Victor-Alexandru Darvariu

Ho Long Fung, Victor-Alexandru Darvariu, Stephen Hailes et al.

An often neglected issue in multi-agent reinforcement learning (MARL) is the potential presence of unreliable agents in the environment whose deviations from expected behavior can prevent a system from accomplishing its intended tasks. In particular, consensus is a fundamental underpinning problem of cooperative distributed multi-agent systems. Consensus requires different agents, situated in a decentralized communication network, to reach an agreement out of a set of initial proposals that they put forward. Learning-based agents should adopt a protocol that allows them to reach consensus despite having one or more unreliable agents in the system. This paper investigates the problem of unreliable agents in MARL, considering consensus as a case study. Echoing established results in the distributed systems literature, our experiments show that even a moderate fraction of such agents can greatly impact the ability of reaching consensus in a networked environment. We propose Reinforcement Learning-based Trusted Consensus (RLTC), a decentralized trust mechanism, in which agents can independently decide which neighbors to communicate with. We empirically demonstrate that our trust mechanism is able to handle unreliable agents effectively, as evidenced by higher consensus success rates.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Network flow problems, which involve distributing traffic such that the underlying infrastructure is used effectively, are ubiquitous in transportation and logistics. Among them, the general Multi-Commodity Network Flow (MCNF) problem concerns the distribution of multiple flows of different sizes between several sources and sinks, while achieving effective utilization of the links. Due to the appeal of data-driven optimization, these problems have increasingly been approached using graph learning methods. In this paper, we propose a novel graph learning architecture for network flow problems called Per-Edge Weights (PEW). This method builds on a Graph Attention Network and uses distinctly parametrized message functions along each link. We extensively evaluate the proposed solution through an Internet flow routing case study using $17$ Service Provider topologies and $2$ routing schemes. We show that PEW yields substantial gains over architectures whose global message function constrains the routing unnecessarily. We also find that an MLP is competitive with other standard architectures. Furthermore, we analyze the relationship between graph structure and predictive performance for data-driven routing of flows, an aspect that has not been considered by existing work in the area.

Christoffel Doorman, Victor-Alexandru Darvariu, Stephen Hailes et al.

A key problem in network theory is how to reconfigure a graph in order to optimize a quantifiable objective. Given the ubiquity of networked systems, such work has broad practical applications in a variety of situations, ranging from drug and material design to telecommunications. The large decision space of possible reconfigurations, however, makes this problem computationally intensive. In this paper, we cast the problem of network rewiring for optimizing a specified structural property as a Markov Decision Process (MDP), in which a decision-maker is given a budget of modifications that are performed sequentially. We then propose a general approach based on the Deep Q-Network (DQN) algorithm and graph neural networks (GNNs) that can efficiently learn strategies for rewiring networks. We then discuss a cybersecurity case study, i.e., an application to the computer network reconfiguration problem for intrusion protection. In a typical scenario, an attacker might have a (partial) map of the system they plan to penetrate; if the network is effectively "scrambled", they would not be able to navigate it since their prior knowledge would become obsolete. This can be viewed as an entropy maximization problem, in which the goal is to increase the surprise of the network. Indeed, entropy acts as a proxy measurement of the difficulty of navigating the network topology. We demonstrate the general ability of the proposed method to obtain better entropy gains than random rewiring on synthetic and real-world graphs while being computationally inexpensive, as well as being able to generalize to larger graphs than those seen during training. Simulations of attack scenarios confirm the effectiveness of the learned rewiring strategies.

Syu-Ning Johnn, Victor-Alexandru Darvariu, Julia Handl et al.

ALNS is a popular metaheuristic with renowned efficiency in solving combinatorial optimisation problems. However, despite 16 years of intensive research into ALNS, whether the embedded adaptive layer can efficiently select operators to improve the incumbent remains an open question. In this work, we formulate the choice of operators as a Markov Decision Process, and propose a practical approach based on Deep Reinforcement Learning and Graph Neural Networks. The results show that our proposed method achieves better performance than the classic ALNS adaptive layer due to the choice of operator being conditioned on the current solution. We also discuss important considerations such as the size of the operator portfolio and the impact of the choice of operator scales. Notably, our approach can also save significant time and labour costs for handcrafting problem-specific operator portfolios.

