Reinforcement learning is a general technique that allows an agent to learn an optimal policy and interact with an environment in sequential decision making problems. The goodness of a policy is measured by its value function starting from some initial state. The focus of this paper is to construct confidence intervals (CIs) for a policy's value in infinite horizon settings where the number of decision points diverges to infinity. We propose to model the action-value state function (Q-function) associated with a policy based on series/sieve method to derive its confidence interval. When the target policy depends on the observed data as well, we propose a SequentiAl Value Evaluation (SAVE) method to recursively update the estimated policy and its value estimator. As long as either the number of trajectories or the number of decision points diverges to infinity, we show that the proposed CI achieves nominal coverage even in cases where the optimal policy is not unique. Simulation studies are conducted to back up our theoretical findings. We apply the proposed method to a dataset from mobile health studies and find that reinforcement learning algorithms could help improve patient's health status. A Python implementation of the proposed procedure is available at https://github.com/shengzhang37/SAVE.
Carnegie Mellon University（卡内基梅隆大学）；Georgia Institute of Technology（佐治亚理工学院）
In this paper, we propose to combine imitation and reinforcement learning via the idea of reward shaping using an oracle. We study the effectiveness of the near-optimal cost-to-go oracle on the planning horizon and demonstrate that the cost-to-go oracle shortens the learner's planning horizon as function of its accuracy: a globally optimal oracle can shorten the planning horizon to one, leading to a one-step greedy Markov Decision Process which is much easier to optimize, while an oracle that is far away from the optimality requires planning over a longer horizon to achieve near-optimal perfor…
Carnegie Mellon University（卡内基梅隆大学）；Institute for Advanced Study（高等研究院）；University of California, Los Angles（加州大学洛杉矶分校）；University of Washington, Seattle（华盛顿大学西雅图分校）；Microsoft Research（微软研究院）
Learning to plan for long horizons is a central challenge in episodic reinforcement learning problems. A fundamental question is to understand how the difficulty of the problem scales as the horizon increases. Here the natural measure of sample complexity is a normalized one: we are interested in the number of episodes it takes to provably discover a policy whose value is $\varepsilon$ near to that of the optimal value, where the value is measured by the normalized cumulative reward in each episode. In a COLT 2018 open problem, Jiang and Agarwal conjectured that, for tabular, episodic reinforc…
Tsinghua University（清华大学）；University of Washington（华盛顿大学）
Episodic reinforcement learning and contextual bandits are two widely studied sequential decision-making problems. Episodic reinforcement learning generalizes contextual bandits and is often perceived to be more difficult due to long planning horizon and unknown state-dependent transitions. The current paper shows that the long planning horizon and the unknown state-dependent transitions (at most) pose little additional difficulty on sample complexity. We consider the episodic reinforcement learning with $S$ states, $A$ actions, planning horizon $H$, total reward bounded by $1$, and the agent …
In this paper we present Horizon, Facebook's open source applied reinforcement learning (RL) platform. Horizon is an end-to-end platform designed to solve industry applied RL problems where datasets are large (millions to billions of observations), the feedback loop is slow (vs. a simulator), and experiments must be done with care because they don't run in a simulator. Unlike other RL platforms, which are often designed for fast prototyping and experimentation, Horizon is designed with production use cases as top of mind. The platform contains workflows to train popular deep RL algorithms and …
We present relay policy learning, a method for imitation and reinforcement learning that can solve multi-stage, long-horizon robotic tasks. This general and universally-applicable, two-phase approach consists of an imitation learning stage that produces goal-conditioned hierarchical policies, and a reinforcement learning phase that finetunes these policies for task performance. Our method, while not necessarily perfect at imitation learning, is very amenable to further improvement via environment interaction, allowing it to scale to challenging long-horizon tasks. We simplify the long-horizon …
University of Alberta（阿尔伯塔大学）；Carnegie Mellon University（卡内基梅隆大学）；Google Brain（谷歌大脑）
Despite its potential to improve sample complexity versus model-free approaches, model-based reinforcement learning can fail catastrophically if the model is inaccurate. An algorithm should ideally be able to trust an imperfect model over a reasonably long planning horizon, and only rely on model-free updates when the model errors get infeasibly large. In this paper, we investigate techniques for choosing the planning horizon on a state-dependent basis, where a state's planning horizon is determined by the maximum cumulative model error around that state. We demonstrate that these state-depend…
