Diederik M. Roijers

Lucas N. Alegre, Ana L. C. Bazzan, Diederik M. Roijers et al.

Multi-objective reinforcement learning (MORL) algorithms tackle sequential decision problems where agents may have different preferences over (possibly conflicting) reward functions. Such algorithms often learn a set of policies (each optimized for a particular agent preference) that can later be used to solve problems with novel preferences. We introduce a novel algorithm that uses Generalized Policy Improvement (GPI) to define principled, formally-derived prioritization schemes that improve sample-efficient learning. They implement active-learning strategies by which the agent can (i) identify the most promising preferences/objectives to train on at each moment, to more rapidly solve a given MORL problem; and (ii) identify which previous experiences are most relevant when learning a policy for a particular agent preference, via a novel Dyna-style MORL method. We prove our algorithm is guaranteed to always converge to an optimal solution in a finite number of steps, or an $ε$-optimal solution (for a bounded $ε$) if the agent is limited and can only identify possibly sub-optimal policies. We also prove that our method monotonically improves the quality of its partial solutions while learning. Finally, we introduce a bound that characterizes the maximum utility loss (with respect to the optimal solution) incurred by the partial solutions computed by our method throughout learning. We empirically show that our method outperforms state-of-the-art MORL algorithms in challenging multi-objective tasks, both with discrete and continuous state and action spaces.

Mathieu Reymond, Conor F. Hayes, Lander Willem et al.

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.

Florian Felten, Umut Ucak, Hicham Azmani et al.

Many challenging tasks such as managing traffic systems, electricity grids, or supply chains involve complex decision-making processes that must balance multiple conflicting objectives and coordinate the actions of various independent decision-makers (DMs). One perspective for formalising and addressing such tasks is multi-objective multi-agent reinforcement learning (MOMARL). MOMARL broadens reinforcement learning (RL) to problems with multiple agents each needing to consider multiple objectives in their learning process. In reinforcement learning research, benchmarks are crucial in facilitating progress, evaluation, and reproducibility. The significance of benchmarks is underscored by the existence of numerous benchmark frameworks developed for various RL paradigms, including single-agent RL (e.g., Gymnasium), multi-agent RL (e.g., PettingZoo), and single-agent multi-objective RL (e.g., MO-Gymnasium). To support the advancement of the MOMARL field, we introduce MOMAland, the first collection of standardised environments for multi-objective multi-agent reinforcement learning. MOMAland addresses the need for comprehensive benchmarking in this emerging field, offering over 10 diverse environments that vary in the number of agents, state representations, reward structures, and utility considerations. To provide strong baselines for future research, MOMAland also includes algorithms capable of learning policies in such settings.

Zuzanna Osika, Jazmin Zatarain Salazar, Diederik M. Roijers et al.

We present a review that unifies decision-support methods for exploring the solutions produced by multi-objective optimization (MOO) algorithms. As MOO is applied to solve diverse problems, approaches for analyzing the trade-offs offered by MOO algorithms are scattered across fields. We provide an overview of the advances on this topic, including methods for visualization, mining the solution set, and uncertainty exploration as well as emerging research directions, including interactivity, explainability, and ethics. We synthesize these methods drawing from different fields of research to build a unified approach, independent of the application. Our goals are to reduce the entry barrier for researchers and practitioners on using MOO algorithms and to provide novel research directions.

Raphael Avalos, Florent Delgrange, Ann Nowé et al.

Partially Observable Markov Decision Processes (POMDPs) are used to model environments where the full state cannot be perceived by an agent. As such the agent needs to reason taking into account the past observations and actions. However, simply remembering the full history is generally intractable due to the exponential growth in the history space. Maintaining a probability distribution that models the belief over what the true state is can be used as a sufficient statistic of the history, but its computation requires access to the model of the environment and is often intractable. While SOTA algorithms use Recurrent Neural Networks to compress the observation-action history aiming to learn a sufficient statistic, they lack guarantees of success and can lead to sub-optimal policies. To overcome this, we propose the Wasserstein Belief Updater, an RL algorithm that learns a latent model of the POMDP and an approximation of the belief update. Our approach comes with theoretical guarantees on the quality of our approximation ensuring that our outputted beliefs allow for learning the optimal value function.

Conor F. Hayes, Mathieu Reymond, Diederik M. Roijers et al.