Michael Groom, Victor-Alexandru Darvariu, Lars Kunze et al.

Unlike standard expected-return Reinforcement Learning (RL), Distributional RL (DRL) models the full return distribution, making it better-suited for uncertainty-aware and risk-sensitive decision-making. Conditional Flow Matching (CFM) critics have recently attracted attention for modelling continuous, multi-modal return distributions. Despite this interest, there remains a substantial metric mismatch: DRL theory relies on the distributional Bellman operator being contractive in the $p$-Wasserstein distance, yet existing CFM critics are trained with arbitrary source-target couplings, so their flow-matching losses are not Wasserstein-aligned surrogates for matching Bellman target return distributions. In this work, we address this mismatch by proposing FlowIQN, a CFM critic that sorts source and Bellman target samples within each mini-batch to approximate the monotone optimal transport coupling, replacing arbitrary pairings with quantile-aligned flow paths. We prove that the loss of our quantile-coupled CFM critic yields a Wasserstein-aligned approximate projection compatible with the foundations of DRL. To our knowledge, FlowIQN is the first flow-matching distributional critic with an explicit Wasserstein-aligned projection guarantee. We further extend FlowIQN with shortcut models for efficient inference. Empirical results show that FlowIQN improves Wasserstein return-distribution accuracy over other CFM critics. It also yields competitive performance on offline RL benchmarks across multiple policy extraction methods, providing a theoretically grounded CFM critic that is readily compatible with DRL pipelines. Code: https://github.com/ori-goals/flowIQN.

Victor-Alexandru Darvariu, Charlotte Z. Reed, Jan Stratmann et al.

Underwater glider robots have become an indispensable tool for ocean sampling. Although stakeholders are calling for tools to manage increasingly large fleets of gliders, successful autonomous long-term deployments have thus far been scarce, which hints at a lack of suitable methodologies and systems. In this work, we formulate glider navigation planning as a stochastic shortest-path Markov Decision Process and propose a sample-based online planner based on Monte Carlo Tree Search. Samples are generated by a physics-informed simulator that captures uncertain execution of controls and ocean current forecasts while remaining computationally tractable. The simulator parameters are fitted using historical glider data. We integrate these methods into an autonomous command-and-control system for Slocum gliders that enables closed-loop replanning at each surfacing. The resulting system was validated in two field deployments in the North Sea totalling approximately 3 months and 1000 km of autonomous operation. Results demonstrate improved efficiency compared to straight-to-goal navigation and show the practicality of sample-based planning for long-term marine autonomy.

Junlin Xiao, Victor-Alexandru Darvariu, Bruno Lacerda et al.

Monte Carlo Tree Search is a cornerstone algorithm for online planning, and its root-parallel variant is widely used when wall clock time is limited but best performance is desired. In environments with continuous action spaces, how to best aggregate statistics from different threads is an important yet underexplored question. In this work, we introduce a method that uses Gaussian Process Regression to obtain value estimates for promising actions that were not trialed in the environment. We perform a systematic evaluation across 6 different domains, demonstrating that our approach outperforms existing aggregation strategies while requiring a modest increase in inference time.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Identifying causal structure is central to many fields ranging from strategic decision-making to biology and economics. In this work, we propose CD-UCT, a model-based reinforcement learning method for causal discovery based on tree search that builds directed acyclic graphs incrementally. We also formalize and prove the correctness of an efficient algorithm for excluding edges that would introduce cycles, which enables deeper discrete search and sampling in DAG space. The proposed method can be applied broadly to causal Bayesian networks with both discrete and continuous random variables. We conduct a comprehensive evaluation on synthetic and real-world datasets, showing that CD-UCT substantially outperforms the state-of-the-art model-free reinforcement learning technique and greedy search, constituting a promising advancement for combinatorial methods.

