Dynamic Pricing in High-Speed Railways Using Multi-Agent Reinforcement Learning

This paper addresses a critical challenge in the high-speed passenger railway industry: designing effective dynamic pricing strategies in the context of competing and cooperating operators. To address this, a multi-agent reinforcement learning (MARL) framework based on a non-zero-sum Markov game is proposed, incorporating random utility models to capture passenger decision making. Unlike prior studies in areas such as energy, airlines, and mobile networks, dynamic pricing for railway systems using deep reinforcement learning has received limited attention. A key contribution of this paper is a parametrisable and versatile reinforcement learning simulator designed to model a variety of railway network configurations and demand patterns while enabling realistic, microscopic modelling of user behaviour, called RailPricing-RL. This environment supports the proposed MARL framework, which models heterogeneous agents competing to maximise individual profits while fostering cooperative behaviour to synchronise connecting services. Experimental results validate the framework, demonstrating how user preferences affect MARL performance and how pricing policies influence passenger choices, utility, and overall system dynamics. This study provides a foundation for advancing dynamic pricing strategies in railway systems, aligning profitability with system-wide efficiency, and supporting future research on optimising pricing policies.

Investigating Relational State Abstraction in Collaborative MARL

This paper explores the impact of relational state abstraction on sample efficiency and performance in collaborative Multi-Agent Reinforcement Learning. The proposed abstraction is based on spatial relationships in environments where direct communication between agents is not allowed, leveraging the ubiquity of spatial reasoning in real-world multi-agent scenarios. We introduce MARC (Multi-Agent Relational Critic), a simple yet effective critic architecture incorporating spatial relational inductive biases by transforming the state into a spatial graph and processing it through a relational graph neural network. The performance of MARC is evaluated across six collaborative tasks, including a novel environment with heterogeneous agents. We conduct a comprehensive empirical analysis, comparing MARC against state-of-the-art MARL baselines, demonstrating improvements in both sample efficiency and asymptotic performance, as well as its potential for generalization. Our findings suggest that a minimal integration of spatial relational inductive biases as abstraction can yield substantial benefits without requiring complex designs or task-specific engineering. This work provides insights into the potential of relational state abstraction to address sample efficiency, a key challenge in MARL, offering a promising direction for developing more efficient algorithms in spatially complex environments.

Achieving Collective Welfare in Multi-Agent Reinforcement Learning via Suggestion Sharing

In human society, the conflict between self-interest and collective well-being often obstructs efforts to achieve shared welfare. Related concepts like the Tragedy of the Commons and Social Dilemmas frequently manifest in our daily lives. As artificial agents increasingly serve as autonomous proxies for humans, we propose using multi-agent reinforcement learning (MARL) to address this issue - learning policies to maximise collective returns even when individual agents' interests conflict with the collective one. Traditional MARL solutions involve sharing rewards, values, and policies or designing intrinsic rewards to encourage agents to learn collectively optimal policies. We introduce a novel MARL approach based on Suggestion Sharing (SS), where agents exchange only action suggestions. This method enables effective cooperation without the need to design intrinsic rewards, achieving strong performance while revealing less private information compared to sharing rewards, values, or policies. Our theoretical analysis establishes a bound on the discrepancy between collective and individual objectives, demonstrating how sharing suggestions can align agents' behaviours with the collective objective. Experimental results demonstrate that SS performs competitively with baselines that rely on value or policy sharing or intrinsic rewards.

Learning on One Mode: Addressing Multi-Modality in Offline Reinforcement Learning

Offline reinforcement learning (RL) seeks to learn optimal policies from static datasets without interacting with the environment. A common challenge is handling multi-modal action distributions, where multiple behaviours are represented in the data. Existing methods often assume unimodal behaviour policies, leading to suboptimal performance when this assumption is violated. We propose Weighted Imitation Learning on One Mode (LOM), a novel approach that focuses on learning from a single, promising mode of the behaviour policy. By using a Gaussian mixture model to identify modes and selecting the best mode based on expected returns, LOM avoids the pitfalls of averaging over conflicting actions. Theoretically, we show that LOM improves performance while maintaining simplicity in policy learning. Empirically, LOM outperforms existing methods on standard D4RL benchmarks and demonstrates its effectiveness in complex, multi-modal scenarios.

An Investigation of Offline Reinforcement Learning in Factorisable Action Spaces

Expanding reinforcement learning (RL) to offline domains generates promising prospects, particularly in sectors where data collection poses substantial challenges or risks. Pivotal to the success of transferring RL offline is mitigating overestimation bias in value estimates for state-action pairs absent from data. Whilst numerous approaches have been proposed in recent years, these tend to focus primarily on continuous or small-scale discrete action spaces. Factorised discrete action spaces, on the other hand, have received relatively little attention, despite many real-world problems naturally having factorisable actions. In this work, we undertake a formative investigation into offline reinforcement learning in factorisable action spaces. Using value-decomposition as formulated in DecQN as a foundation, we present the case for a factorised approach and conduct an extensive empirical evaluation of several offline techniques adapted to the factorised setting. In the absence of established benchmarks, we introduce a suite of our own comprising datasets of varying quality and task complexity. Advocating for reproducible research and innovation, we make all datasets available for public use alongside our code base.

