Policy optimization methods are popular reinforcement learning algorithms, because their incremental and on-policy nature makes them more stable than the value-based counterparts. However, the same properties also make them slow to converge and sample inefficient, as the on-policy requirement precludes data reuse and the incremental updates couple large iteration complexity into the sample complexity. These characteristics have been observed in experiments as well as in theory in the recent work of~\citet{agarwal2020pc}, which provides a policy optimization method PCPG that can robustly find near optimal polices for approximately linear Markov decision processes but suffers from an extremely poor sample complexity compared with value-based techniques.
In this paper, we propose a new algorithm, COPOE, that overcomes the sample complexity issue of PCPG while retaining its robustness to model misspecification. Compared with PCPG, COPOE makes several important algorithmic enhancements, such as enabling data reuse, and uses more refined analysis techniques, which we expect to be more broadly applicable to designing new reinforcement learning algorithms. The result is an improvement in sample complexity from $\widetilde{O}(1/ε^{11})$ for PCPG to $\widetilde{O}(1/ε^3)$ for PCPG, nearly bridging the gap with value-based techniques.
Many reinforcement learning exploration techniques are overly optimistic and try to explore every state. Such exploration is impossible in environments with the unlimited number of states. I propose to use simulated exploration with an optimistic model to discover promising paths for real exploration. This reduces the needs for the real exploration.
Harbin Institute of Technology（哈尔滨工业大学）；Northwestern University（西北大学）；Tencent Robotics X（腾讯 Robotics X）；Tianjin University（天津大学）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
One principled approach for provably efficient exploration is incorporating the upper confidence bound (UCB) into the value function as a bonus. However, UCB is specified to deal with linear and tabular settings and is incompatible with Deep Reinforcement Learning (DRL). In this paper, we propose a principled exploration method for DRL through Optimistic Bootstrapping and Backward Induction (OB2I). OB2I constructs a general-purpose UCB-bonus through non-parametric bootstrap in DRL. The UCB-bonus estimates the epistemic uncertainty of state-action pairs for optimistic exploration. We build theo…
Google Deepmind（谷歌DeepMind）；Stanford University（斯坦福大学）
We discuss the relative merits of optimistic and randomized approaches to exploration in reinforcement learning. Optimistic approaches presented in the literature apply an optimistic boost to the value estimate at each state-action pair and select actions that are greedy with respect to the resulting optimistic value function. Randomized approaches sample from among statistically plausible value functions and select actions that are greedy with respect to the random sample. Prior computational experience suggests that randomized approaches can lead to far more statistically efficient learning.…
Optimistic ε-Greedy Exploration for Cooperative Multi-Agent Reinforcement Learning
University of Electronic Science and Technology of China（电子科技大学）；Southwest Minzu University（西南民族大学）；Chengdu University of Technology（成都理工大学）；Nanyang Technological University（南洋理工大学）
The multi-agent setting is intricate and unpredictable since the behaviors of multiple agents influence one another. To address this environmental uncertainty, distributional reinforcement learning algorithms that incorporate uncertainty via distributional output have been integrated with multi-agent reinforcement learning (MARL) methods, achieving state-of-the-art performance. However, distributional MARL algorithms still rely on the traditional $ε$-greedy, which does not take cooperative strategy into account. In this paper, we present a risk-based exploration that leads to collaboratively o…
Criteo AI Lab（Criteo人工智能实验室）；Facebook AI Research（Facebook人工智能研究院）
We study the exploration-exploitation dilemma in the linear quadratic regulator (LQR) setting. Inspired by the extended value iteration algorithm used in optimistic algorithms for finite MDPs, we propose to relax the optimistic optimization of \ofulq and cast it into a constrained \textit{extended} LQR problem, where an additional control variable implicitly selects the system dynamics within a confidence interval. We then move to the corresponding Lagrangian formulation for which we prove strong duality. As a result, we show that an $ε$-optimistic controller can be computed efficiently by sol…
Optimistic initialisation is an effective strategy for efficient exploration in reinforcement learning (RL). In the tabular case, all provably efficient model-free algorithms rely on it. However, model-free deep RL algorithms do not use optimistic initialisation despite taking inspiration from these provably efficient tabular algorithms. In particular, in scenarios with only positive rewards, Q-values are initialised at their lowest possible values due to commonly used network initialisation schemes, a pessimistic initialisation. Merely initialising the network to output optimistic Q-values is…
