Offline reinforcement learning (RL) enables effective learning from previously collected data without exploration, which shows great promise in real-world applications when exploration is expensive or even infeasible. The discount factor, $γ$, plays a vital role in improving online RL sample efficiency and estimation accuracy, but the role of the discount factor in offline RL is not well explored. This paper examines two distinct effects of $γ$ in offline RL with theoretical analysis, namely the regularization effect and the pessimism effect. On the one hand, $γ$ is a regulator to trade-off optimality with sample efficiency upon existing offline techniques. On the other hand, lower guidance $γ$ can also be seen as a way of pessimism where we optimize the policy's performance in the worst possible models. We empirically verify the above theoretical observation with tabular MDPs and standard D4RL tasks. The results show that the discount factor plays an essential role in the performance of offline RL algorithms, both under small data regimes upon existing offline methods and in large data regimes without other conservative methods.
Nara Institute of Science and Technology（奈良先端科学技术大学院大学）
This paper proposes a new reinforcement learning with hyperbolic discounting. Combining a new temporal difference error with the hyperbolic discounting in recursive manner and reward-punishment framework, a new scheme to learn the optimal policy is derived. In simulations, it is found that the proposal outperforms the standard reinforcement learning, although the performance depends on the design of reward and punishment. In addition, the averages of discount factors w.r.t. reward and punishment are different from each other, like a sign effect in animal behaviors.
Max Planck Institute for Software Systems（马克斯·普朗克软件系统研究所）；University of Oxford（牛津大学）
Existing episodic reinforcement algorithms assume that the length of an episode is fixed across time and known a priori. In this paper, we consider a general framework of episodic reinforcement learning when the length of each episode is drawn from a distribution. We first establish that this problem is equivalent to online reinforcement learning with general discounting where the learner is trying to optimize the expected discounted sum of rewards over an infinite horizon, but where the discounting function is not necessarily geometric. We show that minimizing regret with this new general dis…
When designing algorithms for finite-time-horizon episodic reinforcement learning problems, a common approach is to introduce a fictitious discount factor and use stationary policies for approximations. Empirically, it has been shown that the fictitious discount factor helps reduce variance, and stationary policies serve to save the per-iteration computational cost. Theoretically, however, there is no existing work on convergence analysis for algorithms with this fictitious discount recipe. This paper takes the first step towards analyzing these algorithms. It focuses on two vanilla policy gra…
Microsoft Research Montréal（微软研究院蒙特利尔）；Imperial College London（伦敦帝国学院）
In an effort to better understand the different ways in which the discount factor affects the optimization process in reinforcement learning, we designed a set of experiments to study each effect in isolation. Our analysis reveals that the common perception that poor performance of low discount factors is caused by (too) small action-gaps requires revision. We propose an alternative hypothesis that identifies the size-difference of the action-gap across the state-space as the primary cause. We then introduce a new method that enables more homogeneous action-gaps by mapping value estimates to a…
Diffusion Policies for Risk-Averse Behavior Modeling in Offline Reinforcement Learning
Data 61, CSIRO, Australia（数据61，CSIRO，澳大利亚）；School of Computing, Macquarie University, Australia（计算学院，麦考瑞大学，澳大利亚）；Adobe Research, USA（Adobe研究，美国）；School of Computer Science and Engineering, University of New South Wales, Australia（计算机科学与工程学院，新南威尔士大学，澳大利亚）
Using deep neural nets as function approximator for reinforcement learning tasks have recently been shown to be very powerful for solving problems approaching real-world complexity. Using these results as a benchmark, we discuss the role that the discount factor may play in the quality of the learning process of a deep Q-network (DQN). When the discount factor progressively increases up to its final value, we empirically show that it is possible to significantly reduce the number of learning steps. When used in conjunction with a varying learning rate, we empirically show that it outperforms o…
Tsinghua University（清华大学）；University College London（伦敦大学学院）；Sun Yat-sen University（中山大学）
Most of reinforcement learning algorithms optimize the discounted criterion which is beneficial to accelerate the convergence and reduce the variance of estimates. Although the discounted criterion is appropriate for certain tasks such as financial related problems, many engineering problems treat future rewards equally and prefer a long-run average criterion. In this paper, we study the reinforcement learning problem with the long-run average criterion. Firstly, we develop a unified trust region theory with discounted and average criteria and derive a novel performance bound within the trust …
