This section consists of three parts, with each subsequent part building upon the previous one. Appendix A.1 covers the fundamentals of RL, where the actor-critic method is introduced. Appendix A.2 describes the RL algorithm for a single fulfillment agent, which is the proximal policy Appendix A.3 presents the MARL algorithm for the Currently, policy-based methods [Deisenroth et al., 2013] are prevalent because they are compatible with stochastic To sum up, the complete procedure is given in Algorithm 1.Algorithm 1 Heterogeneous Multi-Agent Reinforcement Learning for Order Fulfillment. With regard to the advantage estimator, we set the GAE parameters [Schulman et al., 2016] To highlight how our proposed benchmark differs from existing approaches focused on sub-tasks of order fulfillment, we compare the objectives, observations, and actions in Table 1. It should be noted that multiple formulations exist for each sub-task.

Neural Information Processing Systems http://nips.cc/

The rapid expansion of platform integration has emerged as an effective solution to mitigate market fragmentation by consolidating multiple ride-hailing platforms into a single application. To address heterogeneous passenger preferences, third-party integrators provide Discount Express service delivered by express drivers at lower trip fares. For the individual platform, encouraging broader participation of drivers in Discount Express services has the potential to expand the accessible demand pool and improve matching efficiency, but often at the cost of reduced profit margins. This study aims to dynamically manage drivers' acceptance of Discount Express from the perspective of an individual platform. The lack of historical data under the new business model necessitates online learning. However, early-stage exploration through trial and error can be costly in practice, highlighting the need for reliable early-stage performance in real-world deployment. To address these challenges, this study formulates the decision regarding the proportion of drivers accepting discount orders as a continuous control task. In response to the high stochasticity and the opaque matching mechanisms employed by third-party integrator, we propose an innovative policy-improved deep deterministic policy gradient (pi-DDPG) framework. The proposed framework incorporates a refiner module to boost policy performance during the early training phase. A customized simulator based on a real-world dataset is developed to validate the effectiveness of the proposed pi-DDPG. Numerical experiments demonstrate that pi-DDPG achieves superior learning efficiency and significantly reduces early-stage training losses, enhancing its applicability to practical ride-hailing scenarios.

With the rapid advances in programmable materials, reconfigurable intelligent surfaces (RIS) have become a pivotal technology for future wireless communications. The simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) can both transmit and reflect signals, enabling comprehensive signal control and expanding application scenarios. This paper introduces an unmanned aerial vehicle (UAV) to further enhance system flexibility and proposes an optimization design for the spectrum efficiency of the STAR-RIS-UAV-assisted wireless communication system. We present a deep reinforcement learning (DRL) algorithm capable of iteratively optimizing beamforming, phase shifts, and UAV positioning to maximize the system's sum rate through continuous interactions with the environment. To improve exploration in deterministic policies, we introduce a stochastic perturbation factor, which enhances exploration capabilities. As exploration is strengthened, the algorithm's ability to accurately evaluate the state-action value function becomes critical. Thus, based on the deep deterministic policy gradient (DDPG) algorithm, we propose a convolution-augmented deep deterministic policy gradient (CA-DDPG) algorithm that balances exploration and evaluation to improve the system's sum rate. The simulation results demonstrate that the CA-DDPG algorithm effectively interacts with the environment, optimizing the beamforming matrix, phase shift matrix, and UAV location, thereby improving system capacity and achieving better performance than other algorithms.

This paper presents Post-Decision Proximal Policy Optimization (PDPPO), a novel variation of the leading deep reinforcement learning method, Proximal Policy Optimization (PPO). The PDPPO state transition process is divided into two steps: a deterministic step resulting in the post-decision state and a stochastic step leading to the next state. Our approach incorporates post-decision states and dual critics to reduce the problem's dimensionality and enhance the accuracy of value function estimation. Lot-sizing is a mixed integer programming problem for which we exemplify such dynamics. The objective of lot-sizing is to optimize production, delivery fulfillment, and inventory levels in uncertain demand and cost parameters. This paper evaluates the performance of PDPPO across various environments and configurations. Notably, PDPPO with a dual critic architecture achieves nearly double the maximum reward of vanilla PPO in specific scenarios, requiring fewer episode iterations and demonstrating faster and more consistent learning across different initializations. On average, PDPPO outperforms PPO in environments with a stochastic component in the state transition. These results support the benefits of using a post-decision state. Integrating this post-decision state in the value function approximation leads to more informed and efficient learning in high-dimensional and stochastic environments.

Multi-agent multi-objective systems (MAMOS) have emerged as powerful frameworks for modelling complex decision-making problems across various real-world domains, such as robotic exploration, autonomous traffic management, and sensor network optimisation. MAMOS offers enhanced scalability and robustness through decentralised control and more accurately reflects inherent trade-offs between conflicting objectives. In MAMOS, each agent uses utility functions that map return vectors to scalar values. Existing MAMOS optimisation methods face challenges in handling heterogeneous objective and utility function settings, where training non-stationarity is intensified due to private utility functions and the associated policies. In this paper, we first theoretically prove that direct access to, or structured modeling of, global utility functions is necessary for the Bayesian Nash Equilibrium under decentralised execution constraints. To access the global utility functions while preserving the decentralised execution, we propose an Agent-Attention Multi-Agent Multi-Objective Reinforcement Learning (AA-MAMORL) framework. Our approach implicitly learns a joint belief over other agents' utility functions and their associated policies during centralised training, effectively mapping global states and utilities to each agent's policy. In execution, each agent independently selects actions based on local observations and its private utility function to approximate a BNE, without relying on inter-agent communication. We conduct comprehensive experiments in both a custom-designed MAMO Particle environment and the standard MOMALand benchmark. The results demonstrate that access to global preferences and our proposed AA-MAMORL significantly improve performance and consistently outperform state-of-the-art methods.