed-wing aircraft to maximize forest fire coverage is a complex problem. The state space is high dimensional, the fire propagates stochastically, the sensor information is imperfect, and the aircraft must coordinate with each other to accomplish their mission. This work presents two deep reinforcement learning approaches for training decentralized controllers that accommodate the high dimensionality and uncertainty inherent in the …
Task-Agnostic Continual Reinforcement Learning: Gaining Insights and Overcoming Challenges
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）；Cleanlab；Seoul National University（首尔国立大学）；HEC Montréal（蒙特利尔高等商学院）；Canada CIFAR AI Chair（加拿大CIFAR人工智能讲席）；Amazon Web Services（亚马逊云科技）
We consider the problem of Reinforcement Learning for nonlinear stochastic dynamical systems. We show that in the RL setting, there is an inherent ``Curse of Variance" in addition to Bellman's infamous ``Curse of Dimensionality", in particular, we show that the variance in the solution grows factorial-exponentially in the order of the approximation. A fundamental consequence is that this precludes the search for anything other than ``local" feedback solutions in RL, in order to control the explosive variance growth, and thus, ensure accuracy. We further show that the deterministic optimal cont…
Exploration in reinforcement learning (RL) suffers from the curse of dimensionality when the state-action space is large. A common practice is to parameterize the high-dimensional value and policy functions using given features. However existing methods either have no theoretical guarantee or suffer a regret that is exponential in the planning horizon $H$. In this paper, we propose an online RL algorithm, namely the MatrixRL, that leverages ideas from linear bandit to learn a low-dimensional representation of the probability transition model while carefully balancing the exploitation-explorati…
Maximum entropy deep reinforcement learning (RL) methods have been demonstrated on a range of challenging continuous tasks. However, existing methods either suffer from severe instability when training on large off-policy data or cannot scale to tasks with very high state and action dimensionality such as 3D humanoid locomotion. Besides, the optimality of desired Boltzmann policy set for non-optimal soft value function is not persuasive enough. In this paper, we first derive soft policy gradient based on entropy regularized expected reward objective for RL with continuous actions. Then, we pre…
Parameter space exploration methods with black-box optimization have recently been shown to outperform state-of-the-art approaches in continuous control reinforcement learning domains. In this paper, we examine reasons why these methods work better and the situations in which they are worse than traditional action space exploration methods. Through a simple theoretical analysis, we show that when the parametric complexity required to solve the reinforcement learning problem is greater than the product of action space dimensionality and horizon length, exploration in action space is preferred. …
University of Georgia（佐治亚大学）；University of Southern Mississippi（南密西西比大学）
Recent renewed interest in multi-agent reinforcement learning (MARL) has generated an impressive array of techniques that leverage deep reinforcement learning, primarily actor-critic architectures, and can be applied to a limited range of settings in terms of observability and communication. However, a continuing limitation of much of this work is the curse of dimensionality when it comes to representations based on joint actions, which grow exponentially with the number of agents. In this paper, we squarely focus on this challenge of scalability. We apply the key insight of action anonymity, …
We consider the problem of providing users of deep Reinforcement Learning (RL) based systems with a better understanding of when their output can be trusted. We offer an explainable artificial intelligence (XAI) framework that provides a three-fold explanation: a graphical depiction of the systems generalization and performance in the current game state, how well the agent would play in semantically similar environments, and a narrative explanation of what the graphical information implies. We created a user-interface for our XAI framework and evaluated its efficacy via a human-user experiment…
Department of Statistics, University of Oxford（牛津大学统计系）
Cooperative multi-agent reinforcement learning is a decentralized paradigm in sequential decision making where agents distributed over a network iteratively collaborate with neighbors to maximize global (network-wide) notions of rewards. Exact computations typically involve a complexity that scales exponentially with the number of agents. To address this curse of dimensionality, we design a scalable algorithm based on the Natural Policy Gradient framework that uses local information and only requires agents to communicate with neighbors within a certain range. Under standard assumptions on the…
TU Kaiserslautern（凯泽斯劳滕工业大学）；German Research Center for Artificial Intelligence（德国人工智能研究中心）
The problem of finding K-nearest neighbors in the given dataset for a given query point has been worked upon since several years. In very high dimensional spaces the K-nearest neighbor search (KNNS) suffers in terms of complexity in computation of high dimensional distances. With the issue of curse of dimensionality, it gets quite tedious to reliably bank on the results of variety approximate nearest neighbor search approaches. In this paper, we survey some novel K-Nearest Neighbor Search approaches that tackles the problem of Search from the perspectives of computations, the accuracy of appro…
OpenAI；University of California, Berkeley（加州大学伯克利分校）
Exploration in environments with sparse rewards has been a persistent problem in reinforcement learning (RL). Many tasks are natural to specify with a sparse reward, and manually shaping a reward function can result in suboptimal performance. However, finding a non-zero reward is exponentially more difficult with increasing task horizon or action dimensionality. This puts many real-world tasks out of practical reach of RL methods. In this work, we use demonstrations to overcome the exploration problem and successfully learn to perform long-horizon, multi-step robotics tasks with continuous con…
Inverse reinforcement learning (IRL) seeks to infer a cost function that explains the underlying goals and preferences of expert demonstrations. This paper presents receding horizon inverse reinforcement learning (RHIRL), a new IRL algorithm for high-dimensional, noisy, continuous systems with black-box dynamic models. RHIRL addresses two key challenges of IRL: scalability and robustness. To handle high-dimensional continuous systems, RHIRL matches the induced optimal trajectories with expert demonstrations locally in a receding horizon manner and 'stitches' together the local solutions to lea…
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 surveys the field of deep multiagent reinforcement learning. The combination of deep neural networks with reinforcement learning has gained increased traction in recent years and is slowly shifting the focus from single-agent to multiagent environments. Dealing with multiple agents is inherently more complex as (a) the future rewards depend on multiple players' joint actions and (b) the computational complexity increases. We present the most common multiagent problem representations and their main challenges, and identify five research areas that address one or more of these challen…
