Many popular policy gradient methods for reinforcement learning follow a biased approximation of the policy gradient known as the discounted approximation. While it has been shown that the discounted approximation of the policy gradient is not the gradient of any objective function, little else is known about its convergence behavior or properties. In this paper, we show that if the discounted approximation is followed such that the discount factor is increased slowly at a rate related to a decreasing learning rate, the resulting method recovers the standard guarantees of gradient ascent on the undiscounted objective.

In this paper we consider deterministic policy gradient algorithms for reinforcement learning with continuous actions. The deterministic policy gradient has a particularly appealing form: it is the expected gradient of the action-value function. This simple form means that the deterministic policy gradient can be estimated much more efficiently than the usual stochastic policy gradient. To ensure adequate exploration, we introduce an off-policy actor-critic algorithm that learns a deterministic target policy from an exploratory behaviour policy. We demonstrate that deterministic policy gradient algorithms can significantly outperform their stochastic counterparts in high-dimensional action spaces.

由于策略梯度定理导致的策略设置存在各种理论上 - 声音策略梯度算法，其为梯度提供了简化的形式。然而，由于存在多重目标和缺乏明确的脱助政策政策梯度定理，截止策略设置不太明确。在这项工作中，我们将这些目标统一到一个违规目标，并为此统一目标提供了政策梯度定理。推导涉及强调的权重和利息职能。我们显示多种策略来近似梯度，以识别权重（ACE）称为Actor评论家的算法。我们证明了以前（半梯度）脱离政策演员 - 评论家 - 特别是offpac和DPG - 收敛到错误的解决方案，而Ace找到最佳解决方案。我们还强调为什么这些半梯度方法仍然可以在实践中表现良好，表明ace中的方差策略。我们经验研究了两个经典控制环境的若干ACE变体和基于图像的环境，旨在说明每个梯度近似的权衡。我们发现，通过直接逼近强调权重，ACE在所有测试的所有设置中执行或优于offpac。

In many sequential decision-making problems one is interested in minimizing an expected cumulative cost while taking into account risk, i.e., increased awareness of events of small probability and high consequences. Accordingly, the objective of this paper is to present efficient reinforcement learning algorithms for risk-constrained Markov decision processes (MDPs), where risk is represented via a chance constraint or a constraint on the conditional value-at-risk (CVaR) of the cumulative cost. We collectively refer to such problems as percentile risk-constrained MDPs. Specifically, we first derive a formula for computing the gradient of the Lagrangian function for percentile riskconstrained MDPs. Then, we devise policy gradient and actor-critic algorithms that (1) estimate such gradient, (2) update the policy in the descent direction, and (3) update the Lagrange multiplier in the ascent direction. For these algorithms we prove convergence to locally optimal policies. Finally, we demonstrate the effectiveness of our algorithms in an optimal stopping problem and an online marketing application.

从现有数据中学习最佳行为是加强学习（RL）中最重要的问题之一。这被称为RL中的“非政策控制”，其中代理的目标是根据从给定策略（称为行为策略）获得的数据计算最佳策略。由于最佳策略可能与行为策略有很大不同，因此与“政体”设置相比，学习最佳行为非常困难，在学习中将利用来自策略更新的新数据。这项工作提出了一种非政策的天然参与者批评算法，该算法利用州行动分布校正来处理外部行为和样本效率的自然政策梯度。具有收敛保证的现有基于天然梯度的参与者批评算法需要固定功能，以近似策略和价值功能。这通常会导致许多RL应用中的次级学习。另一方面，我们提出的算法利用兼容功能，使人们能够使用任意神经网络近似策略和价值功能，并保证收敛到本地最佳策略。我们通过将其与基准RL任务上的香草梯度参与者 - 批评算法进行比较，说明了提出的非政策自然梯度算法的好处。

民间传说表明，政策梯度比其相对，近似政策迭代更为强大。本文研究了国家聚集表示的案例，该案例是对状态空间进行分区的情况，并且在分区上保持了策略或价值函数近似。本文显示了一种策略梯度方法收敛到政策，该政策的遗憾是由$ \ epsilon $界定的，这是属于公共分区的国家行动值函数的两个要素之间的最大区别。通过相同的表示，近似政策迭代和近似价值迭代都可以产生政策，其遗憾的比例为$ \ epsilon/（1- \ gamma）$，其中$ \ gamma $是折扣因子。面对固有的近似误差，局部优化真实决策目标的方法可以更加健壮。