Alexei Pisacane, Victor-Alexandru Darvariu, Mirco Musolesi

Graph path search is a classic computer science problem that has been recently approached with Reinforcement Learning (RL) due to its potential to outperform prior methods. Existing RL techniques typically assume a global view of the network, which is not suitable for large-scale, dynamic, and privacy-sensitive settings. An area of particular interest is search in social networks due to its numerous applications. Inspired by seminal work in experimental sociology, which showed that decentralized yet efficient search is possible in social networks, we frame the problem as a collaborative task between multiple agents equipped with a limited local view of the network. We propose a multi-agent approach for graph path search that successfully leverages both homophily and structural heterogeneity. Our experiments, carried out over synthetic and real-world social networks, demonstrate that our model significantly outperforms learned and heuristic baselines. Furthermore, our results show that meaningful embeddings for graph navigation can be constructed using reward-driven learning.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures, are often challenging due to the rapid growth of the solution space. The trial-and-error paradigm of Reinforcement Learning has recently emerged as a promising alternative to traditional methods, such as exact algorithms and (meta)heuristics, for discovering better decision-making strategies in a variety of disciplines including chemistry, computer science, and statistics. Despite the fact that they arose in markedly different fields, these techniques share significant commonalities. Therefore, we set out to synthesize this work in a unifying perspective that we term Graph Reinforcement Learning, interpreting it as a constructive decision-making method for graph problems. After covering the relevant technical background, we review works along the dividing line of whether the goal is to optimize graph structure given a process of interest, or to optimize the outcome of the process itself under fixed graph structure. Finally, we discuss the common challenges facing the field and open research questions. In contrast with other surveys, the present work focuses on non-canonical graph problems for which performant algorithms are typically not known and Reinforcement Learning is able to provide efficient and effective solutions.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Causal structure discovery from observations can be improved by integrating background knowledge provided by an expert to reduce the hypothesis space. Recently, Large Language Models (LLMs) have begun to be considered as sources of prior information given the low cost of querying them relative to a human expert. In this work, firstly, we propose a set of metrics for assessing LLM judgments for causal graph discovery independently of the downstream algorithm. Secondly, we systematically study a set of prompting designs that allows the model to specify priors about the structure of the causal graph. Finally, we present a general methodology for the integration of LLM priors in graph discovery algorithms, finding that they help improve performance on common-sense benchmarks and especially when used for assessing edge directionality. Our work highlights the potential as well as the shortcomings of the use of LLMs in this problem space.

Ufuk Çakır, Victor-Alexandru Darvariu, Bruno Lacerda et al.

Artificial intelligence methods are increasingly being explored for managing wildfires and other natural hazards. In particular, reinforcement learning (RL) is a promising path towards improving outcomes in such uncertain decision-making scenarios and moving beyond reactive strategies. However, training RL agents requires many environment interactions, and the speed of existing wildfire simulators is a severely limiting factor. We introduce $\texttt{JaxWildfire}$, a simulator underpinned by a principled probabilistic fire spread model based on cellular automata. It is implemented in JAX and enables vectorized simulations using $\texttt{vmap}$, allowing high throughput of simulations on GPUs. We demonstrate that $\texttt{JaxWildfire}$ achieves 6-35x speedup over existing software and enables gradient-based optimization of simulator parameters. Furthermore, we show that $\texttt{JaxWildfire}$ can be used to train RL agents to learn wildfire suppression policies. Our work is an important step towards enabling the advancement of RL techniques for managing natural hazards.

Alex Schutz, Victor-Alexandru Darvariu, Efimia Panagiotaki et al.

Neural Algorithmic Reasoning (NAR) is a paradigm that trains neural networks to execute classic algorithms by supervised learning. Despite its successes, important limitations remain: inability to construct valid solutions without post-processing and to reason about multiple correct ones, poor performance on combinatorial NP-hard problems, and inapplicability to problems for which strong algorithms are not yet known. To address these limitations, we reframe the problem of learning algorithm trajectories as a Markov Decision Process, which imposes structure on the solution construction procedure and unlocks the powerful tools of imitation and reinforcement learning (RL). We propose the GNARL framework, encompassing the methodology to translate problem formulations from NAR to RL and a learning architecture suitable for a wide range of graph-based problems. We achieve very high graph accuracy results on several CLRS-30 problems, performance matching or exceeding much narrower NAR approaches for NP-hard problems and, remarkably, applicability even when lacking an expert algorithm.

