强化学习旨在通过与动态未知的环境的互动来学习最佳政策。许多方法依赖于价值函数的近似来得出近乎最佳的策略。在部分可观察到的环境中，这些功能取决于观测和过去的动作的完整顺序，称为历史。在这项工作中，我们从经验上表明，经过验证的复发性神经网络在内部近似于这种价值函数，从而在内部过滤了鉴于历史记录的当前状态的后验概率分布，称为信念。更确切地说，我们表明，随着经常性神经网络了解Q功能，其隐藏状态与与最佳控制相关的状态变量的信念越来越相关。这种相关性是通过其共同信息来衡量的。此外，我们表明，代理的预期回报随着其经常性架构在其隐藏状态和信念之间达到高度相互信息的能力而增加。最后，我们表明，隐藏状态与变量的信念之间的相互信息与最佳控制无关，从而通过学习过程降低。总而言之，这项工作表明，在其隐藏状态下，近似可观察到的环境的Q功能的经常性神经网络从历史上复制了足够的统计量，该统计数据与采取最佳动作的信念相关的部分相关。

Reinforcement learning (RL) gained considerable attention by creating decision-making agents that maximize rewards received from fully observable environments. However, many real-world problems are partially or noisily observable by nature, where agents do not receive the true and complete state of the environment. Such problems are formulated as partially observable Markov decision processes (POMDPs). Some studies applied RL to POMDPs by recalling previous decisions and observations or inferring the true state of the environment from received observations. Nevertheless, aggregating observations and decisions over time is impractical for environments with high-dimensional continuous state and action spaces. Moreover, so-called inference-based RL approaches require large number of samples to perform well since agents eschew uncertainty in the inferred state for the decision-making. Active inference is a framework that is naturally formulated in POMDPs and directs agents to select decisions by minimising expected free energy (EFE). This supplies reward-maximising (exploitative) behaviour in RL, with an information-seeking (exploratory) behaviour. Despite this exploratory behaviour of active inference, its usage is limited to discrete state and action spaces due to the computational difficulty of the EFE. We propose a unified principle for joint information-seeking and reward maximization that clarifies a theoretical connection between active inference and RL, unifies active inference and RL, and overcomes their aforementioned limitations. Our findings are supported by strong theoretical analysis. The proposed framework's superior exploration property is also validated by experimental results on partial observable tasks with high-dimensional continuous state and action spaces. Moreover, the results show that our model solves reward-free problems, making task reward design optional.

由于数据量增加，金融业的快速变化已经彻底改变了数据处理和数据分析的技术，并带来了新的理论和计算挑战。与古典随机控制理论和解决财务决策问题的其他分析方法相比，解决模型假设的财务决策问题，强化学习（RL）的新发展能够充分利用具有更少模型假设的大量财务数据并改善复杂的金融环境中的决策。该调查纸目的旨在审查最近的资金途径的发展和使用RL方法。我们介绍了马尔可夫决策过程，这是许多常用的RL方法的设置。然后引入各种算法，重点介绍不需要任何模型假设的基于价值和基于策略的方法。连接是用神经网络进行的，以扩展框架以包含深的RL算法。我们的调查通过讨论了这些RL算法在金融中各种决策问题中的应用，包括最佳执行，投资组合优化，期权定价和对冲，市场制作，智能订单路由和Robo-Awaring。

Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are continuous or hybrid, which is often the case for physical systems. While recent online sampling-based POMDP algorithms that plan with observation likelihood weighting have shown practical effectiveness, a general theory characterizing the approximation error of the particle filtering techniques that these algorithms use has not previously been proposed. Our main contribution is bounding the error between any POMDP and its corresponding finite sample particle belief MDP (PB-MDP) approximation. This fundamental bridge between PB-MDPs and POMDPs allows us to adapt any sampling-based MDP algorithm to a POMDP by solving the corresponding particle belief MDP, thereby extending the convergence guarantees of the MDP algorithm to the POMDP. Practically, this is implemented by using the particle filter belief transition model as the generative model for the MDP solver. While this requires access to the observation density model from the POMDP, it only increases the transition sampling complexity of the MDP solver by a factor of $\mathcal{O}(C)$, where $C$ is the number of particles. Thus, when combined with sparse sampling MDP algorithms, this approach can yield algorithms for POMDPs that have no direct theoretical dependence on the size of the state and observation spaces. In addition to our theoretical contribution, we perform five numerical experiments on benchmark POMDPs to demonstrate that a simple MDP algorithm adapted using PB-MDP approximation, Sparse-PFT, achieves performance competitive with other leading continuous observation POMDP solvers.

