Insuch applications, a team of agents aim to maximize a joint expected utility through a single global reward.

We consider the 3 fully cooperative tasks from the original set shown in Figure 1(a):Spread, Comm,andReference. "Use feature normalization" refers to whether the feature normalization is applied to the networkinput. In this appendix section, we include results which demonstrate the benefit of parameter sharing. Note that our global state to the value network has agent-specific information, such as available actions and relative distances to other agents. When an agent dies, these agent-specific features become zero, while the remaining agent-agnostic features remain nonzero -this leads to adrastic distribution shift in the critic input compared to states in which the agent is alive.

Inthiswork, we carefully study the performance of PPO in cooperative multi-agent settings.

This work presents a conceptual study on the application of Multi-Agent Reinforcement Learning (MARL) for decentralized control of unmanned aerial vehicles to relay a critical data package to a known position. For this purpose, a family of deterministic games is introduced, designed for scaling studies for MARL. A robust baseline policy is proposed, which is based on restricting agent motion envelopes and applying Dijkstra's algorithm. Experimental results show that two off-the-shelf MARL algorithms perform competitively with the baseline for a small number of agents, but scalability issues arise as the number of agents increase.

This work investigates resource optimization in heterogeneous satellite clusters performing autonomous Earth Observation (EO) missions using Reinforcement Learning (RL). In the proposed setting, two optical satellites and one Synthetic Aperture Radar (SAR) satellite operate cooperatively in low Earth orbit to capture ground targets and manage their limited onboard resources efficiently. Traditional optimization methods struggle to handle the real-time, uncertain, and decentralized nature of EO operations, motivating the use of RL and Multi-Agent Reinforcement Learning (MARL) for adaptive decision-making. This study systematically formulates the optimization problem from single-satellite to multi-satellite scenarios, addressing key challenges including energy and memory constraints, partial observability, and agent heterogeneity arising from diverse payload capabilities. Using a near-realistic simulation environment built on the Basilisk and BSK-RL frameworks, we evaluate the performance and stability of state-of-the-art MARL algorithms such as MAPPO, HAPPO, and HATRPO. Results show that MARL enables effective coordination across heterogeneous satellites, balancing imaging performance and resource utilization while mitigating non-stationarity and inter-agent reward coupling. The findings provide practical insights into scalable, autonomous satellite operations and contribute a foundation for future research on intelligent EO mission planning under heterogeneous and dynamic conditions.

Progress in multi-agent reinforcement learning (MARL) requires challenging benchmarks that assess the limits of current methods. However, existing benchmarks often target narrow short-horizon challenges that do not adequately stress the long-term dependencies and generalization capabilities inherent in many multi-agent systems. To address this, we first present \textit{Craftax-MA}: an extension of the popular open-ended RL environment, Craftax, that supports multiple agents and evaluates a wide range of general abilities within a single environment. Written in JAX, \textit{Craftax-MA} is exceptionally fast with a training run using 250 million environment interactions completing in under an hour. To provide a more compelling challenge for MARL, we also present \textit{Craftax-Coop}, an extension introducing heterogeneous agents, trading and more mechanics that require complex cooperation among agents for success. We provide analysis demonstrating that existing algorithms struggle with key challenges in this benchmark, including long-horizon credit assignment, exploration and cooperation, and argue for its potential to drive long-term research in MARL.

This paper presents a quantitative comparison between centralised and distributed multi-agent reinforcement learning (MARL) architectures for controlling a soft robotic arm modelled as a Cosserat rod in simulation. Using PyElastica and the OpenAI Gym interface, we train both a global Proximal Policy Optimisation (PPO) controller and a Multi-Agent PPO (MAPPO) under identical budgets. Both approaches are based on the arm having $n$ number of controlled sections. The study systematically varies $n$ and evaluates the performance of the arm to reach a fixed target in three scenarios: default baseline condition, recovery from external disturbance, and adaptation to actuator failure. Quantitative metrics used for the evaluation are mean action magnitude, mean final distance, mean episode length, and success rate. The results show that there are no significant benefits of the distributed policy when the number of controlled sections $n\le4$. In very simple systems, when $n\le2$, the centralised policy outperforms the distributed one. When $n$ increases to $4< n\le 12$, the distributed policy shows a high sample efficiency. In these systems, distributed policy promotes a stronger success rate, resilience, and robustness under local observability and yields faster convergence given the same sample size. However, centralised policies achieve much higher time efficiency during training as it takes much less time to train the same size of samples. These findings highlight the trade-offs between centralised and distributed policy in reinforcement learning-based control for soft robotic systems and provide actionable design guidance for future sim-to-real transfer in soft rod-like manipulators.

Dynamic pricing in retail requires policies that adapt to shifting demand while coordinating decisions across related products. We present a systematic empirical study of multi-agent reinforcement learning for retail price optimization, comparing a strong MAPPO baseline with a graph-attention-augmented variant (MAPPO+GAT) that leverages learned interactions among products. Using a simulated pricing environment derived from real transaction data, we evaluate profit, stability across random seeds, fairness across products, and training efficiency under a standardized evaluation protocol. The results indicate that MAPPO provides a robust and reproducible foundation for portfolio-level price control, and that MAPPO+GAT further enhances performance by sharing information over the product graph without inducing excessive price volatility. These results indicate that graph-integrated MARL provides a more scalable and stable solution than independent learners for dynamic retail pricing, offering practical advantages in multi-product decision-making.