We revisit the estimation bias in policy gradients for the discounted episodic Markov decision process (MDP) from Deep Reinforcement Learning (DRL) perspective. The objective is formulated theoretically as the expected returns discounted over the time horizon. One of the major policy gradient biases is the state distribution shift: the state distribution used to estimate the gradients differs from the theoretical formulation in that it does not take into account the discount factor. Existing discussion of the influence of this bias was limited to the tabular and softmax cases in the literature. Therefore, in this paper, we extend it to the DRL setting where the policy is parameterized and demonstrate how this bias can lead to suboptimal policies theoretically. We then discuss why the empirically inaccurate implementations with shifted state distribution can still be effective. We show that, despite such state distribution shift, the policy gradient estimation bias can be reduced in the following three ways: 1) a small learning rate; 2) an adaptive-learning-rate-based optimizer; and 3) KL regularization. Specifically, we show that a smaller learning rate, or, an adaptive learning rate, such as that used by Adam and RSMProp optimizers, makes the policy optimization robust to the bias. We further draw connections between optimizers and the optimization regularization to show that both the KL and the reverse KL regularization can significantly rectify this bias. Moreover, we provide extensive experiments on continuous control tasks to support our analysis. Our paper sheds light on how successful PG algorithms optimize policies in the DRL setting, and contributes insights into the practical issues in DRL.

Q-learning and SARSA with $\epsilon$-greedy exploration are leading reinforcement learning methods. Their tabular forms converge to the optimal Q-function under reasonable conditions. However, with function approximation, these methods exhibit strange behaviors such as policy oscillation, chattering, and convergence to different attractors (possibly even the worst policy) on different runs, apart from the usual instability. A theory to explain these phenomena has been a long-standing open problem, even for basic linear function approximation (Sutton, 1999). Our work uses differential inclusion to provide the first framework for resolving this problem. We also provide numerical examples to illustrate our framework's prowess in explaining these algorithms' behaviors.

Reaching tasks with random targets and obstacles is a challenging task for robotic manipulators. In this study, we propose a novel model-free reinforcement learning approach based on proximal policy optimization (PPO) for training a deep policy to map the task space to the joint space of a 6-DoF manipulator. To facilitate the training process in a large workspace, we develop an efficient representation of environmental inputs and outputs. The calculation of the distance between obstacles and manipulator links is incorporated into the state representation using a geometry-based method. Additionally, to enhance the performance of the model in reaching tasks, we introduce the action ensembles method and design the policy to directly participate in value function updates in PPO. To overcome the challenges associated with training in real-robot environments, we develop a simulation environment in Gazebo to train the model as it produces a smaller Sim-to-Real gap compared to other simulators. However, training in Gazebo is time-intensive. To address this issue, we propose a Sim-to-Sim method to significantly reduce the training time. The trained model is then directly applied in a real-robot setup without fine-tuning. To evaluate the performance of the proposed approach, we perform several rounds of experiments in both simulated and real robots. We also compare the performance of the proposed approach with six baselines. The experimental results demonstrate the effectiveness of the proposed method in performing reaching tasks with and without obstacles. our method outperformed the selected baselines by a large margin in different reaching task scenarios. A video of these experiments has been attached to the paper as supplementary material.

Generalizable manipulation skills, which can be composed to tackle long-horizon and complex daily chores, are one of the cornerstones of Embodied AI. However, existing benchmarks, mostly composed of a suite of simulatable environments, are insufficient to push cutting-edge research works because they lack object-level topological and geometric variations, are not based on fully dynamic simulation, or are short of native support for multiple types of manipulation tasks. To this end, we present ManiSkill2, the next generation of the SAPIEN ManiSkill benchmark, to address critical pain points often encountered by researchers when using benchmarks for generalizable manipulation skills. ManiSkill2 includes 20 manipulation task families with 2000+ object models and 4M+ demonstration frames, which cover stationary/mobile-base, single/dual-arm, and rigid/soft-body manipulation tasks with 2D/3D-input data simulated by fully dynamic engines. It defines a unified interface and evaluation protocol to support a wide range of algorithms (e.g., classic sense-plan-act, RL, IL), visual observations (point cloud, RGBD), and controllers (e.g., action type and parameterization). Moreover, it empowers fast visual input learning algorithms so that a CNN-based policy can collect samples at about 2000 FPS with 1 GPU and 16 processes on a regular workstation. It implements a render server infrastructure to allow sharing rendering resources across all environments, thereby significantly reducing memory usage. We open-source all codes of our benchmark (simulator, environments, and baselines) and host an online challenge open to interdisciplinary researchers.

Abstract--Multi-Agent Reinforcement Learning (MARL) is a promising area of research that can model and control multiple, autonomous decision-making agents. During online training, MARL algorithms involve performance-intensive computations such as exploration and exploitation phases originating from large observation-action space belonging to multiple agents. In this article, we seek to characterize the scalability bottlenecks in several popular classes of MARL algorithms during their training phases. Our experimental results reveal new insights into the key modules of MARL algorithms that limit the scalability, and outline potential strategies that may help address these performance issues. Distributed Artificial Intelligence < I.2 Artificial Intelligence < I Computing Methodologies The function that determines the action is known as a policy.