Model-free reinforcement learning is known to be memory and computation efficient and more amendable to large scale problems. In this paper, two model-free algorithms are introduced for learning infinite-horizon average-reward Markov Decision Processes (MDPs). The first algorithm reduces the problem to the discounted-reward version and achieves $\mathcal{O}(T^{2/3})$ regret after $T$ steps, under the minimal assumption of weakly communicating MDPs. To our knowledge, this is the first model-free algorithm for general MDPs in this setting. The second algorithm makes use of recent advances in ada…
Off-policy evaluation (OPE) in reinforcement learning is an important problem in settings where experimentation is limited, such as education and healthcare. But, in these very same settings, observed actions are often confounded by unobserved variables making OPE even more difficult. We study an OPE problem in an infinite-horizon, ergodic Markov decision process with unobserved confounders, where states and actions can act as proxies for the unobserved confounders. We show how, given only a latent variable model for states and actions, policy value can be identified from off-policy data. Our …
University of Alberta（阿尔伯塔大学）；University of Toronto（多伦多大学）；Huawei Technologies Canada, Ltd.（加拿大华为技术有限公司）
We explore fixed-horizon temporal difference (TD) methods, reinforcement learning algorithms for a new kind of value function that predicts the sum of rewards over a $\textit{fixed}$ number of future time steps. To learn the value function for horizon $h$, these algorithms bootstrap from the value function for horizon $h-1$, or some shorter horizon. Because no value function bootstraps from itself, fixed-horizon methods are immune to the stability problems that plague other off-policy TD methods using function approximation (also known as "the deadly triad"). Although fixed-horizon methods req…
Recent studies have shown that episodic reinforcement learning (RL) is not more difficult than contextual bandits, even with a long planning horizon and unknown state transitions. However, these results are limited to either tabular Markov decision processes (MDPs) or computationally inefficient algorithms for linear mixture MDPs. In this paper, we propose the first computationally efficient horizon-free algorithm for linear mixture MDPs, which achieves the optimal $\tilde O(d\sqrt{K} +d^2)$ regret up to logarithmic factors. Our algorithm adapts a weighted least square estimator for the unknow…
University of Torontoland（多伦多兰大学）；University of Edenborrow（伊登伯勒大学）
Off-policy evaluation of sequential decision policies from observational data is necessary in applications of batch reinforcement learning such as education and healthcare. In such settings, however, unobserved variables confound observed actions, rendering exact evaluation of new policies impossible, i.e., unidentifiable. We develop a robust approach that estimates sharp bounds on the (unidentifiable) value of a given policy in an infinite-horizon problem given data from another policy with unobserved confounding, subject to a sensitivity model. We consider stationary or baseline unobserved c…
EDF R&D（法国电力公司研发部）；FIME（FIME实验室）；University of California, Berkeley（加州大学伯克利分校）；University of Oxford（牛津大学）
We study finite-time horizon continuous-time linear-quadratic reinforcement learning problems in an episodic setting, where both the state and control coefficients are unknown to the controller. We first propose a least-squares algorithm based on continuous-time observations and controls, and establish a logarithmic regret bound of order $O((\ln M)(\ln\ln M))$, with $M$ being the number of learning episodes. The analysis consists of two parts: perturbation analysis, which exploits the regularity and robustness of the associated Riccati differential equation; and parameter estimation error, whi…
Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an interactive learning agent operates for a fixed or bounded period of time, for example tutoring students for exams or handling customer service requests. Such scenarios can often be better treated as episodic fixed-horizon MDPs, for which only looser bounds on the sample complexity exist. A natural notion of sample complexity in this setting is the number of …
Hierarchical Soft Actor-Critic for Sparse-Reward Long-Horizon Reinforcement Learning
National Engineering School of Tunis, University of Tunis El Manar（突尼斯艾尔玛纳尔大学突尼斯国立工程师学校）；University of Tripoli（的黎波里大学）；University of Picardie Jules Verne Amiens（亚眠皮卡第朱尔斯·凡尔纳大学）
University of Toronto（多伦多大学）；Vector Institute（Vector研究所）
What goals should a multi-goal reinforcement learning agent pursue during training in long-horizon tasks? When the desired (test time) goal distribution is too distant to offer a useful learning signal, we argue that the agent should not pursue unobtainable goals. Instead, it should set its own intrinsic goals that maximize the entropy of the historical achieved goal distribution. We propose to optimize this objective by having the agent pursue past achieved goals in sparsely explored areas of the goal space, which focuses exploration on the frontier of the achievable goal set. We show that ou…
Off-policy estimation for long-horizon problems is important in many real-life applications such as healthcare and robotics, where high-fidelity simulators may not be available and on-policy evaluation is expensive or impossible. Recently, \cite{liu18breaking} proposed an approach that avoids the \emph{curse of horizon} suffered by typical importance-sampling-based methods. While showing promising results, this approach is limited in practice as it requires data be drawn from the \emph{stationary distribution} of a \emph{known} behavior policy. In this work, we propose a novel approach that el…
