Divide and Conquer: Provably Unveiling the Pareto Front with Multi-Objective Reinforcement Learning

A significant challenge in multi-objective reinforcement learning is obtaining a Pareto front of policies that attain optimal performance under different preferences. We introduce Iterated Pareto Referent Optimisation (IPRO), a principled algorithm that decomposes the task of finding the Pareto front into a sequence of single-objective problems for which various solution methods exist. This enables us to establish convergence guarantees while providing an upper bound on the distance to undiscovered Pareto optimal solutions at each step. Empirical evaluations demonstrate that IPRO matches or outperforms methods that require additional domain knowledge. By leveraging problem-specific single-objective solvers, our approach also holds promise for applications beyond multi-objective reinforcement learning, such as in pathfinding and optimisation.

Utility-Based Reinforcement Learning: Unifying Single-objective and Multi-objective Reinforcement Learning

Research in multi-objective reinforcement learning (MORL) has introduced the utility-based paradigm, which makes use of both environmental rewards and a function that defines the utility derived by the user from those rewards. In this paper we extend this paradigm to the context of single-objective reinforcement learning (RL), and outline multiple potential benefits including the ability to perform multi-policy learning across tasks relating to uncertain objectives, risk-aware RL, discounting, and safe RL. We also examine the algorithmic implications of adopting a utility-based approach.

Emergent Cooperation under Uncertain Incentive Alignment

Understanding the emergence of cooperation in systems of computational agents is crucial for the development of effective cooperative AI. Interaction among individuals in real-world settings are often sparse and occur within a broad spectrum of incentives, which often are only partially known. In this work, we explore how cooperation can arise among reinforcement learning agents in scenarios characterised by infrequent encounters, and where agents face uncertainty about the alignment of their incentives with those of others. To do so, we train the agents under a wide spectrum of environments ranging from fully competitive, to fully cooperative, to mixed-motives. Under this type of uncertainty we study the effects of mechanisms, such as reputation and intrinsic rewards, that have been proposed in the literature to foster cooperation in mixed-motives environments. Our findings show that uncertainty substantially lowers the agents' ability to engage in cooperative behaviour, when that would be the best course of action. In this scenario, the use of effective reputation mechanisms and intrinsic rewards boosts the agents' capability to act nearly-optimally in cooperative environments, while greatly enhancing cooperation in mixed-motive environments as well.

Exploring the Pareto front of multi-objective COVID-19 mitigation policies using reinforcement learning

Infectious disease outbreaks can have a disruptive impact on public health and societal processes. As decision making in the context of epidemic mitigation is hard, reinforcement learning provides a methodology to automatically learn prevention strategies in combination with complex epidemic models. Current research focuses on optimizing policies w.r.t. a single objective, such as the pathogen's attack rate. However, as the mitigation of epidemics involves distinct, and possibly conflicting criteria (i.a., prevalence, mortality, morbidity, cost), a multi-objective approach is warranted to learn balanced policies. To lift this decision-making process to real-world epidemic models, we apply deep multi-objective reinforcement learning and build upon a state-of-the-art algorithm, Pareto Conditioned Networks (PCN), to learn a set of solutions that approximates the Pareto front of the decision problem. We consider the first wave of the Belgian COVID-19 epidemic, which was mitigated by a lockdown, and study different deconfinement strategies, aiming to minimize both COVID-19 cases (i.e., infections and hospitalizations) and the societal burden that is induced by the applied mitigation measures. We contribute a multi-objective Markov decision process that encapsulates the stochastic compartment model that was used to inform policy makers during the COVID-19 epidemic. As these social mitigation measures are implemented in a continuous action space that modulates the contact matrix of the age-structured epidemic model, we extend PCN to this setting. We evaluate the solution returned by PCN, and observe that it correctly learns to reduce the social burden whenever the hospitalization rates are sufficiently low. In this work, we thus show that multi-objective reinforcement learning is attainable in complex epidemiological models and provides essential insights to balance complex mitigation policies.

Preference Communication in Multi-Objective Normal-Form Games

We study the problem of multiple agents learning concurrently in a multi-objective environment. Specifically, we consider two agents that repeatedly play a multi-objective normal-form game. In such games, the payoffs resulting from joint actions are vector valued. Taking a utility-based approach, we assume a utility function exists that maps vectors to scalar utilities and consider agents that aim to maximise the utility of expected payoff vectors. As agents do not necessarily know their opponent's utility function or strategy, they must learn optimal policies to interact with each other. To aid agents in arriving at adequate solutions, we introduce four novel preference communication protocols for both cooperative as well as self-interested communication. Each approach describes a specific protocol for one agent communicating preferences over their actions and how another agent responds. These protocols are subsequently evaluated on a set of five benchmark games against baseline agents that do not communicate. We find that preference communication can drastically alter the learning process and lead to the emergence of cyclic Nash equilibria which had not been previously observed in this setting. Additionally, we introduce a communication scheme where agents must learn when to communicate. For agents in games with Nash equilibria, we find that communication can be beneficial but difficult to learn when agents have different preferred equilibria. When this is not the case, agents become indifferent to communication. In games without Nash equilibria, our results show differences across learning rates. When using faster learners, we observe that explicit communication becomes more prevalent at around 50% of the time, as it helps them in learning a compromise joint policy. Slower learners retain this pattern to a lesser degree, but show increased indifference.

