Kernel-Based Reinforcement Learning: A Finite-Time Analysis
Inria Lille（里尔法国国家信息与自动化研究所）；Université de Lille（里尔大学）；Otto von Guericke University（奥托·冯·格里克大学）；Facebook AI Research（脸书人工智能研究院）；CNRS（法国国家科学研究中心）；DeepMind Paris（深度思维巴黎研究院）
Omar Darwiche Domingues, Pierre Ménard, Matteo Pirotta, Emilie Kaufmann, Michal Valko
备注：
Update following the publication in ICML 2021, including fixed typos
We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning problems whose state-action space is endowed with a metric. We introduce Kernel-UCBVI, a model-based optimistic algorithm that leverages the smoothness of the MDP and a non-parametric kernel estimator of the rewards and transitions to efficiently balance exploration and exploitation. For problems with $K$ episodes and horizon $H$, we provide a regret bound of $\widetilde{O}\left( H^3 K^{\frac{2d}{2d+1}}\right)$, where $d$ is the covering dimension of the joint state-action space. This is the first regret bound for kernel-based RL using smoothing kernels, which requires very weak assumptions on the MDP and has been previously applied to a wide range of tasks. We empirically validate our approach in continuous MDPs with sparse rewards.
McGill University（麦吉尔大学）；Mila - Quebec Artificial Intelligence Institute（魁北克人工智能研究所（Mila））；Université du Québec à Montréal（魁北克大学蒙特利尔分校）；Facebook AI Research（Facebook人工智能研究）；CIFAR AI chair（CIFAR人工智能主席职位）；DeepMind；Université de Montréal（蒙特利尔大学）
We propose a general framework for policy representation for reinforcement learning tasks. This framework involves finding a low-dimensional embedding of the policy on a reproducing kernel Hilbert space (RKHS). The usage of RKHS based methods allows us to derive strong theoretical guarantees on the expected return of the reconstructed policy. Such guarantees are typically lacking in black-box models, but are very desirable in tasks requiring stability. We conduct several experiments on classic RL domains. The results confirm that the policies can be robustly embedded in a low-dimensional space…
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…
Inria Lille（里尔法国国家信息与自动化研究所）；Université de Lille（里尔大学）；OvGU（马格德堡大学）；Facebook AI Research（脸书人工智能研究院）；CNRS（法国国家科学研究中心）；DeepMind Paris（深度思维巴黎）
In this work, we propose KeRNS: an algorithm for episodic reinforcement learning in non-stationary Markov Decision Processes (MDPs) whose state-action set is endowed with a metric. Using a non-parametric model of the MDP built with time-dependent kernels, we prove a regret bound that scales with the covering dimension of the state-action space and the total variation of the MDP with time, which quantifies its level of non-stationarity. Our method generalizes previous approaches based on sliding windows and exponential discounting used to handle changing environments. We further propose a pract…
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex nonlinear embeddings, but do not naturally quantify uncertainty and are often data-inefficient to train. GPs infer posterior distributions over functions, but popular kernels exhibit limited expressivity on complex and high-dimensional data. Fortunately, recently discovered conjugate and neural tangent kernel functions encode the behavior of overparameterized neural netw…
Harvard University（哈佛大学）；Imperial College London（帝国理工学院）；MIT（麻省理工学院）
Sepsis is the leading cause of mortality in the ICU. It is challenging to manage because individual patients respond differently to treatment. Thus, tailoring treatment to the individual patient is essential for the best outcomes. In this paper, we take steps toward this goal by applying a mixture-of-experts framework to personalize sepsis treatment. The mixture model selectively alternates between neighbor-based (kernel) and deep reinforcement learning (DRL) experts depending on patient's current history. On a large retrospective cohort, this mixture-based approach outperforms physician, kern…
Laboratório Nacional de Computação Científica（国家科学计算实验室）；McGill University（麦吉尔大学）
Kernel-based reinforcement learning (KBRL) stands out among reinforcement learning algorithms for its strong theoretical guarantees. By casting the learning problem as a local kernel approximation, KBRL provides a way of computing a decision policy which is statistically consistent and converges to a unique solution. Unfortunately, the model constructed by KBRL grows with the number of sample transitions, resulting in a computational cost that precludes its application to large-scale or on-line domains. In this paper we introduce an algorithm that turns KBRL into a practical reinforcement lear…