Policy gradient methods are an appealing approach in reinforcement learning because they directly optimize the cumulative reward and can straightforwardly be used with nonlinear function approximators such as neural networks. The two main challenges are the large number of samples typically required, and the difficulty of obtaining stable and steady improvement despite the nonstationarity of the incoming data. We address the first challenge by using value functions to substantially reduce the variance of policy gradient estimates at the cost of some bias, with an exponentially-weighted estimator of the advantage function that is analogous to TD(λ). We address the second challenge by using trust region optimization procedure for both the policy and the value function, which are represented by neural networks. Our approach yields strong empirical results on highly challenging 3D locomotion tasks, learning running gaits for bipedal and quadrupedal simulated robots, and learning a policy for getting the biped to stand up from starting out lying on the ground. In contrast to a body of prior work that uses hand-crafted policy representations, our neural network policies map directly from raw kinematics to joint torques. Our algorithm is fully model-free, and the amount of simulated experience required for the learning tasks on 3D bipeds corresponds to 1-2 weeks of real time.

We propose and analyze a class of actor-critic algorithms for simulation-based optimization of a Markov decision process over a parameterized family of randomized stationary policies. These are two-time-scale algorithms in which the critic uses TD learning with a linear approximation architecture and the actor is updated in an approximate gradient direction based on information provided by the critic. We show that the features for the critic should span a subspace prescribed by the choice of parameterization of the actor. We conclude by discussing convergence properties and some open problems.

Model-free deep reinforcement learning (RL) algorithms have been demonstrated on a range of challenging decision making and control tasks. However, these methods typically suffer from two major challenges: very high sample complexity and brittle convergence properties, which necessitate meticulous hyperparameter tuning. Both of these challenges severely limit the applicability of such methods to complex, real-world domains. In this paper, we propose soft actor-critic, an offpolicy actor-critic deep RL algorithm based on the maximum entropy reinforcement learning framework. In this framework, the actor aims to maximize expected reward while also maximizing entropy. That is, to succeed at the task while acting as randomly as possible. Prior deep RL methods based on this framework have been formulated as Q-learning methods. By combining off-policy updates with a stable stochastic actor-critic formulation, our method achieves state-of-the-art performance on a range of continuous control benchmark tasks, outperforming prior on-policy and off-policy methods. Furthermore, we demonstrate that, in contrast to other off-policy algorithms, our approach is very stable, achieving very similar performance across different random seeds.

在标准数据分析框架中，首先收集数据（全部一次），然后进行数据分析。此外，通常认为数据生成过程是外源性的。当数据分析师对数据的生成方式没有影响时，这种方法是自然的。但是，数字技术的进步使公司促进了从数据中学习并同时做出决策。随着这些决定生成新数据，数据分析师（业务经理或算法）也成为数据生成器。这种相互作用会产生一种新型的偏见 - 增强偏见 - 加剧了静态数据分析中的内生性问题。因果推理技术应该被纳入加强学习中以解决此类问题。

In this work we introduce reinforcement learning techniques for solving lexicographic multi-objective problems. These are problems that involve multiple reward signals, and where the goal is to learn a policy that maximises the first reward signal, and subject to this constraint also maximises the second reward signal, and so on. We present a family of both action-value and policy gradient algorithms that can be used to solve such problems, and prove that they converge to policies that are lexicographically optimal. We evaluate the scalability and performance of these algorithms empirically, demonstrating their practical applicability. As a more specific application, we show how our algorithms can be used to impose safety constraints on the behaviour of an agent, and compare their performance in this context with that of other constrained reinforcement learning algorithms.

策略梯度方法适用于复杂的，不理解的，通过对参数化的策略进行随机梯度下降来控制问题。不幸的是，即使对于可以通过标准动态编程技术解决的简单控制问题，策略梯度算法也会面临非凸优化问题，并且被广泛理解为仅收敛到固定点。这项工作确定了结构属性 - 通过几个经典控制问题共享 - 确保策略梯度目标函数尽管是非凸面，但没有次优的固定点。当这些条件得到加强时，该目标满足了产生收敛速率的Polyak-lojasiewicz（梯度优势）条件。当其中一些条件放松时，我们还可以在任何固定点的最佳差距上提供界限。

我们研究了Wang等人介绍的熵调查的，探索性扩散过程制定的Q-学习（RL）的Q-学习（RL）的持续时间对应物。 （2020）随着常规（大）Q功能在连续的时间崩溃，我们考虑其一阶近似，并在“（小）Q功能”一词中造成术语。此功能与瞬时优势率函数以及哈密顿量有关。我们围绕时间离散化独立于Q功能开发了“ Q学习”理论。鉴于随机策略，我们通过某些随机过程的martingale条件共同表征了相关的Q功能和价值函数。然后，我们将理论应用来设计不同的参与者批评算法来解决潜在的RL问题，具体取决于是否可以明确计算从Q功能产生的Gibbs测量的密度函数。我们的一种算法解释了著名的Q学习算法SARSA，另一个算法恢复了基于政策梯度（PG）在Jia和Zhou（2021）中提出的基于策略梯度（PG）。最后，我们进行了仿真实验，以将我们的算法的性能与JIA和Zhou（2021）中的PG基算法的性能以及时间消化的常规Q学习算法进行比较。