In many risk-aware and multi-objective reinforcement learning settings, the utility of the user is derived from a single execution of a policy. In these settings, making decisions based on the average future returns is not suitable. For example, in a medical setting a patient may only have one opportunity to treat their illness. Making decisions using just the expected future returns -- known in reinforcement learning as the value -- cannot account for the potential range of adverse or positive outcomes a decision may have. Therefore, we should use the distribution over expected future returns differently to represent the critical information that the agent requires at decision time by taking both the future and accrued returns into consideration. In this paper, we propose two novel Monte Carlo tree search algorithms. Firstly, we present a Monte Carlo tree search algorithm that can compute policies for nonlinear utility functions (NLU-MCTS) by optimising the utility of the different possible returns attainable from individual policy executions, resulting in good policies for both risk-aware and multi-objective settings. Secondly, we propose a distributional Monte Carlo tree search algorithm (DMCTS) which extends NLU-MCTS. DMCTS computes an approximate posterior distribution over the utility of the returns, and utilises Thompson sampling during planning to compute policies in risk-aware and multi-objective settings. Both algorithms outperform the state-of-the-art in multi-objective reinforcement learning for the expected utility of the returns.

Conor F. Hayes, Timothy Verstraeten, Diederik M. Roijers et al.

Many real-world problems contain multiple objectives and agents, where a trade-off exists between objectives. Key to solving such problems is to exploit sparse dependency structures that exist between agents. For example, in wind farm control a trade-off exists between maximising power and minimising stress on the systems components. Dependencies between turbines arise due to the wake effect. We model such sparse dependencies between agents as a multi-objective coordination graph (MO-CoG). In multi-objective reinforcement learning a utility function is typically used to model a users preferences over objectives, which may be unknown a priori. In such settings a set of optimal policies must be computed. Which policies are optimal depends on which optimality criterion applies. If the utility function of a user is derived from multiple executions of a policy, the scalarised expected returns (SER) must be optimised. If the utility of a user is derived from a single execution of a policy, the expected scalarised returns (ESR) criterion must be optimised. For example, wind farms are subjected to constraints and regulations that must be adhered to at all times, therefore the ESR criterion must be optimised. For MO-CoGs, the state-of-the-art algorithms can only compute a set of optimal policies for the SER criterion, leaving the ESR criterion understudied. To compute a set of optimal polices under the ESR criterion, also known as the ESR set, distributions over the returns must be maintained. Therefore, to compute a set of optimal policies under the ESR criterion for MO-CoGs, we present a novel distributional multi-objective variable elimination (DMOVE) algorithm. We evaluate DMOVE in realistic wind farm simulations. Given the returns in real-world wind farm settings are continuous, we utilise a model known as real-NVP to learn the continuous return distributions to calculate the ESR set.

Raphael Avalos, Eugenio Bargiacchi, Ann Nowé et al.

In key real-world problems, full state information is sometimes available but only at a high cost, like activating precise yet energy-intensive sensors or consulting humans, thereby compelling the agent to operate under partial observability. For this scenario, we propose AEMS-SR (Anytime Error Minimization Search with State Requests), a principled online planning algorithm tailored for POMDPs with state requests. By representing the search space as a graph instead of a tree, AEMS-SR avoids the exponential growth of the search space originating from state requests. Theoretical analysis demonstrates AEMS-SR's $\varepsilon$-optimality, ensuring solution quality, while empirical evaluations illustrate its effectiveness compared with AEMS and POMCP, two SOTA online planning algorithms. AEMS-SR enables efficient planning in domains characterized by partial observability and costly state requests offering practical benefits across various applications.

Cláudia Fonseca Pinhão, Chris Eijgenstein, Iva Gornishka et al.

Obstacles on the sidewalk often block the path, limiting passage and resulting in frustration and wasted time, especially for citizens and visitors who use assistive devices (wheelchairs, walkers, strollers, canes, etc). To enable equal participation and use of the city, all citizens should be able to perform and complete their daily activities in a similar amount of time and effort. Therefore, we aim to offer accessibility information regarding sidewalks, so that citizens can better plan their routes, and to help city officials identify the location of bottlenecks and act on them. In this paper we propose a novel pipeline to estimate obstacle-free sidewalk widths based on 3D point cloud data of the city of Amsterdam, as the first step to offer a more complete set of information regarding sidewalk accessibility.

Denis Steckelmacher, Hélène Plisnier, Diederik M. Roijers et al.