Adequately assigning credit to actions for future outcomes based on their contributions is a long-standing open challenge in Reinforcement Learning. The assumptions of the most commonly used credit assignment method are disadvantageous in tasks where the effects of decisions are not immediately evident. Furthermore, this method can only evaluate actions that have been selected by the agent, making it highly inefficient. Still, no alternative methods have been widely adopted in the field. Hindsight Credit Assignment is a promising, but still unexplored candidate, which aims to solve the problems of both long-term and counterfactual credit assignment. In this thesis, we empirically investigate Hindsight Credit Assignment to identify its main benefits, and key points to improve. Then, we apply it to factored state representations, and in particular to state representations based on the causal structure of the environment. In this setting, we propose a variant of Hindsight Credit Assignment that effectively exploits a given causal structure. We show that our modification greatly decreases the workload of Hindsight Credit Assignment, making it more efficient and enabling it to outperform the baseline credit assignment method on various tasks. This opens the way to other methods based on given or learned causal structures.

我们介绍了一种改进政策改进的方法，该方法在基于价值的强化学习（RL）的贪婪方法与基于模型的RL的典型计划方法之间进行了插值。新方法建立在几何视野模型（GHM，也称为伽马模型）的概念上，该模型对给定策略的折现状态验证分布进行了建模。我们表明，我们可以通过仔细的基本策略GHM的仔细组成，而无需任何其他学习，可以评估任何非马尔科夫策略，以固定的概率在一组基本马尔可夫策略之间切换。然后，我们可以将广义政策改进（GPI）应用于此类非马尔科夫政策的收集，以获得新的马尔可夫政策，通常将其表现优于其先驱。我们对这种方法提供了彻底的理论分析，开发了转移和标准RL的应用，并在经验上证明了其对标准GPI的有效性，对充满挑战的深度RL连续控制任务。我们还提供了GHM培训方法的分析，证明了关于先前提出的方法的新型收敛结果，并显示了如何在深度RL设置中稳定训练这些模型。

在实际应用中，尽管这种知识对于确定反应性控制系统与环境的精确相互作用很重要，但我们很少可以完全观察到系统的环境。因此，我们提出了一种在部分可观察到的环境中进行加固学习方法（RL）。在假设环境的行为就像是可观察到的马尔可夫决策过程，但我们对其结构或过渡概率不了解。我们的方法将Q学习与IOALERGIA结合在一起，这是一种学习马尔可夫决策过程（MDP）的方法。通过从RL代理的发作中学习环境的MDP模型，我们可以在不明确的部分可观察到的域中启用RL，而没有明确的记忆，以跟踪以前的相互作用，以处理由部分可观察性引起的歧义。相反，我们通过模拟学习环境模型上的新体验以跟踪探索状态，以抽象环境状态的形式提供其他观察结果。在我们的评估中，我们报告了方法的有效性及其有希望的性能，与六种具有复发性神经网络和固定记忆的最先进的深度RL技术相比。

离线RL算法必须说明其提供的数据集可能使环境的许多方面未知。应对这一挑战的最常见方法是采用悲观或保守的方法，避免行为与培训数据集中的行为过于不同。但是，仅依靠保守主义存在缺点：绩效对保守主义的确切程度很敏感，保守的目标可以恢复高度最佳的政策。在这项工作中，我们建议在不确定性的情况下，脱机RL方法应该是适应性的。我们表明，在贝叶斯的意义上，在离线RL中最佳作用涉及解决隐式POMDP。结果，离线RL的最佳策略必须是自适应的，这不仅取决于当前状态，而且还取决于迄今为止在评估期间看到的所有过渡。我们提出了一种无模型的算法，用于近似于此最佳自适应策略，并证明在离线RL基准测试中学习此类适应性政策。