The endeavor of artificial intelligence (AI) is to design autonomous agents capable of achieving complex tasks. Namely, reinforcement learning (RL) proposes a theoretical background to learn optimal behaviors. In practice, RL algorithms rely on geometric discounts to evaluate this optimality. Unfortunately, this does not cover decision processes where future returns are not exponentially less valuable. Depending on the problem, this limitation induces sample-inefficiency (as feed-backs are exponentially decayed) and requires additional curricula/exploration mechanisms (to deal with sparse, dec…
L3S Research Center（L3S研究中心）；Leibniz University Hannover（汉诺威莱布尼茨大学）
The success of deep reinforcement learning (DRL) hinges on the availability of training data, which is typically obtained via a large number of environment interactions. In many real-world scenarios, costs and risks are associated with gathering these data. The field of offline reinforcement learning addresses these issues through outsourcing the collection of data to a domain expert or a carefully monitored program and subsequently searching for a batch-constrained optimal policy. With the emergence of data markets, an alternative to constructing a dataset in-house is to purchase external dat…
School of Information Technology and Electrical Engineering（信息技术与电气工程学院）；University of Queensland（昆士兰大学）
In reinforcement learning (RL), the goal is to obtain an optimal policy, for which the optimality criterion is fundamentally important. Two major optimality criteria are average and discounted rewards. While the latter is more popular, it is problematic to apply in environments without an inherent notion of discounting. This motivates us to revisit a) the progression of optimality criteria in dynamic programming, b) justification for and complication of an artificial discount factor, and c) benefits of directly maximizing the average reward criterion, which is discounting-free. Our contributio…
UM-SJTU Joint Institute, Shanghai Jiao Tong University（上海交通大学密西根学院）；Department of Automation, Shanghai Jiao Tong University（上海交通大学自动化系）
As the operations of autonomous systems generally affect simultaneously several users, it is crucial that their designs account for fairness considerations. In contrast to standard (deep) reinforcement learning (RL), we investigate the problem of learning a policy that treats its users equitably. In this paper, we formulate this novel RL problem, in which an objective function, which encodes a notion of fairness that we formally define, is optimized. For this problem, we provide a theoretical discussion where we examine the case of discounted rewards and that of average rewards. During this an…
Although in recent years reinforcement learning has become very popular the number of successful applications to different kinds of operations research problems is rather scarce. Reinforcement learning is based on the well-studied dynamic programming technique and thus also aims at finding the best stationary policy for a given Markov Decision Process, but in contrast does not require any model knowledge. The policy is assessed solely on consecutive states (or state-action pairs), which are observed while an agent explores the solution space. The contributions of this paper are manifold. First…
We study the reinforcement learning problem for discounted Markov Decision Processes (MDPs) under the tabular setting. We propose a model-based algorithm named UCBVI-$γ$, which is based on the \emph{optimism in the face of uncertainty principle} and the Bernstein-type bonus. We show that UCBVI-$γ$ achieves an $\tilde{O}\big({\sqrt{SAT}}/{(1-γ)^{1.5}}\big)$ regret, where $S$ is the number of states, $A$ is the number of actions, $γ$ is the discount factor and $T$ is the number of steps. In addition, we construct a class of hard MDPs and show that for any algorithm, the expected regret is at lea…
University of Toronto（多伦多大学）；Vector Institute（Vector研究所）
Reinforcement learning (RL) agents have traditionally been tasked with maximizing the value function of a Markov decision process (MDP), either in continuous settings, with fixed discount factor $γ< 1$, or in episodic settings, with $γ= 1$. While this has proven effective for specific tasks with well-defined objectives (e.g., games), it has never been established that fixed discounting is suitable for general purpose use (e.g., as a model of human preferences). This paper characterizes rationality in sequential decision making using a set of seven axioms and arrives at a form of discounting th…
Nanjing University（南京大学）；The University of Hong Kong（香港大学）
Value function estimation is an indispensable subroutine in reinforcement learning, which becomes more challenging in the offline setting. In this paper, we propose Hybrid Value Estimation (HVE) to reduce value estimation error, which trades off bias and variance by balancing between the value estimation from offline data and the learned model. Theoretical analysis discloses that HVE enjoys a better error bound than the direct methods. HVE can be leveraged in both off-policy evaluation and offline reinforcement learning settings. We, therefore, provide two concrete algorithms Off-policy HVE (O…
Reinforcement Learning for Exponential Utility: Algorithms and Convergence in Discounted MDPs