Value-based reinforcement-learning algorithms provide state-of-the-art results in model-free discrete-action settings, and tend to outperform actor-critic algorithms. We argue that actor-critic algorithms are limited by their need for an on-policy critic. We propose Bootstrapped Dual Policy Iteration (BDPI), a novel model-free reinforcement-learning algorithm for continuous states and discrete actions, with an actor and several off-policy critics. Off-policy critics are compatible with experience replay, ensuring high sample-efficiency, without the need for off-policy corrections. The actor, by slowly imitating the average greedy policy of the critics, leads to high-quality and state-specific exploration, which we compare to Thompson sampling. Because the actor and critics are fully decoupled, BDPI is remarkably stable, and unusually robust to its hyper-parameters. BDPI is significantly more sample-efficient than Bootstrapped DQN, PPO, and ACKTR, on discrete, continuous and pixel-based tasks. Source code: https://github.com/vub-ai-lab/bdpi.

Peter Vamplew, Cameron Foale, Conor F. Hayes et al.

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.

Dimitris Michailidis, Willem Röpke, Diederik M. Roijers et al.

Multi-Objective Reinforcement Learning (MORL) aims to learn a set of policies that optimize trade-offs between multiple, often conflicting objectives. MORL is computationally more complex than single-objective RL, particularly as the number of objectives increases. Additionally, when objectives involve the preferences of agents or groups, ensuring fairness is socially desirable. This paper introduces a principled algorithm that incorporates fairness into MORL while improving scalability to many-objective problems. We propose using Lorenz dominance to identify policies with equitable reward distributions and introduce λ-Lorenz dominance to enable flexible fairness preferences. We release a new, large-scale real-world transport planning environment and demonstrate that our method encourages the discovery of fair policies, showing improved scalability in two large cities (Xi'an and Amsterdam). Our methods outperform common multi-objective approaches, particularly in high-dimensional objective spaces.

Paolo Speziali, Arno De Greef, Mehrdad Asadi et al.

We propose the Preference Guided Iterated Pareto Referent Optimisation (PG-IPRO) for urban route planning for people with different accessibility requirements and preferences. With this algorithm the user can interact with the system by giving feedback on a route, i.e., the user can say which objective should be further minimized, or conversely can be relaxed. This leads to intuitive user interaction, that is especially effective during early iterations compared to information-gain-based interaction. Furthermore, due to PG-IPRO's iterative nature, the full set of alternative, possibly optimal policies (the Pareto front), is never computed, leading to higher computational efficiency and shorter waiting times for users.

Jesse van Remmerden, Maurice Kenter, Diederik M. Roijers et al.

In this paper, we introduce Multi-Objective Deep Centralized Multi-Agent Actor-Critic (MO- DCMAC), a multi-objective reinforcement learning (MORL) method for infrastructural maintenance optimization, an area traditionally dominated by single-objective reinforcement learning (RL) approaches. Previous single-objective RL methods combine multiple objectives, such as probability of collapse and cost, into a singular reward signal through reward-shaping. In contrast, MO-DCMAC can optimize a policy for multiple objectives directly, even when the utility function is non-linear. We evaluated MO-DCMAC using two utility functions, which use probability of collapse and cost as input. The first utility function is the Threshold utility, in which MO-DCMAC should minimize cost so that the probability of collapse is never above the threshold. The second is based on the Failure Mode, Effects, and Criticality Analysis (FMECA) methodology used by asset managers to asses maintenance plans. We evaluated MO-DCMAC, with both utility functions, in multiple maintenance environments, including ones based on a case study of the historical quay walls of Amsterdam. The performance of MO-DCMAC was compared against multiple rule-based policies based on heuristics currently used for constructing maintenance plans. Our results demonstrate that MO-DCMAC outperforms traditional rule-based policies across various environments and utility functions.

Willem Röpke, Mathieu Reymond, Patrick Mannion et al.

An important challenge in multi-objective reinforcement learning is obtaining a Pareto front of policies to attain optimal performance under different preferences. We introduce Iterated Pareto Referent Optimisation (IPRO), which decomposes finding the Pareto front into a sequence of constrained single-objective problems. This enables us to guarantee convergence while providing an upper bound on the distance to undiscovered Pareto optimal solutions at each step. We evaluate IPRO using utility-based metrics and its hypervolume and find that it matches or outperforms methods that require additional assumptions. By leveraging problem-specific single-objective solvers, our approach also holds promise for applications beyond multi-objective reinforcement learning, such as planning and pathfinding.