Mitigating Relative Over-Generalization in Multi-Agent Reinforcement Learning

In decentralized multi-agent reinforcement learning, agents learning in isolation can lead to relative over-generalization (RO), where optimal joint actions are undervalued in favor of suboptimal ones. This hinders effective coordination in cooperative tasks, as agents tend to choose actions that are individually rational but collectively suboptimal. To address this issue, we introduce MaxMax Q-Learning (MMQ), which employs an iterative process of sampling and evaluating potential next states, selecting those with maximal Q-values for learning. This approach refines approximations of ideal state transitions, aligning more closely with the optimal joint policy of collaborating agents. We provide theoretical analysis supporting MMQ's potential and present empirical evaluations across various environments susceptible to RO. Our results demonstrate that MMQ frequently outperforms existing baselines, exhibiting enhanced convergence and sample efficiency.

State-Constrained Offline Reinforcement Learning

Traditional offline reinforcement learning methods predominantly operate in a batch-constrained setting. This confines the algorithms to a specific state-action distribution present in the dataset, reducing the effects of distributional shift but restricting the algorithm greatly. In this paper, we alleviate this limitation by introducing a novel framework named \emph{state-constrained} offline reinforcement learning. By exclusively focusing on the dataset's state distribution, our framework significantly enhances learning potential and reduces previous limitations. The proposed setting not only broadens the learning horizon but also improves the ability to combine different trajectories from the dataset effectively, a desirable property inherent in offline reinforcement learning. Our research is underpinned by solid theoretical findings that pave the way for subsequent advancements in this domain. Additionally, we introduce StaCQ, a deep learning algorithm that is both performance-driven on the D4RL benchmark datasets and closely aligned with our theoretical propositions. StaCQ establishes a strong baseline for forthcoming explorations in state-constrained offline reinforcement learning.

REValueD: Regularised Ensemble Value-Decomposition for Factorisable Markov Decision Processes

Discrete-action reinforcement learning algorithms often falter in tasks with high-dimensional discrete action spaces due to the vast number of possible actions. A recent advancement leverages value-decomposition, a concept from multi-agent reinforcement learning, to tackle this challenge. This study delves deep into the effects of this value-decomposition, revealing that whilst it curtails the over-estimation bias inherent to Q-learning algorithms, it amplifies target variance. To counteract this, we present an ensemble of critics to mitigate target variance. Moreover, we introduce a regularisation loss that helps to mitigate the effects that exploratory actions in one dimension can have on the value of optimal actions in other dimensions. Our novel algorithm, REValueD, tested on discretised versions of the DeepMind Control Suite tasks, showcases superior performance, especially in the challenging humanoid and dog tasks. We further dissect the factors influencing REValueD's performance, evaluating the significance of the regularisation loss and the scalability of REValueD with increasing sub-actions per dimension.

Generating a Graph Colouring Heuristic with Deep Q-Learning and Graph Neural Networks

The graph colouring problem consists of assigning labels, or colours, to the vertices of a graph such that no two adjacent vertices share the same colour. In this work we investigate whether deep reinforcement learning can be used to discover a competitive construction heuristic for graph colouring. Our proposed approach, ReLCol, uses deep Q-learning together with a graph neural network for feature extraction, and employs a novel way of parameterising the graph that results in improved performance. Using standard benchmark graphs with varied topologies, we empirically evaluate the benefits and limitations of the heuristic learned by ReLCol relative to existing construction algorithms, and demonstrate that reinforcement learning is a promising direction for further research on the graph colouring problem.

Balancing policy constraint and ensemble size in uncertainty-based offline reinforcement learning

Offline reinforcement learning agents seek optimal policies from fixed data sets. With environmental interaction prohibited, agents face significant challenges in preventing errors in value estimates from compounding and subsequently causing the learning process to collapse. Uncertainty estimation using ensembles compensates for this by penalising high-variance value estimates, allowing agents to learn robust policies based on data-driven actions. However, the requirement for large ensembles to facilitate sufficient penalisation results in significant computational overhead. In this work, we examine the role of policy constraints as a mechanism for regulating uncertainty, and the corresponding balance between level of constraint and ensemble size. By incorporating behavioural cloning into policy updates, we show empirically that sufficient penalisation can be achieved with a much smaller ensemble size, substantially reducing computational demand while retaining state-of-the-art performance on benchmarking tasks. Furthermore, we show how such an approach can facilitate stable online fine tuning, allowing for continued policy improvement while avoiding severe performance drops.