While reinforcement learning algorithms provide automated acquisition of optimal policies, practical application of such methods requires a number of design decisions, such as manually designing reward functions that not only define the task, but also provide sufficient shaping to accomplish it. In this paper, we view reinforcement learning as inferring policies that achieve desired outcomes, rather than as a problem of maximizing rewards. To solve this inference problem, we establish a novel variational inference formulation that allows us to derive a well-shaped reward function which can be learned directly from environment interactions. From the corresponding variational objective, we also derive a new probabilistic Bellman backup operator and use it to develop an off-policy algorithm to solve goal-directed tasks. We empirically demonstrate that this method eliminates the need to hand-craft reward functions for a suite of diverse manipulation and locomotion tasks and leads to effective goal-directed behaviors.

学习评估和改善政策是加强学习（RL）的核心问题。传统的RL算法学习为单个策略定义的值函数。最近探索的竞争选择是学习许多策略的单个价值功能。在这里，我们结合了基于参数的价值函数的参与者批判性架构和策略评估网络的策略嵌入，以学习评估（并从而有助于改善）的单个价值函数，以改善深度神经网络（NN）代表的任何策略。该方法产生竞争性的实验结果。在无限多个状态的连续控制问题中，我们的价值函数通过同时学习一小部分“探测状态”和从探测状态在策略返回中产生的动作的映射来最大程度地减少其预测错误。该方法以极少数状态的形式提取有关环境的重要抽象知识，足以完全指定许多政策的行为。策略仅通过改变探测状态的动作，遵循值函数的预测的梯度来改善。令人惊讶的是，只有通过分别知道如何在3和5的5个这样的国家中采取行动，才有可能克隆在游泳者V3和Hopper-V3环境中近乎最佳政策的行为。值得注意的是，我们经过评估NN策略的培训的价值功能也与政策体系结构的变化也不变：我们表明，它允许零拍学习线性策略的竞争力与培训中最佳政策竞争。我们的代码是公开的。

Many practical applications of reinforcement learning constrain agents to learn from a fixed batch of data which has already been gathered, without offering further possibility for data collection. In this paper, we demonstrate that due to errors introduced by extrapolation, standard offpolicy deep reinforcement learning algorithms, such as DQN and DDPG, are incapable of learning without data correlated to the distribution under the current policy, making them ineffective for this fixed batch setting. We introduce a novel class of off-policy algorithms, batch-constrained reinforcement learning, which restricts the action space in order to force the agent towards behaving close to on-policy with respect to a subset of the given data. We present the first continuous control deep reinforcement learning algorithm which can learn effectively from arbitrary, fixed batch data, and empirically demonstrate the quality of its behavior in several tasks.

资产分配（或投资组合管理）是确定如何最佳将有限预算的资金分配给一系列金融工具/资产（例如股票）的任务。这项研究调查了使用无模型的深RL代理应用于投资组合管理的增强学习（RL）的性能。我们培训了几个RL代理商的现实股票价格，以学习如何执行资产分配。我们比较了这些RL剂与某些基线剂的性能。我们还比较了RL代理，以了解哪些类别的代理表现更好。从我们的分析中，RL代理可以执行投资组合管理的任务，因为它们的表现明显优于基线代理（随机分配和均匀分配）。四个RL代理（A2C，SAC，PPO和TRPO）总体上优于最佳基线MPT。这显示了RL代理商发现更有利可图的交易策略的能力。此外，基于价值和基于策略的RL代理之间没有显着的性能差异。演员批评者的表现比其他类型的药物更好。同样，在政策代理商方面的表现要好，因为它们在政策评估方面更好，样品效率在投资组合管理中并不是一个重大问题。这项研究表明，RL代理可以大大改善资产分配，因为它们的表现优于强基础。基于我们的分析，在政策上，参与者批评的RL药物显示出最大的希望。