We provide a natural gradient method that represents the steepest descent direction based on the underlying structure of the parameter space. Although gradient methods cannot make large changes in the values of the parameters, we show that the natural gradient is moving toward choosing a greedy optimal action rather than just a better action. These greedy optimal actions are those that would be chosen under one improvement step of policy iteration with approximate, compatible value functions, as defined by Sutton et al. [9]. We then show drastic performance improvements in simple MDPs and in the more challenging MDP of Tetris.

基于我们先前关于绿色仿真辅助政策梯度（GS-PG）的研究，重点是基于轨迹的重复使用，在本文中，我们考虑了无限 - 马尔可夫马尔可夫决策过程，并创建了一种新的重要性采样策略梯度优化的方法来支持动态决策制造。现有的GS-PG方法旨在从完整的剧集或过程轨迹中学习，这将其适用性限制在低数据状态和灵活的在线过程控制中。为了克服这一限制，提出的方法可以选择性地重复使用最相关的部分轨迹，即，重用单元基于每步或每次派遣的历史观察。具体而言，我们创建了基于混合的可能性比率（MLR）策略梯度优化，该优化可以利用不同行为政策下产生的历史状态行动转变中的信息。提出的减少差异经验重播（VRER）方法可以智能地选择和重复使用最相关的过渡观察，改善策略梯度估计并加速最佳政策的学习。我们的实证研究表明，它可以改善优化融合并增强最先进的政策优化方法的性能，例如Actor-Critic方法和近端政策优化。

我们在王等人开发的正规化探索制剂下，研究政策梯度（PG），以便在连续时间和空间中进行加强学习。 （2020）。我们代表值函数的梯度相对于给定的参数化随机策略，作为可以使用样本和当前值函数进行评估的辅助运行奖励函数的预期集成。这有效地将PG转化为策略评估（PE）问题，使我们能够应用贾和周最近开发的Martingale方法来解决我们的PG问题。基于此分析，我们为RL提出了两种类型的演员 - 批评算法，在那里我们同时和交替地学习和更新值函数和策略。第一类型直接基于上述表示，涉及未来的轨迹，因此是离线的。专为在线学习的第二种类型使用了政策梯度的一阶条件，并将其转化为Martingale正交状态。然后在更新策略时使用随机近似并入这些条件。最后，我们通过模拟在两个具体示例中展示了算法。

While risk-neutral reinforcement learning has shown experimental success in a number of applications, it is well-known to be non-robust with respect to noise and perturbations in the parameters of the system. For this reason, risk-sensitive reinforcement learning algorithms have been studied to introduce robustness and sample efficiency, and lead to better real-life performance. In this work, we introduce new model-free risk-sensitive reinforcement learning algorithms as variations of widely-used Policy Gradient algorithms with similar implementation properties. In particular, we study the effect of exponential criteria on the risk-sensitivity of the policy of a reinforcement learning agent, and develop variants of the Monte Carlo Policy Gradient algorithm and the online (temporal-difference) Actor-Critic algorithm. Analytical results showcase that the use of exponential criteria generalize commonly used ad-hoc regularization approaches. The implementation, performance, and robustness properties of the proposed methods are evaluated in simulated experiments.

政策梯度（PG）算法是备受期待的强化学习对现实世界控制任务（例如机器人技术）的最佳候选人之一。但是，每当必须在物理系统上执行学习过程本身或涉及任何形式的人类计算机相互作用时，这些方法的反复试验性质就会提出安全问题。在本文中，我们解决了一种特定的安全公式，其中目标和危险都以标量奖励信号进行编码，并且学习代理被限制为从不恶化其性能，以衡量为预期的奖励总和。通过从随机优化的角度研究仅行为者的政策梯度，我们为广泛的参数政策建立了改进保证，从而将现有结果推广到高斯政策上。这与策略梯度估计器的差异的新型上限一起，使我们能够识别出具有很高概率的单调改进的元参数计划。两个关键的元参数是参数更新的步长和梯度估计的批处理大小。通过对这些元参数的联合自适应选择，我们获得了具有单调改进保证的政策梯度算法。

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。