Tsinghua University（清华大学）；University of Washington（华盛顿大学）
This paper gives the first polynomial-time algorithm for tabular Markov Decision Processes (MDP) that enjoys a regret bound \emph{independent on the planning horizon}. Specifically, we consider tabular MDP with $S$ states, $A$ actions, a planning horizon $H$, total reward bounded by $1$, and the agent plays for $K$ episodes. We design an algorithm that achieves an $O\left(\mathrm{poly}(S,A,\log K)\sqrt{K}\right)$ regret in contrast to existing bounds which either has an additional $\mathrm{polylog}(H)$ dependency~\citep{zhang2020reinforcement} or has an exponential dependency on $S$~\citep{li2…
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）
Recently there is a surge of interest in understanding the horizon-dependence of the sample complexity in reinforcement learning (RL). Notably, for an RL environment with horizon length $H$, previous work have shown that there is a probably approximately correct (PAC) algorithm that learns an $O(1)$-optimal policy using $\mathrm{polylog}(H)$ episodes of environment interactions when the number of states and actions is fixed. It is yet unknown whether the $\mathrm{polylog}(H)$ dependence is necessary or not. In this work, we resolve this question by developing an algorithm that achieves the sam…
Seoul National University（首尔国立大学）；Artificial Intelligence Institute of Seoul National University (AIIS)（首尔国立大学人工智能研究所（AIIS））；Automation and Systems Research Institute (ASRI)（自动化与系统研究所（ASRI））
Hierarchical Reinforcement Learning (HRL) has made notable progress in complex control tasks by leveraging temporal abstraction. However, previous HRL algorithms often suffer from serious data inefficiency as environments get large. The extended components, $i.e.$, goal space and length of episodes, impose a burden on either one or both high-level and low-level policies since both levels share the total horizon of the episode. In this paper, we present a method of Decoupling Horizons Using a Graph in Hierarchical Reinforcement Learning (DHRL) which can alleviate this problem by decoupling the …
Off-policy evaluation (OPE) in reinforcement learning is notoriously difficult in long- and infinite-horizon settings due to diminishing overlap between behavior and target policies. In this paper, we study the role of Markovian and time-invariant structure in efficient OPE. We first derive the efficiency bounds for OPE when one assumes each of these structures. This precisely characterizes the curse of horizon: in time-variant processes, OPE is only feasible in the near-on-policy setting, where behavior and target policies are sufficiently similar. But, in time-invariant Markov decision proce…
Stanford University（斯坦福大学）；New York University（纽约大学）
We establish that an optimistic variant of Q-learning applied to a fixed-horizon episodic Markov decision process with an aggregated state representation incurs regret $\tilde{\mathcal{O}}(\sqrt{H^5 M K} + εHK)$, where $H$ is the horizon, $M$ is the number of aggregate states, $K$ is the number of episodes, and $ε$ is the largest difference between any pair of optimal state-action values associated with a common aggregate state. Notably, this regret bound does not depend on the number of states or actions and indicates that asymptotic per-period regret is no greater than $ε$, independent of ho…
Indian Institute of Technology (BHU)（印度理工学院（贝拿勒斯印度教大学））；Indian Institute of Technology, Hyderabad（印度理工学院海得拉巴分校）
We consider the finite horizon continuous reinforcement learning problem. Our contribution is three-fold. First,we give a tractable algorithm based on optimistic value iteration for the problem. Next,we give a lower bound on regret of order $Ω(T^{2/3})$ for any algorithm discretizes the state space, improving the previous regret bound of $Ω(T^{1/2})$ of Ortner and Ryabko \cite{contrl} for the same problem. Next,under the assumption that the rewards and transitions are Hölder Continuous we show that the upper bound on the discretization error is $const.Ln^{-α}T$. Finally,we give some simple exp…
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…
Offline Reinforcement Learning with Universal Horizon Models
Interdisciplinary Program in Artificial Intelligence and ASRI, Seoul National University（人工智能交叉学科项目及首尔国立大学ASRI）；Department of Electrical and Computer Engineering, Seoul National University（电气与计算机工程系，首尔国立大学）
We study session-based recommendation scenarios where we want to recommend items to users during sequential interactions to improve their long-term utility. Optimizing a long-term metric is challenging because the learning signal (whether the recommendations achieved their desired goals) is delayed and confounded by other user interactions with the system. Targeting immediately measurable proxies such as clicks can lead to suboptimal recommendations due to misalignment with the long-term metric. We develop a new reinforcement learning algorithm called Short Horizon Policy Improvement (SHPI) th…
This paper investigates the problem of bounding possible output from a counterfactual query given a set of observational data. While various works of literature have described methodologies to generate efficient algorithms that provide an optimal bound for the counterfactual query, all of them assume a finite-horizon causal diagram. This paper aims to extend the previous work by modifying Q-learning algorithm to provide informative bounds of a causal query given an infinite-horizon causal diagram. Through simulations, our algorithms are proven to perform better compared to existing algorithm.