Safe reinforcement learning is extremely challenging--not only must the agent explore an unknown environment, it must do so while ensuring no safety constraint violations. We formulate this safe reinforcement learning (RL) problem using the framework of a finite-horizon Constrained Markov Decision Process (CMDP) with an unknown transition probability function, where we model the safety requirements as constraints on the expected cumulative costs that must be satisfied during all episodes of learning. We propose a model-based safe RL algorithm that we call Doubly Optimistic and Pessimistic Expl…
Off-Policy Safe Reinforcement Learning with Constrained Optimistic Exploration
Faculty of Mechanical Engineering（机械工程学院）；Delft University of Technology（代尔夫特理工大学）；Faculty of Electrical Engineering, Mathematics and Computer Science（电气工程、数学和计算机科学学院）
University of Cambridge（剑桥大学）；Tencent RoboticsX（腾讯机器人X实验室）；Hong Kong University of Science and Technology（香港科技大学）；Tsinghua University（清华大学）；IDEA（粤港澳大湾区数字经济研究院）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
In this work, we study the simple yet universally applicable case of reward shaping in value-based Deep Reinforcement Learning (DRL). We show that reward shifting in the form of the linear transformation is equivalent to changing the initialization of the $Q$-function in function approximation. Based on such an equivalence, we bring the key insight that a positive reward shifting leads to conservative exploitation, while a negative reward shifting leads to curiosity-driven exploration. Accordingly, conservative exploitation improves offline RL value estimation, and optimistic value estimation …
Conditionally Optimistic Exploration for Cooperative Deep Multi-Agent Reinforcement Learning
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；École Polytechnique de Montréal（蒙特利尔综合理工学院）；University of Oxford（牛津大学）；University of Alberta（阿尔伯塔大学）；Université de Montréal（蒙特利尔大学）
UC Santa Barbara（加州大学圣巴巴拉分校）；Georgia Institute of Technology（佐治亚理工学院）；Amazon（亚马逊公司）；Cruise（克鲁斯公司）；Horizon Robotics（地平线机器人）
Improving the sample efficiency of reinforcement learning algorithms requires effective exploration. Following the principle of $\textit{optimism in the face of uncertainty}$ (OFU), we train a separate exploration policy to maximize the approximate upper confidence bound of the critics in an off-policy actor-critic framework. However, this introduces extra differences between the replay buffer and the target policy regarding their stationary state-action distributions. To mitigate the off-policy-ness, we adapt the recently introduced DICE framework to learn a distribution correction ratio for …
ETH Zurich（苏黎世联邦理工学院）；Bosch Center for Artificial Intelligence（博世人工智能中心）
Model-based reinforcement learning algorithms with probabilistic dynamical models are amongst the most data-efficient learning methods. This is often attributed to their ability to distinguish between epistemic and aleatoric uncertainty. However, while most algorithms distinguish these two uncertainties for learning the model, they ignore it when optimizing the policy, which leads to greedy and insufficient exploration. At the same time, there are no practical solvers for optimistic exploration algorithms. In this paper, we propose a practical optimistic exploration algorithm (H-UCRL). H-UCRL …
Microsoft Research Cambridge（微软研究院剑桥分院）；University of California San Diego（加州大学圣迭戈分校）
Actor-critic methods, a type of model-free Reinforcement Learning, have been successfully applied to challenging tasks in continuous control, often achieving state-of-the art performance. However, wide-scale adoption of these methods in real-world domains is made difficult by their poor sample efficiency. We address this problem both theoretically and empirically. On the theoretical side, we identify two phenomena preventing efficient exploration in existing state-of-the-art algorithms such as Soft Actor Critic. First, combining a greedy actor update with a pessimistic estimate of the critic l…
We consider online sequential decision problems where an agent must balance exploration and exploitation. We derive a set of Bayesian `optimistic' policies which, in the stochastic multi-armed bandit case, includes the Thompson sampling policy. We provide a new analysis showing that any algorithm producing policies in the optimistic set enjoys $\tilde O(\sqrt{AT})$ Bayesian regret for a problem with $A$ actions after $T$ rounds. We extend the regret analysis for optimistic policies to bilinear saddle-point problems which include zero-sum matrix games and constrained bandits as special cases. I…
Reinforcement Learning and Artificial Intelligence Laboratory（强化学习与人工智能实验室）；University of Alberta（阿尔伯塔大学）
In Reinforcement Learning (RL), it is common to use optimistic initialization of value functions to encourage exploration. However, such an approach generally depends on the domain, viz., the scale of the rewards must be known, and the feature representation must have a constant norm. We present a simple approach that performs optimistic initialization with less dependence on the domain.