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…
Boston University（波士顿大学）；The University of Sydney（悉尼大学）
We consider the regret minimization problem in reinforcement learning (RL) in the episodic setting. In many real-world RL environments, the state and action spaces are continuous or very large. Existing approaches establish regret guarantees by either a low-dimensional representation of the stochastic transition model or an approximation of the $Q$-functions. However, the understanding of function approximation schemes for state-value functions largely remains missing. In this paper, we propose an online model-based RL algorithm, namely the CME-RL, that learns representations of transition dis…
This paper presents a constrained policy gradient algorithm. We introduce constraints for safe learning with the following steps. First, learning is slowed down (lazy learning) so that the episodic policy change can be computed with the help of the policy gradient theorem and the neural tangent kernel. Then, this enables us the evaluation of the policy at arbitrary states too. In the same spirit, learning can be guided, ensuring safety via augmenting episode batches with states where the desired action probabilities are prescribed. Finally, exogenous discounted sum of future rewards (returns) …
This study addresses the problem of selecting dynamically, at each time instance, the ``optimal'' p-norm to combat outliers in linear adaptive filtering without any knowledge on the potentially time-varying probability distribution function of the outliers. To this end, an online and data-driven framework is designed via kernel-based reinforcement learning (KBRL). Novel Bellman mappings on reproducing kernel Hilbert spaces (RKHSs) are introduced that need no knowledge on transition probabilities of Markov decision processes, and are nonexpansive with respect to the underlying Hilbertian norm. …
A model of music needs to have the ability to recall past details and have a clear, coherent understanding of musical structure. Detailed in the paper is a deep reinforcement learning architecture that predicts and generates polyphonic music aligned with musical rules. The probabilistic model presented is a Bi-axial LSTM trained with a pseudo-kernel reminiscent of a convolutional kernel. To encourage exploration and impose greater global coherence on the generated music, a deep reinforcement learning approach DQN is adopted. When analyzed quantitatively and qualitatively, this approach perform…
TuneAgent: Agentic Operating System Kernel Tuning with Reinforcement Learning
Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Nanyang Technological University（南洋理工大学）
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Baidu Inc.（百度公司）
Robust Reinforcement Learning aims to find the optimal policy with some extent of robustness to environmental dynamics. Existing learning algorithms usually enable the robustness through disturbing the current state or simulating environmental parameters in a heuristic way, which lack quantified robustness to the system dynamics (i.e. transition probability). To overcome this issue, we leverage Wasserstein distance to measure the disturbance to the reference transition kernel. With Wasserstein distance, we are able to connect transition kernel disturbance to the state disturbance, i.e. reduce …
University of Science and Technology of China（中国科学技术大学）
This paper addresses the average cost minimization problem for discrete-time systems with multiplicative and additive noises via reinforcement learning. By using Q-function, we propose an online learning scheme to estimate the kernel matrix of Q-function and to update the control gain using the data along the system trajectories. The obtained control gain and kernel matrix are proved to converge to the optimal ones. To implement the proposed learning scheme, an online model-free reinforcement learning algorithm is given, where recursive least squares method is used to estimate the kernel matri…