Alberto Jesu, Victor-Alexandru Darvariu, Alessandro Staffolani et al.

The growing number of applications of Reinforcement Learning (RL) in real-world domains has led to the development of privacy-preserving techniques due to the inherently sensitive nature of data. Most existing works focus on differential privacy, in which information is revealed in the clear to an agent whose learned model should be robust against information leakage to malicious third parties. Motivated by use cases in which only encrypted data might be shared, such as information from sensitive sites, in this work we consider scenarios in which the inputs themselves are sensitive and cannot be revealed. We develop a simple extension to the MDP framework which provides for the encryption of states. We present a preliminary, experimental study of how a DQN agent trained on encrypted states performs in environments with discrete and continuous state spaces. Our results highlight that the agent is still capable of learning in small state spaces even in presence of non-deterministic encryption, but performance collapses in more complex environments.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

We tackle the problem of goal-directed graph construction: given a starting graph, a budget of modifications, and a global objective function, the aim is to find a set of edges whose addition to the graph achieves the maximum improvement in the objective (e.g., communication efficiency). This problem emerges in many networks of great importance for society such as transportation and critical infrastructure networks. We identify two significant shortcomings with present methods. Firstly, they focus exclusively on network topology while ignoring spatial information; however, in many real-world networks, nodes are embedded in space, which yields different global objectives and governs the range and density of realizable connections. Secondly, existing RL methods scale poorly to large networks due to the high cost of training a model and the scaling factors of the action space and global objectives. In this work, we formulate this problem as a deterministic MDP. We adopt the Monte Carlo Tree Search framework for planning in this domain, prioritizing the optimality of final solutions over the speed of policy evaluation. We propose several improvements over the standard UCT algorithm for this family of problems, addressing their single-agent nature, the trade-off between the costs of edges and their contribution to the objective, and an action space linear in the number of nodes. We demonstrate the suitability of this approach for improving the global efficiency and attack resilience of a variety of synthetic and real-world networks, including Internet backbone networks and metro systems. Our approach obtains a 24% improvement in these metrics compared to UCT on the largest networks tested and scalability superior to previous methods.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Public goods games represent insightful settings for studying incentives for individual agents to make contributions that, while costly for each of them, benefit the wider society. In this work, we adopt the perspective of a central planner with a global view of a network of self-interested agents and the goal of maximizing some desired property in the context of a best-shot public goods game. Existing algorithms for this known NP-complete problem find solutions that are sub-optimal and cannot optimize for criteria other than social welfare. In order to efficiently solve public goods games, our proposed method directly exploits the correspondence between equilibria and the Maximal Independent Set (mIS) structural property of graphs. In particular, we define a Markov Decision Process which incrementally generates an mIS, and adopt a planning method to search for equilibria, outperforming existing methods. Furthermore, we devise a graph imitation learning technique that uses demonstrations of the search to obtain a graph neural network parametrized policy which quickly generalizes to unseen game instances. Our evaluation results show that this policy is able to reach 99.5% of the performance of the planning method while being three orders of magnitude faster to evaluate on the largest graphs tested. The methods presented in this work can be applied to a large class of public goods games of potentially high societal impact and more broadly to other graph combinatorial optimization problems.

Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given a target objective. In this work, we formulate the construction of a graph as a decision-making process in which a central agent creates topologies by trial and error and receives rewards proportional to the value of the target objective. By means of this conceptual framework, we propose an algorithm based on reinforcement learning and graph neural networks to learn graph construction and improvement strategies. Our core case study focuses on robustness to failures and attacks, a property relevant for the infrastructure and communication networks that power modern society. Experiments on synthetic and real-world graphs show that this approach can outperform existing methods while being cheaper to evaluate. It also allows generalization to out-of-sample graphs, as well as to larger out-of-distribution graphs in some cases. The approach is applicable to the optimization of other global structural properties of graphs.