Computer Science and Automation, Indian Institute of Science, Bengaluru（印度科学研究院计算机科学与自动化部门，班加罗尔）；Computer Science and Engineering, Indian Institute of Technology Madras, Chennai（印度理工学院马德拉斯分校计算机科学与工程系，钦奈）；Tata Consultancy Services Limited, Hyderabad（海得拉巴市塔塔咨询公司）
Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
With the success of offline reinforcement learning (RL), offline trained RL policies have the potential to be further improved when deployed online. A smooth transfer of the policy matters in safe real-world deployment. Besides, fast adaptation of the policy plays a vital role in practical online performance improvement. To tackle these challenges, we propose a simple yet efficient algorithm, Model-based Offline-to-Online Reinforcement learning (MOORe), which employs a prioritized sampling scheme that can dynamically adjust the offline and online data for smooth and efficient online adaptation…
Technion - Israel Institute of Technology（以色列理工学院）；Microsoft Research（微软研究院）
Specifying a Reinforcement Learning (RL) task involves choosing a suitable planning horizon, which is typically modeled by a discount factor. It is known that applying RL algorithms with a lower discount factor can act as a regularizer, improving performance in the limited data regime. Yet the exact nature of this regularizer has not been investigated. In this work, we fill in this gap. For several Temporal-Difference (TD) learning methods, we show an explicit equivalence between using a reduced discount factor and adding an explicit regularization term to the algorithm's loss. Motivated by th…
Centre for Cognitive Science（认知科学中心）；Technische Universität Darmstadt（达姆施塔特工业大学）
Commonly in reinforcement learning (RL), rewards are discounted over time using an exponential function to model time preference, thereby bounding the expected long-term reward. In contrast, in economics and psychology, it has been shown that humans often adopt a hyperbolic discounting scheme, which is optimal when a specific task termination time distribution is assumed. In this work, we propose a theory for continuous-time model-based reinforcement learning generalized to arbitrary discount functions. This formulation covers the case in which there is a non-exponential random termination tim…
In this work, we provide theoretical guarantees for reward decomposition in deterministic MDPs. Reward decomposition is a special case of Hierarchical Reinforcement Learning, that allows one to learn many policies in parallel and combine them into a composite solution. Our approach builds on mapping this problem into a Reward Discounted Traveling Salesman Problem, and then deriving approximate solutions for it. In particular, we focus on approximate solutions that are local, i.e., solutions that only observe information about the current state. Local policies are easy to implement and do not r…
Siemens Technology（西门子技术）；Technical University of Munich（慕尼黑工业大学）
In offline reinforcement learning, a policy needs to be learned from a single pre-collected dataset. Typically, policies are thus regularized during training to behave similarly to the data generating policy, by adding a penalty based on a divergence between action distributions of generating and trained policy. We propose a new algorithm, which constrains the policy directly in its weight space instead, and demonstrate its effectiveness in experiments.
Offline reinforcement learning (RL) allows for the training of competent agents from offline datasets without any interaction with the environment. Online finetuning of such offline models can further improve performance. But how should we ideally finetune agents obtained from offline RL training? While offline RL algorithms can in principle be used for finetuning, in practice, their online performance improves slowly. In contrast, we show that it is possible to use standard online off-policy algorithms for faster improvement. However, we find this approach may suffer from policy collapse, whe…
Westlake University（西湖大学）；Zhejiang University（浙江大学）；Westlake Institute for Advanced Study（西湖高等研究院）
Offline reinforcement learning algorithms promise to be applicable in settings where a fixed dataset is available and no new experience can be acquired. However, such formulation is inevitably offline-data-hungry and, in practice, collecting a large offline dataset for one specific task over one specific environment is also costly and laborious. In this paper, we thus 1) formulate the offline dynamics adaptation by using (source) offline data collected from another dynamics to relax the requirement for the extensive (target) offline data, 2) characterize the dynamics shift problem in which pri…
Siemens Technology（西门子技术部）；Technical University of Munich（慕尼黑工业大学）
Offline reinforcement learning (RL) Algorithms are often designed with environments such as MuJoCo in mind, in which the planning horizon is extremely long and no noise exists. We compare model-free, model-based, as well as hybrid offline RL approaches on various industrial benchmark (IB) datasets to test the algorithms in settings closer to real world problems, including complex noise and partially observable states. We find that on the IB, hybrid approaches face severe difficulties and that simpler algorithms, such as rollout based algorithms or model-free algorithms with simpler regularizer…