TU Delft（代尔夫特理工大学）；Microsoft Research NYC（微软研究院纽约）；Microsoft Research Cambridge（微软研究院剑桥）
High sample complexity remains a barrier to the application of reinforcement learning (RL), particularly in multi-agent systems. A large body of work has demonstrated that exploration mechanisms based on the principle of optimism under uncertainty can significantly improve the sample efficiency of RL in single agent tasks. This work seeks to understand the role of optimistic exploration in non-cooperative multi-agent settings. We will show that, in zero-sum games, optimistic exploration can cause the learner to waste time sampling parts of the state space that are irrelevant to strategic play,…
We study algorithms using randomized value functions for exploration in reinforcement learning. This type of algorithms enjoys appealing empirical performance. We show that when we use 1) a single random seed in each episode, and 2) a Bernstein-type magnitude of noise, we obtain a worst-case $\widetilde{O}\left(H\sqrt{SAT}\right)$ regret bound for episodic time-inhomogeneous Markov Decision Process where $S$ is the size of state space, $A$ is the size of action space, $H$ is the planning horizon and $T$ is the number of interactions. This bound polynomially improves all existing bounds for alg…
SLOPE: Optimistic Potential Landscape Shaping for Model-based Reinforcement Learning
Beijing Institute of Technology（北京理工大学）；Heriot-Watt University（赫瑞-沃森大学）；Shenzhen Institutes of Advanced Technology, CAS（深圳先进技术研究院）；Microsoft Research NY（微软研究院纽约分部）；Tsinghua University（清华大学）；Jilin University（吉林大学）
We consider model-based multi-agent reinforcement learning, where the environment transition model is unknown and can only be learned via expensive interactions with the environment. We propose H-MARL (Hallucinated Multi-Agent Reinforcement Learning), a novel sample-efficient algorithm that can efficiently balance exploration, i.e., learning about the environment, and exploitation, i.e., achieve good equilibrium performance in the underlying general-sum Markov game. H-MARL builds high-probability confidence intervals around the unknown transition model and sequentially updates them based on ne…
HSE University（高等经济大学）；Artificial Intelligence Research Institute（人工智能研究院）；Duisburg-Essen University（杜伊斯堡-埃森大学）；DeepMind（深度思维）；Otto von Guericke University（奥托·冯·格里克大学）
We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order $\widetilde{O}(\sqrt{H^3SAT})$ where $H$ is the length of one episode, $S$ is the number of states, $A$ the number of actions, $T$ the number of episodes, that matches the lower-bound of $Ω(\sqrt{H^3SAT})$…
KAIST（韩国科学技术院）；Kim Jaechul Graduate School of Artificial Intelligence（金在澈人工智能研究生院）
Distributional reinforcement learning demonstrates state-of-the-art performance in continuous and discrete control settings with the features of variance and risk, which can be used to explore. However, the exploration method employing the risk property is hard to find, although numerous exploration methods in Distributional RL employ the variance of return distribution per action. In this paper, we present risk scheduling approaches that explore risk levels and optimistic behaviors from a risk perspective. We demonstrate the performance enhancement of the DMIX algorithm using risk scheduling …
Reinforcement Learning (RL) has been able to solve hard problems such as playing Atari games or solving the game of Go, with a unified approach. Yet modern deep RL approaches are still not widely used in real-world applications. One reason could be the lack of guarantees on the performance of the intermediate executed policies, compared to an existing (already working) baseline policy. In this paper, we propose an online model-free algorithm that solves conservative exploration in the policy optimization problem. We show that the regret of the proposed approach is bounded by $\tilde{\mathcal{O…
Model-based Bayesian Reinforcement Learning (BRL) allows a found formalization of the problem of acting optimally while facing an unknown environment, i.e., avoiding the exploration-exploitation dilemma. However, algorithms explicitly addressing BRL suffer from such a combinatorial explosion that a large body of work relies on heuristic algorithms. This paper introduces BOLT, a simple and (almost) deterministic heuristic algorithm for BRL which is optimistic about the transition function. We analyze BOLT's sample complexity, and show that under certain parameters, the algorithm is near-optimal…
Research on reinforcement learning has demonstrated promising results in manifold applications and domains. Still, efficiently learning effective robot behaviors is very difficult, due to unstructured scenarios, high uncertainties, and large state dimensionality (e.g. multi-agent systems or hyper-redundant robots). To alleviate this problem, we present DOP, a deep model-based reinforcement learning algorithm, which exploits action values to both (1) guide the exploration of the state space and (2) plan effective policies. Specifically, we exploit deep neural networks to learn Q-functions that …
Rutgers University（罗格斯大学）；Massachusetts Institute of Technology（麻省理工学院）
We present a modular approach to reinforcement learning that uses a Bayesian representation of the uncertainty over models. The approach, BOSS (Best of Sampled Set), drives exploration by sampling multiple models from the posterior and selecting actions optimistically. It extends previous work by providing a rule for deciding when to resample and how to combine the models. We show that our algorithm achieves nearoptimal reward with high probability with a sample complexity that is low relative to the speed at which the posterior distribution converges during learning. We demonstrate that BOSS …