Willem Röpke, Conor F. Hayes, Patrick Mannion et al.

For effective decision support in scenarios with conflicting objectives, sets of potentially optimal solutions can be presented to the decision maker. We explore both what policies these sets should contain and how such sets can be computed efficiently. With this in mind, we take a distributional approach and introduce a novel dominance criterion relating return distributions of policies directly. Based on this criterion, we present the distributional undominated set and show that it contains optimal policies otherwise ignored by the Pareto front. In addition, we propose the convex distributional undominated set and prove that it comprises all policies that maximise expected utility for multivariate risk-averse decision makers. We propose a novel algorithm to learn the distributional undominated set and further contribute pruning operators to reduce the set to the convex distributional undominated set. Through experiments, we demonstrate the feasibility and effectiveness of these methods, making this a valuable new approach for decision support in real-world problems.

Raphaël Avalos, Mathieu Reymond, Ann Nowé et al.

Many recent successful off-policy multi-agent reinforcement learning (MARL) algorithms for cooperative partially observable environments focus on finding factorized value functions, leading to convoluted network structures. Building on the structure of independent Q-learners, our LAN algorithm takes a radically different approach, leveraging a dueling architecture to learn for each agent a decentralized best-response policies via individual advantage functions. The learning is stabilized by a centralized critic whose primary objective is to reduce the moving target problem of the individual advantages. The critic, whose network's size is independent of the number of agents, is cast aside after learning. Evaluation on the StarCraft II multi-agent challenge benchmark shows that LAN reaches state-of-the-art performance and is highly scalable with respect to the number of agents, opening up a promising alternative direction for MARL research.

Peter Vamplew, Benjamin J. Smith, Johan Kallstrom et al.

The recent paper `"Reward is Enough" by Silver, Singh, Precup and Sutton posits that the concept of reward maximisation is sufficient to underpin all intelligence, both natural and artificial. We contest the underlying assumption of Silver et al. that such reward can be scalar-valued. In this paper we explain why scalar rewards are insufficient to account for some aspects of both biological and computational intelligence, and argue in favour of explicitly multi-objective models of reward maximisation. Furthermore, we contend that even if scalar reward functions can trigger intelligent behaviour in specific cases, it is still undesirable to use this approach for the development of artificial general intelligence due to unacceptable risks of unsafe or unethical behaviour.

Willem Röpke, Diederik M. Roijers, Ann Nowé et al.

We consider preference communication in two-player multi-objective normal-form games. In such games, the payoffs resulting from joint actions are vector-valued. Taking a utility-based approach, we assume there exists a utility function for each player which maps vectors to scalar utilities and consider agents that aim to maximise the utility of expected payoff vectors. As agents typically do not know their opponent's utility function or strategy, they must learn policies to interact with each other. Inspired by Stackelberg games, we introduce four novel preference communication protocols to aid agents in arriving at adequate solutions. Each protocol describes a specific approach for one agent to communicate preferences over their actions and how another agent responds. Additionally, to study when communication emerges, we introduce a communication protocol where agents must learn when to communicate. 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 alter the learning process and lead to the emergence of cyclic policies which had not been previously observed in this setting. We further observe that the resulting policies can heavily depend on the characteristics of the game that is played. Lastly, we find that communication naturally emerges in both cooperative and self-interested settings.

Conor F. Hayes, Timothy Verstraeten, Diederik M. Roijers et al.

In many real-world scenarios, the utility of a user is derived from the single execution of a policy. In this case, to apply multi-objective reinforcement learning, the expected utility of the returns must be optimised. Various scenarios exist where a user's preferences over objectives (also known as the utility function) are unknown or difficult to specify. In such scenarios, a set of optimal policies must be learned. However, settings where the expected utility must be maximised have been largely overlooked by the multi-objective reinforcement learning community and, as a consequence, a set of optimal solutions has yet to be defined. In this paper we address this challenge by proposing first-order stochastic dominance as a criterion to build solution sets to maximise expected utility. We also propose a new dominance criterion, known as expected scalarised returns (ESR) dominance, that extends first-order stochastic dominance to allow a set of optimal policies to be learned in practice. We then define a new solution concept called the ESR set, which is a set of policies that are ESR dominant. Finally, we define a new multi-objective distributional tabular reinforcement learning (MOT-DRL) algorithm to learn the ESR set in a multi-objective multi-armed bandit setting.