Mobile parcel lockers have been recently proposed by logistics operators as a technology that could help reduce traffic congestion and operational costs in urban freight distribution. Given their ability to relocate throughout their area of deployment, they hold the potential to improve customer accessibility and convenience. In this study, we formulate the Mobile Parcel Locker Problem (MPLP) , a special case of the Location-Routing Problem (LRP) which determines the optimal stopover location for MPLs throughout the day and plans corresponding delivery routes. A Hybrid Q Learning Network based Method (HQM) is developed to resolve the computational complexity of the resulting large problem instances while escaping local optima. In addition, the HQM is integrated with global and local search mechanisms to resolve the dilemma of exploration and exploitation faced by classic reinforcement learning methods. We examine the performance of HQM under different problem sizes (up to 200 nodes) and benchmarked it against the exact approach and Genetic Algorithm (GA). Our results indicate that HQM achieves better optimisation performance with shorter computation time than the exact approach solved by the Gurobi solver in large problem instances. Additionally, the average reward obtained by HQM is 1.96 times greater than GA, which demonstrates that HQM has a better optimisation ability. Further, we identify critical factors that contribute to fleet size requirements, travel distances, and service delays. Our findings outline that the efficiency of MPLs is mainly contingent on the length of time windows and the deployment of MPL stopovers. Finally, we highlight managerial implications based on parametric analysis to provide guidance for logistics operators in the context of efficient last-mile distribution operations.

Crop management involves a series of critical, interdependent decisions or actions in a complex and highly uncertain environment, which exhibit distinct spatial and temporal variations. Managing resource inputs such as fertilizer and irrigation in the face of climate change, dwindling supply, and soaring prices is nothing short of a Herculean task. The ability of machine learning to efficiently interrogate complex, nonlinear, and high-dimensional datasets can revolutionize decision-making in agriculture. In this paper, we introduce a reinforcement learning (RL) environment that leverages the dynamics in the Soil and Water Assessment Tool (SWAT) and enables management practices to be assessed and evaluated on a watershed level. This drastically saves time and resources that would have been otherwise deployed during a full-growing season. We consider crop management as an optimization problem where the objective is to produce higher crop yield while minimizing the use of external farming inputs (specifically, fertilizer and irrigation amounts). The problem is naturally subject to environmental factors such as precipitation, solar radiation, temperature, and soil water content. We demonstrate the utility of our framework by developing and benchmarking various decision-making agents following management strategies informed by standard farming practices and state-of-the-art RL algorithms.

One of the gnarliest challenges in reinforcement learning (RL) is exploration that scales to vast domains, where novelty-, or coverage-seeking behaviour falls short. Goal-directed, purposeful behaviours are able to overcome this, but rely on a good goal space. The core challenge in goal discovery is finding the right balance between generality (not hand-crafted) and tractability (useful, not too many). Our approach explicitly seeks the middle ground, enabling the human designer to specify a vast but meaningful proto-goal space, and an autonomous discovery process to refine this to a narrower space of controllable, reachable, novel, and relevant goals. The effectiveness of goal-conditioned exploration with the latter is then demonstrated in three challenging environments.

Given a dataset on actions and resulting long-term rewards, a direct estimation approach fits value functions that minimize prediction error on the training data. Temporal difference learning (TD) methods instead fit value functions by minimizing the degree of temporal inconsistency between estimates made at successive time-steps. Focusing on finite state Markov chains, we provide a crisp asymptotic theory of the statistical advantages of this approach. First, we show that an intuitive inverse trajectory pooling coefficient completely characterizes the percent reduction in mean-squared error of value estimates. Depending on problem structure, the reduction could be enormous or nonexistent. Next, we prove that there can be dramatic improvements in estimates of the difference in value-to-go for two states: TD's errors are bounded in terms of a novel measure - the problem's trajectory crossing time - which can be much smaller than the problem's time horizon.

Deep reinforcement learning repeatedly succeeds in closed, well-defined domains such as games (Chess, Go, StarCraft). The next frontier is real-world scenarios, where setups are numerous and varied. For this, agents need to learn the underlying rules governing the environment, so as to robustly generalise to conditions that differ from those they were trained on. Model-based reinforcement learning algorithms, such as the highly successful MuZero, aim to accomplish this by learning a world model. However, leveraging a world model has not consistently shown greater generalisation capabilities compared to model-free alternatives. In this work, we propose improving the data efficiency and generalisation capabilities of MuZero by explicitly incorporating the symmetries of the environment in its world-model architecture. We prove that, so long as the neural networks used by MuZero are equivariant to a particular symmetry group acting on the environment, the entirety of MuZero's action-selection algorithm will also be equivariant to that group. We evaluate Equivariant MuZero on procedurally-generated MiniPacman and on Chaser from the ProcGen suite: training on a set of mazes, and then testing on unseen rotated versions, demonstrating the benefits of equivariance. Further, we verify that our performance improvements hold even when only some of the components of Equivariant MuZero obey strict equivariance, which highlights the robustness of our construction.