在强化学习中，代理成功使用了以马尔可夫决策过程（MDP）建模的环境。但是，在许多问题域中，代理可能会遭受嘈杂的观察或随机时间，直到其随后的决定为止。尽管可观察到的马尔可夫决策过程（POMDP）已经处理了嘈杂的观察，但他们尚未处理未知的时间方面。当然，人们可以离散时间，但这导致了贝尔曼的维度诅咒。为了将连续的寄居时间分布纳入代理商的决策中，我们建议部分可观察到的半马尔可夫决策过程（POSMDP）在这方面有所帮助。我们扩展了\ citet {spaan2005a}基于随机点的值迭代（PBVI）\ textsc {perseus}算法，用于POMDP，通过结合连续的SOJOURN时间分布并使用重要性来减少求解器复杂性。我们称此新的PBVI算法为POSMDPS -\ textsc {ChronoSperSeus}，其重要性采样。这进一步允许通过将此信息移至pOMSDP的状态周时间来进行压缩的复杂POMDP，需要时间状态信息。第二个见解是，可以在单个备份中使用一组抽样的时间并通过其可能性加权。这有助于进一步降低算法复杂性。该求解器还针对情节性和非疾病问题。我们以两个示例结束了论文，一个情节的巴士问题和非剧烈的维护问题。

我们考虑在一个有限时间范围内的离散时间随机动力系统的联合设计和控制。我们将问题作为一个多步优化问题，在寻求识别系统设计和控制政策的不确定性下，共同最大化所考虑的时间范围内收集的预期奖励总和。转换函数，奖励函数和策略都是参数化的，假设与其参数有所不同。然后，我们引入了一种深度加强学习算法，将策略梯度方法与基于模型的优化技术相结合以解决这个问题。从本质上讲，我们的算法迭代地估计通过Monte-Carlo采样和自动分化的预期返回的梯度，并在环境和策略参数空间中投影梯度上升步骤。该算法称为直接环境和策略搜索（DEPS）。我们评估我们算法在三个环境中的性能，分别在三种环境中进行了一个群众弹簧阻尼系统的设计和控制，分别小型离网电力系统和无人机。此外，我们的算法是针对用于解决联合设计和控制问题的最先进的深增强学习算法的基准测试。我们表明，在所有三种环境中，DEPS至少在或更好地执行，始终如一地产生更高的迭代返回的解决方案。最后，通过我们的算法产生的解决方案也与由算法产生的解决方案相比，不共同优化环境和策略参数，突出显示在执行联合优化时可以实现更高返回的事实。

在这项工作中，我们提出并评估了一种新的增强学习方法，紧凑体验重放（编者），它使用基于相似转换集的复发的预测目标值的时间差异学习，以及基于两个转换的经验重放的新方法记忆。我们的目标是减少在长期累计累计奖励的经纪人培训所需的经验。它与强化学习的相关性与少量观察结果有关，即它需要实现类似于文献中的相关方法获得的结果，这通常需要数百万视频框架来培训ATARI 2600游戏。我们举报了在八个挑战街机学习环境（ALE）挑战游戏中，为仅10万帧的培训试验和大约25,000次迭代的培训试验中报告了培训试验。我们还在与基线的同一游戏中具有相同的实验协议的DQN代理呈现结果。为了验证从较少数量的观察结果近似于良好的政策，我们还将其结果与从啤酒的基准上呈现的数百万帧中获得的结果进行比较。

具有很多玩家的非合作和合作游戏具有许多应用程序，但是当玩家数量增加时，通常仍然很棘手。由Lasry和Lions以及Huang，Caines和Malham \'E引入的，平均野外运动会（MFGS）依靠平均场外近似值，以使玩家数量可以成长为无穷大。解决这些游戏的传统方法通常依赖于以完全了解模型的了解来求解部分或随机微分方程。最近，增强学习（RL）似乎有望解决复杂问题。通过组合MFGS和RL，我们希望在人口规模和环境复杂性方面能够大规模解决游戏。在这项调查中，我们回顾了有关学习MFG中NASH均衡的最新文献。我们首先确定最常见的设置（静态，固定和进化）。然后，我们为经典迭代方法（基于最佳响应计算或策略评估）提供了一个通用框架，以确切的方式解决MFG。在这些算法和与马尔可夫决策过程的联系的基础上，我们解释了如何使用RL以无模型的方式学习MFG解决方案。最后，我们在基准问题上介绍了数值插图，并以某些视角得出结论。