Technion（以色列理工学院）；Facebook AI Research（Facebook人工智能研究院）
In many sequential decision-making problems, the goal is to optimize a utility function while satisfying a set of constraints on different utilities. This learning problem is formalized through Constrained Markov Decision Processes (CMDPs). In this paper, we investigate the exploration-exploitation dilemma in CMDPs. While learning in an unknown CMDP, an agent should trade-off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward while satisfying the constraints. While the agent will eventually learn a good or optimal policy, we …
Mila；McGill University（麦吉尔大学）；Peking University（北京大学）；Amii（阿尔伯塔机器智能研究所）；University of Alberta（阿尔伯塔大学）；Princeton University（普林斯顿大学）；Northwestern University（西北大学）；DeepMind；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
We propose a model-free reinforcement learning algorithm inspired by the popular randomized least squares value iteration (RLSVI) algorithm as well as the optimism principle. Unlike existing upper-confidence-bound (UCB) based approaches, which are often computationally intractable, our algorithm drives exploration by simply perturbing the training data with judiciously chosen i.i.d. scalar noises. To attain optimistic value function estimation without resorting to a UCB-style bonus, we introduce an optimistic reward sampling procedure. When the value functions can be represented by a function …
Technion - Israel Institute of Technology（以色列理工学院）；Tel Aviv University（特拉维夫大学）
Policy optimization methods are one of the most widely used classes of Reinforcement Learning (RL) algorithms. Yet, so far, such methods have been mostly analyzed from an optimization perspective, without addressing the problem of exploration, or by making strong assumptions on the interaction with the environment. In this paper we consider model-based RL in the tabular finite-horizon MDP setting with unknown transitions and bandit feedback. For this setting, we propose an optimistic trust region policy optimization (TRPO) algorithm for which we establish $\tilde O(\sqrt{S^2 A H^4 K})$ regret …
Beyond-Expert Performance with Limited Demonstrations: Efficient Imitation Learning with Double Exploration
Department of Computer Science, University of California, Los Angeles（加州大学洛杉矶分校计算机科学系）；IHPC, Agency for Science, Technology and Research, Singapore（新加坡科技研究局信息与通信技术研究所）；CFAR, Agency for Science, Technology and Research, Singapore（新加坡科技研究局癌症研究基金会）
Optimistic Actor-Critic with Parametric Policies for Linear Markov Decision Processes
Simon Fraser University（西蒙菲莎大学）；University of Pennsylvania（宾夕法尼亚大学）；Mila, McGill University（Mila，麦吉尔大学）；Google DeepMind（谷歌DeepMind）；University of Alberta（阿尔伯塔大学）
I study a game of strategic exploration with private payoffs and public actions in a Bayesian bandit setting. In particular, I look at cascade equilibria, in which agents switch over time from the risky action to the riskless action only when they become sufficiently pessimistic. I show that these equilibria exist under some conditions and establish their salient properties. Individual exploration in these equilibria can be more or less than the single-agent level depending on whether the agents start out with a common prior or not, but the most optimistic agent always underexplores. I also sh…
Sequel Team - Inria Lille（Inria Lille Sequel团队）；Facebook AI Research（Facebook人工智能研究）
While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). This leads to defining weakly-communicating or multi-chain MDPs. In this paper, we introduce \tucrl, the first algorithm able to perform efficient exploration-exploitation in any finite Markov Decision Process (MDP) without requiring any form of prior knowledge. In particular, for any MDP with $S^{\texttt{C}}$ communicating states, $A$ actions and $Γ…
University of Michigan（密歇根大学）；ShanghaiTech University（上海科技大学）
Multi-armed bandit (MAB) is a classic model for understanding the exploration-exploitation trade-off. The traditional MAB model for recommendation systems assumes the user stays in the system for the entire learning horizon. In new online education platforms such as ALEKS or new video recommendation systems such as TikTok and YouTube Shorts, the amount of time a user spends on the app depends on how engaging the recommended contents are. Users may temporarily leave the system if the recommended items cannot engage the users. To understand the exploration, exploitation, and engagement in these …
While learning in an unknown Markov Decision Process (MDP), an agent should trade off exploration to discover new information about the MDP, and exploitation of the current knowledge to maximize the reward. Although the agent will eventually learn a good or optimal policy, there is no guarantee on the quality of the intermediate policies. This lack of control is undesired in real-world applications where a minimum requirement is that the executed policies are guaranteed to perform at least as well as an existing baseline. In this paper, we introduce the notion of conservative exploration for a…
Google Research（谷歌研究院）；Inria Lille Nord Europe（法国国家信息与自动化研究所里尔-北欧欧洲分部）
Self-imitation learning is a Reinforcement Learning (RL) method that encourages actions whose returns were higher than expected, which helps in hard exploration and sparse reward problems. It was shown to improve the performance of on-policy actor-critic methods in several discrete control tasks. Nevertheless, applying self-imitation to the mostly action-value based off-policy RL methods is not straightforward. We propose SAIL, a novel generalization of self-imitation learning for off-policy RL, based on a modification of the Bellman optimality operator that we connect to Advantage Learning. C…