Learning efficiently from small amounts of data has long been the focus of model-based reinforcement learning, both for the online case when interacting with the environment and the offline case when learning from a fixed dataset. However, to date no single unified algorithm could demonstrate state-of-the-art results in both settings. In this work, we describe the Reanalyse algorithm which uses model-based policy and value improvement operators to compute new improved training targets on existing data points, allowing efficient learning for data budgets varying by several orders of magnitude. …
Training Reinforcement Learning (RL) agents in high-stakes applications might be too prohibitive due to the risk associated to exploration. Thus, the agent can only use data previously collected by safe policies. While previous work considers optimizing the average performance using offline data, we focus on optimizing a risk-averse criteria, namely the CVaR. In particular, we present the Offline Risk-Averse Actor-Critic (O-RAAC), a model-free RL algorithm that is able to learn risk-averse policies in a fully offline setting. We show that O-RAAC learns policies with higher CVaR than risk-neutr…
Sufficient exploration is paramount for the success of a reinforcement learning agent. Yet, exploration is rarely assessed in an algorithm-independent way. We compare the behavior of three data-based, offline exploration metrics described in the literature on intuitive simple distributions and highlight problems to be aware of when using them. We propose a fourth metric,uniform relative entropy, and implement it using either a k-nearest-neighbor or a nearest-neighbor-ratio estimator, highlighting that the implementation choices have a profound impact on these measures.
Modern tasks in reinforcement learning have large state and action spaces. To deal with them efficiently, one often uses predefined feature mapping to represent states and actions in a low-dimensional space. In this paper, we study reinforcement learning for discounted Markov Decision Processes (MDPs), where the transition kernel can be parameterized as a linear function of certain feature mapping. We propose a novel algorithm that makes use of the feature mapping and obtains a $\tilde O(d\sqrt{T}/(1-γ)^2)$ regret, where $d$ is the dimension of the feature space, $T$ is the time horizon and $γ…
We present a model-based offline reinforcement learning policy performance lower bound that explicitly captures dynamics model misspecification and distribution mismatch and we propose an empirical algorithm for optimal offline policy selection. Theoretically, we prove a novel safe policy improvement theorem by establishing pessimism approximations to the value function. Our key insight is to jointly consider selecting over dynamics models and policies: as long as a dynamics model can accurately represent the dynamics of the state-action pairs visited by a given policy, it is possible to appro…
New York University（纽约大学）；Google Research（谷歌研究院）；Google DeepMind（谷歌DeepMind）
Many modern approaches to offline Reinforcement Learning (RL) utilize behavior regularization, typically augmenting a model-free actor critic algorithm with a penalty measuring divergence of the policy from the offline data. In this work, we propose an alternative approach to encouraging the learned policy to stay close to the data, namely parameterizing the critic as the log-behavior-policy, which generated the offline data, plus a state-action value offset term, which can be learned using a neural network. Behavior regularization then corresponds to an appropriate regularizer on the offset t…
Offline reinforcement learning algorithms still lack trust in practice due to the risk that the learned policy performs worse than the original policy that generated the dataset or behaves in an unexpected way that is unfamiliar to the user. At the same time, offline RL algorithms are not able to tune their most important hyperparameter - the proximity of the learned policy to the original policy. We propose an algorithm that allows the user to tune this hyperparameter at runtime, thereby addressing both of the above mentioned issues simultaneously. This allows users to start with the original…
Google Brain（谷歌大脑）；UC Berkeley（加州大学伯克利分校）；MIT（麻省理工学院）；Google Research（谷歌研究院）
Reinforcement learning (RL) has achieved impressive performance in a variety of online settings in which an agent's ability to query the environment for transitions and rewards is effectively unlimited. However, in many practical applications, the situation is reversed: an agent may have access to large amounts of undirected offline experience data, while access to the online environment is severely limited. In this work, we focus on this offline setting. Our main insight is that, when presented with offline data composed of a variety of behaviors, an effective way to leverage this data is to …
In offline reinforcement learning, a policy learns to maximize cumulative rewards with a fixed collection of data. Towards conservative strategy, current methods choose to regularize the behavior policy or learn a lower bound of the value function. However, exorbitant conservation tends to impair the policy's generalization ability and degrade its performance, especially for the mixed datasets. In this paper, we propose the method of reducing conservativeness oriented reinforcement learning. On the one hand, the policy is trained to pay more attention to the minority samples in the static data…