钢筋学习的最新进展证明了其在超级人类水平上解决硬质孕代环境互动任务的能力。然而，由于大多数RL最先进的算法的样本低效率，即，需要大量培训集，因此在实际和现实世界任务中的应用目前有限。例如，在Dota 2中击败人类参与者的Openai五种算法已经训练了数千年的游戏时间。存在解决样本低效问题的几种方法，可以通过更好地探索环境来提供更有效的使用或旨在获得更相关和多样化的经验。然而，为了我们的知识，没有用于基于模型的算法的这种方法，其在求解具有高维状态空间的硬控制任务方面的高采样效率。这项工作连接了探索技术和基于模型的加强学习。我们设计了一种新颖的探索方法，考虑了基于模型的方法的特征。我们还通过实验证明我们的方法显着提高了基于模型的算法梦想家的性能。

基于价值的增强学习算法在游戏，机器人技术和其他现实世界应用中表现出了很强的性能。最受欢迎的基于样本的方法是$ q $ - 学习。随后，它通过将当前$ Q $ estimate调整为观察到的奖励和下一个状态的$ Q $估计值来执行更新。该过程引入了最大化偏置，其方法是Double $ Q $ - 学习。我们从统计上构架了偏置问题，并认为它是估计一组随机变量的最大期望值（MEV）的实例。我们根据平均值的两样本测试提出了$ t $估计器（TE），该测试通过调整基本假设检验的显着性水平来灵活地插入过度和低估之间。称为$ k $ estimator（KE）的概括，在依靠几乎任意的内核函数的同时，遵守与TE相同的偏差和差异界限。我们使用TE和KE介绍了$ Q $ - 学习的修改和引导Deep $ Q $ -NETWORK（BDQN）。此外，我们提出了基于TE的BDQN的自适应变体，该变体会动态调整显着性水平，以最大程度地减少绝对估计偏置。所有提出的估计器和算法均经过彻底的测试和验证，并在不同的任务和环境上进行了验证，以说明TE和KE的偏见控制和性能潜力。

Model-Based Reinforcement Learning (RL) is widely believed to have the potential to improve sample efficiency by allowing an agent to synthesize large amounts of imagined experience. Experience Replay (ER) can be considered a simple kind of model, which has proved extremely effective at improving the stability and efficiency of deep RL. In principle, a learned parametric model could improve on ER by generalizing from real experience to augment the dataset with additional plausible experience. However, owing to the many design choices involved in empirically successful algorithms, it can be very hard to establish where the benefits are actually coming from. Here, we provide theoretical and empirical insight into when, and how, we can expect data generated by a learned model to be useful. First, we provide a general theorem motivating how learning a model as an intermediate step can narrow down the set of possible value functions more than learning a value function directly from data using the Bellman equation. Second, we provide an illustrative example showing empirically how a similar effect occurs in a more concrete setting with neural network function approximation. Finally, we provide extensive experiments showing the benefit of model-based learning for online RL in environments with combinatorial complexity, but factored structure that allows a learned model to generalize. In these experiments, we take care to control for other factors in order to isolate, insofar as possible, the benefit of using experience generated by a learned model relative to ER alone.

Transfer in Reinforcement Learning aims to improve learning performance on target tasks using knowledge from experienced source tasks. Successor Representations (SR) and their extension Successor Features (SF) are prominent transfer mechanisms in domains where reward functions change between tasks. They reevaluate the expected return of previously learned policies in a new target task to transfer their knowledge. The SF framework extended SR by linearly decomposing rewards into successor features and a reward weight vector allowing their application in high-dimensional tasks. But this came with the cost of having a linear relationship between reward functions and successor features, limiting its application to such tasks. We propose a novel formulation of SR based on learning the cumulative discounted probability of successor features, called Successor Feature Representations (SFR). Crucially, SFR allows to reevaluate the expected return of policies for general reward functions. We introduce different SFR variations, prove its convergence, and provide a guarantee on its transfer performance. Experimental evaluations based on SFR with function approximation demonstrate its advantage over SF not only for general reward functions but also in the case of linearly decomposable reward functions.