A Practical Guide to Multi-Objective Reinforcement Learning and Planning

Real-world decision-making tasks are generally complex, requiring trade-offs between multiple, often conflicting, objectives. Despite this, the majority of research in reinforcement learning and decision-theoretic planning either assumes only a single objective, or that multiple objectives can be adequately handled via a simple linear combination. Such approaches may oversimplify the underlying problem and hence produce suboptimal results. This paper serves as a guide to the application of multi-objective methods to difficult problems, and is aimed at researchers who are already familiar with single-objective reinforcement learning and planning methods who wish to adopt a multi-objective perspective on their research, as well as practitioners who encounter multi-objective decision problems in practice. It identifies the factors that may influence the nature of the desired solution, and illustrates by example how these influence the design of multi-objective decision-making systems for complex problems.

Opponent Learning Awareness and Modelling in Multi-Objective Normal Form Games

Many real-world multi-agent interactions consider multiple distinct criteria, i.e. the payoffs are multi-objective in nature. However, the same multi-objective payoff vector may lead to different utilities for each participant. Therefore, it is essential for an agent to learn about the behaviour of other agents in the system. In this work, we present the first study of the effects of such opponent modelling on multi-objective multi-agent interactions with non-linear utilities. Specifically, we consider two-player multi-objective normal form games with non-linear utility functions under the scalarised expected returns optimisation criterion. We contribute novel actor-critic and policy gradient formulations to allow reinforcement learning of mixed strategies in this setting, along with extensions that incorporate opponent policy reconstruction and learning with opponent learning awareness (i.e., learning while considering the impact of one's policy when anticipating the opponent's learning step). Empirical results in five different MONFGs demonstrate that opponent learning awareness and modelling can drastically alter the learning dynamics in this setting. When equilibria are present, opponent modelling can confer significant benefits on agents that implement it. When there are no Nash equilibria, opponent learning awareness and modelling allows agents to still converge to meaningful solutions that approximate equilibria.

A utility-based analysis of equilibria in multi-objective normal form games

In multi-objective multi-agent systems (MOMAS), agents explicitly consider the possible tradeoffs between conflicting objective functions. We argue that compromises between competing objectives in MOMAS should be analysed on the basis of the utility that these compromises have for the users of a system, where an agent's utility function maps their payoff vectors to scalar utility values. This utility-based approach naturally leads to two different optimisation criteria for agents in a MOMAS: expected scalarised returns (ESR) and scalarised expected returns (SER). In this article, we explore the differences between these two criteria using the framework of multi-objective normal form games (MONFGs). We demonstrate that the choice of optimisation criterion (ESR or SER) can radically alter the set of equilibria in a MONFG when non-linear utility functions are used.

Multi-Objective Multi-Agent Decision Making: A Utility-based Analysis and Survey

The majority of multi-agent system (MAS) implementations aim to optimise agents' policies with respect to a single objective, despite the fact that many real-world problem domains are inherently multi-objective in nature. Multi-objective multi-agent systems (MOMAS) explicitly consider the possible trade-offs between conflicting objective functions. We argue that, in MOMAS, such compromises should be analysed on the basis of the utility that these compromises have for the users of a system. As is standard in multi-objective optimisation, we model the user utility using utility functions that map value or return vectors to scalar values. This approach naturally leads to two different optimisation criteria: expected scalarised returns (ESR) and scalarised expected returns (SER). We develop a new taxonomy which classifies multi-objective multi-agent decision making settings, on the basis of the reward structures, and which and how utility functions are applied. This allows us to offer a structured view of the field, to clearly delineate the current state-of-the-art in multi-objective multi-agent decision making approaches and to identify promising directions for future research. Starting from the execution phase, in which the selected policies are applied and the utility for the users is attained, we analyse which solution concepts apply to the different settings in our taxonomy. Furthermore, we define and discuss these solution concepts under both ESR and SER optimisation criteria. We conclude with a summary of our main findings and a discussion of many promising future research directions in multi-objective multi-agent systems.

Analysing Congestion Problems in Multi-agent Reinforcement Learning

Congestion problems are omnipresent in today's complex networks and represent a challenge in many research domains. In the context of Multi-agent Reinforcement Learning (MARL), approaches like difference rewards and resource abstraction have shown promising results in tackling such problems. Resource abstraction was shown to be an ideal candidate for solving large-scale resource allocation problems in a fully decentralized manner. However, its performance and applicability strongly depends on some, until now, undocumented assumptions. Two of the main congestion benchmark problems considered in the literature are: the Beach Problem Domain and the Traffic Lane Domain. In both settings the highest system utility is achieved when overcrowding one resource and keeping the rest at optimum capacity. We analyse how abstract grouping can promote this behaviour and how feasible it is to apply this approach in a real-world domain (i.e., what assumptions need to be satisfied and what knowledge is necessary). We introduce a new test problem, the Road Network Domain (RND), where the resources are no longer independent, but rather part of a network (e.g., road network), thus choosing one path will also impact the load on other paths having common road segments. We demonstrate the application of state-of-the-art MARL methods for this new congestion model and analyse their performance. RND allows us to highlight an important limitation of resource abstraction and show that the difference rewards approach manages to better capture and inform the agents about the dynamics of the environment.