Most existing theoretical analysis of reinforcement learning (RL) is limited to the tabular setting or linear models due to the difficulty in dealing with function approximation in high dimensional space with an uncertain environment. This work offers a fresh perspective into this challenge by analyzing RL in a general reproducing kernel Hilbert space (RKHS). We consider a family of Markov decision processes $\mathcal{M}$ of which the reward functions lie in the unit ball of an RKHS and transition probabilities lie in a given arbitrary set. We define a quantity called perturbational complexity…
University of Queensland（昆士兰大学）；University of Cambridge（剑桥大学）
A simple, flexible approach to creating expressive priors in Gaussian process (GP) models makes new kernels from a combination of basic kernels, e.g. summing a periodic and linear kernel can capture seasonal variation with a long term trend. Despite a well-studied link between GPs and Bayesian neural networks (BNNs), the BNN analogue of this has not yet been explored. This paper derives BNN architectures mirroring such kernel combinations. Furthermore, it shows how BNNs can produce periodic kernels, which are often useful in this context. These ideas provide a principled approach to designing …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Reinforcement learning (RL) workloads take a notoriously long time to train due to the large number of samples collected at run-time from simulators. Unfortunately, cluster scale-up approaches remain expensive, and commonly used CPU implementations of simulators induce high overhead when switching back and forth between GPU computations. We explore two optimizations that increase RL data collection efficiency by increasing GPU utilization: (1) GPU vectorization: parallelizing simulation on the GPU for increased hardware parallelism, and (2) simulator kernel fusion: fusing multiple simulation s…
We address the problem of model selection for the finite horizon episodic Reinforcement Learning (RL) problem where the transition kernel $P^*$ belongs to a family of models $\mathcal{P}^*$ with finite metric entropy. In the model selection framework, instead of $\mathcal{P}^*$, we are given $M$ nested families of transition kernels $\cP_1 \subset \cP_2 \subset \ldots \subset \cP_M$. We propose and analyze a novel algorithm, namely \emph{Adaptive Reinforcement Learning (General)} (\texttt{ARL-GEN}) that adapts to the smallest such family where the true transition kernel $P^*$ lies. \texttt{ARL…
INRIA Lille - Nord Europe（法国国家信息与自动化研究所里尔-北欧分部）；University of Bristol（布里斯托大学）
We tackle the problem of online reward maximisation over a large finite set of actions described by their contexts. We focus on the case when the number of actions is too big to sample all of them even once. However we assume that we have access to the similarities between actions' contexts and that the expected reward is an arbitrary linear function of the contexts' images in the related reproducing kernel Hilbert space (RKHS). We propose KernelUCB, a kernelised UCB algorithm, and give a cumulative regret bound through a frequentist analysis. For contextual bandits, the related algorithm GP-U…
Department of Electrical & Computer Engineering University of Washington（华盛顿大学电气与计算机工程系）
Constrained Markov Decision Processes are a class of stochastic decision problems in which the decision maker must select a policy that satisfies auxiliary cost constraints. This paper extends upper confidence reinforcement learning for settings in which the reward function and the constraints, described by cost functions, are unknown a priori but the transition kernel is known. Such a setting is well-motivated by a number of applications including exploration of unknown, potentially unsafe, environments. We present an algorithm C-UCRL and show that it achieves sub-linear regret ($ O(T^{\frac{…
Kernel Density Bayesian Inverse Reinforcement Learning
Stanford University（斯坦福大学）；University of North Carolina（北卡罗来纳大学）；Columbia University（哥伦比亚大学）；Princeton University（普林斯顿大学）；Flatiron Institute（Flatiron研究所）；Gladstone Institutes（Gladstone研究所）
Towards Surrogate Based Dequantization of Quantum Reinforcement Learning
University of the Basque Country UPV/EHU（巴斯克大学 UPV/EHU）；TECNALIA, Basque Research and Technology Alliance (BRTA)（TECNALIA，巴斯克研究与技术联盟（BRTA））；Freie Universität Berlin（柏林自由大学）；Helmholtz-Zentrum Berlin für Materialien und Energie（亥姆霍兹柏林材料与能源中心）；IKERBASQUE, Basque Foundation for Science（IKERBASQUE，巴斯克科学基金会）；Basque Center for Applied Mathematics (BCAM)（巴斯克应用数学中心（BCAM））；African Institute for Mathematical Sciences (AIMS)（非洲数学科学研究所（AIMS））；Stellenbosch University（斯泰伦博斯大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（国家理论与计算科学研究所（NITheCS））