SPLASH! Sample-efficient Preference-based inverse reinforcement learning for Long-horizon Adversarial tasks from Suboptimal Hierarchical demonstrations
Boston University（波士顿大学）；MIT Lincoln Laboratory（麻省理工学院林肯实验室）；MIT Pavlab（麻省理工学院 Pavlab 实验室）；Woods Hole Oceanographic Institution（伍兹霍尔海洋研究所）；University of Maryland, College Park（马里兰大学学院公园分校）
SINTEF Digital（SINTEF数字研究院）；Department of Engineering Cybernetics, NTNU（挪威科技大学工程控制论系）；Centre for Autonomous Marine Operations and Systems（自主海洋作业与系统中心）
Model predictive control (MPC) is a powerful trajectory optimization control technique capable of controlling complex nonlinear systems while respecting system constraints and ensuring safe operation. The MPC's capabilities come at the cost of a high online computational complexity, the requirement of an accurate model of the system dynamics, and the necessity of tuning its parameters to the specific control application. The main tunable parameter affecting the computational complexity is the prediction horizon length, controlling how far into the future the MPC predicts the system response an…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Existing model-based value expansion methods typically leverage a world model for value estimation with a fixed rollout horizon to assist policy learning. However, the fixed rollout with an inaccurate model has a potential to harm the learning process. In this paper, we investigate the idea of using the model knowledge for value expansion adaptively. We propose a novel method called Dynamic-horizon Model-based Value Expansion (DMVE) to adjust the world model usage with different rollout horizons. Inspired by reconstruction-based techniques that can be applied for visual data novelty detection,…
Safe Reinforcement Learning using Finite-Horizon Gradient-based Estimation
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；The State Key Lab of Brain-Machine Intelligence, Zhejiang University（浙江大学脑机智能国家重点实验室）；Center for AI Safety and Governance, Peking University（北京大学人工智能安全与治理中心）
Decision-making for Autonomous Vehicles on Highway: Deep Reinforcement Learning with Continuous Action Horizon
College of Mechanical and Vehicle Engineering, Chongqing University（重庆大学机械与运载工程学院）；Department of Industrial Design, Chongqing Normal University（重庆师范大学工业设计系）
vivo AI Lab（vivo人工智能实验室）；Zhejiang Lab（浙江实验室）；CUHK MMLab（香港大学多模态实验室）；Hubei University（湖北省大学）；Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）
In this paper, we study the problem of learning a repertoire of low-level skills from raw images that can be sequenced to complete long-horizon visuomotor tasks. Reinforcement learning (RL) is a promising approach for acquiring short-horizon skills autonomously. However, the focus of RL algorithms has largely been on the success of those individual skills, more so than learning and grounding a large repertoire of skills that can be sequenced to complete extended multi-stage tasks. The latter demands robustness and persistence, as errors in skills can compound over time, and may require the rob…
University of Michigan（密歇根大学）；LG AI Research（LG人工智能研究院）
Operating in the real-world often requires agents to learn about a complex environment and apply this understanding to achieve a breadth of goals. This problem, known as goal-conditioned reinforcement learning (GCRL), becomes especially challenging for long-horizon goals. Current methods have tackled this problem by augmenting goal-conditioned policies with graph-based planning algorithms. However, they struggle to scale to large, high-dimensional state spaces and assume access to exploration mechanisms for efficiently collecting training data. In this work, we introduce Successor Feature Land…