Reinforcement learning (RL) is currently a popular research topic in control engineering and has the potential to make its way to industrial and commercial applications. Corresponding RL controllers are trained in direct interaction with the controlled system, rendering them data-driven and performance-oriented solutions. The best practice of exploring starts (ES) is used by default to support the learning process via randomly picked initial states. However, this method might deliver strongly biased results if the system's dynamic and constraints lead to unfavorable sample distributions in the…
Offline reinforcement learning (RL) leverages previously collected data for policy optimization without any further active exploration. Despite the recent interest in this problem, its theoretical results in neural network function approximation settings remain elusive. In this paper, we study the statistical theory of offline RL with deep ReLU network function approximation. In particular, we establish the sample complexity of $n = \tilde{\mathcal{O}}( H^{4 + 4 \frac{d}α} κ_μ^{1 + \frac{d}α} ε^{-2 - 2\frac{d}α} )$ for offline RL with deep ReLU networks, where $κ_μ$ is a measure of distributio…
Cornell University（康奈尔大学）；University of Connecticut（康涅狄格大学）
Inverse reinforcement learning (IRL) aims to estimate the reward function of optimizing agents by observing their response (estimates or actions). This paper considers IRL when noisy estimates of the gradient of a reward function generated by multiple stochastic gradient agents are observed. We present a generalized Langevin dynamics algorithm to estimate the reward function $R(θ)$; specifically, the resulting Langevin algorithm asymptotically generates samples from the distribution proportional to $\exp(R(θ))$. The proposed IRL algorithms use kernel-based passive learning schemes. We also con…
Vector-Valued Distributional Reinforcement Learning Policy Evaluation: A Hilbert Space Embedding Approach
Department of Statistics, University of Illinois Urbana-Champaign（统计系，伊利诺伊大学厄巴纳-香槟分校）；Department of Bioinformatics and Biostatistics, University of Louisville（生物信息学与生物统计学系，路易斯维尔大学）
Norwegian University of Science and Technology (NTNU)（挪威科技大学 (NTNU)）
We investigate the effect of including domain knowledge about a robotic system's causal relations when generating explanations. To this end, we compare two methods from explainable artificial intelligence, the popular KernelSHAP and the recent causal SHAP, on a deep neural network trained using deep reinforcement learning on the task of controlling a lever using a robotic manipulator. A primary disadvantage of KernelSHAP is that its explanations represent only the features' direct effects on a model's output, not considering the indirect effects a feature can have on the output by affecting ot…
On the Convergence and Stability of Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning, and Online Decision Transformers
Dalle Molle Institute for Artificial Intelligence (IDSIA) - USI/SUPSI（达摩信息技术研究所（IDSIA）- USI/SUPSI）；Center of Excellence for Generative AI, King Abdullah University of Science and Technology（生成人工智能卓越中心，国王阿卜杜勒阿齐兹大学科学与技术学院）；NNAISENSE
Opportunistic spectrum access is one of the emerging techniques for maximizing throughput in congested bands and is enabled by predicting idle slots in spectrum. We propose a kernel-based reinforcement learning approach coupled with a novel budget-constrained sparsification technique that efficiently captures the environment to find the best channel access actions. This approach allows learning and planning over the intrinsic state-action space and extends well to large state spaces. We apply our methods to evaluate coexistence of a reinforcement learning-based radio with a multi-channel adver…
Joint replacement is the most common inpatient surgical treatment in the US. We investigate the clinical pathway optimization for knee replacement, which is a sequential decision process from onset to recovery. Based on episodic claims from previous cases, we view the pathway optimization as an intelligence crowdsourcing problem and learn the optimal decision policy from data by imitating the best expert at every intermediate state. We develop a reinforcement learning-based pipeline that uses value iteration, state compression and aggregation learning, kernel representation and cross validatio…