Conor F. Hayes, Roxana Rădulescu, Eugenio Bargiacchi et al.

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.

Conor F. Hayes, Mathieu Reymond, Diederik M. Roijers et al.

In many risk-aware and multi-objective reinforcement learning settings, the utility of the user is derived from the single execution of a policy. In these settings, making decisions based on the average future returns is not suitable. For example, in a medical setting a patient may only have one opportunity to treat their illness. When making a decision, just the expected return -- known in reinforcement learning as the value -- cannot account for the potential range of adverse or positive outcomes a decision may have. Our key insight is that we should use the distribution over expected future returns differently to represent the critical information that the agent requires at decision time. In this paper, we propose Distributional Monte Carlo Tree Search, an algorithm that learns a posterior distribution over the utility of the different possible returns attainable from individual policy executions, resulting in good policies for both risk-aware and multi-objective settings. Moreover, our algorithm outperforms the state-of-the-art in multi-objective reinforcement learning for the expected utility of the returns.

Timothy Verstraeten, Pieter-Jan Daems, Eugenio Bargiacchi et al.

Wind farms are a crucial driver toward the generation of ecological and renewable energy. Due to their rapid increase in capacity, contemporary wind farms need to adhere to strict constraints on power output to ensure stability of the electricity grid. Specifically, a wind farm controller is required to match the farm's power production with a power demand imposed by the grid operator. This is a non-trivial optimization problem, as complex dependencies exist between the wind turbines. State-of-the-art wind farm control typically relies on physics-based heuristics that fail to capture the full load spectrum that defines a turbine's health status. When this is not taken into account, the long-term viability of the farm's turbines is put at risk. Given the complex dependencies that determine a turbine's lifetime, learning a flexible and optimal control strategy requires a data-driven approach. However, as wind farms are large-scale multi-agent systems, optimizing control strategies over the full joint action space is intractable. We propose a new learning method for wind farm control that leverages the sparse wind farm structure to factorize the optimization problem. Using a Bayesian approach, based on multi-agent Thompson sampling, we explore the factored joint action space for configurations that match the demand, while considering the lifetime of turbines. We apply our method to a grid-like wind farm layout, and evaluate configurations using a state-of-the-art wind flow simulator. Our results are competitive with a physics-based heuristic approach in terms of demand error, while, contrary to the heuristic, our method prolongs the lifetime of high-risk turbines.

Roxana Rădulescu, Timothy Verstraeten, Yijie Zhang et al.

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.

Gongjin Lan, Jakub M. Tomczak, Diederik M. Roijers et al.

Not all generate-and-test search algorithms are created equal. Bayesian Optimization (BO) invests a lot of computation time to generate the candidate solution that best balances the predicted value and the uncertainty given all previous data, taking increasingly more time as the number of evaluations performed grows. Evolutionary Algorithms (EA) on the other hand rely on search heuristics that typically do not depend on all previous data and can be done in constant time. Both the BO and EA community typically assess their performance as a function of the number of evaluations. However, this is unfair once we start to compare the efficiency of these classes of algorithms, as the overhead times to generate candidate solutions are significantly different. We suggest to measure the efficiency of generate-and-test search algorithms as the expected gain in the objective value per unit of computation time spent. We observe that the preference of an algorithm to be used can change after a number of function evaluations. We therefore propose a new algorithm, a combination of Bayesian optimization and an Evolutionary Algorithm, BEA for short, that starts with BO, then transfers knowledge to an EA, and subsequently runs the EA. We compare the BEA with BO and the EA. The results show that BEA outperforms both BO and the EA in terms of time efficiency, and ultimately leads to better performance on well-known benchmark objective functions with many local optima. Moreover, we test the three algorithms on nine test cases of robot learning problems and here again we find that BEA outperforms the other algorithms.

Gongjin Lan, Matteo De Carlo, Fuda van Diggelen et al.

We generalize the well-studied problem of gait learning in modular robots in two dimensions. Firstly, we address locomotion in a given target direction that goes beyond learning a typical undirected gait. Secondly, rather than studying one fixed robot morphology we consider a test suite of different modular robots. This study is based on our interest in evolutionary robot systems where both morphologies and controllers evolve. In such a system, newborn robots have to learn to control their own body that is a random combination of the bodies of the parents. We apply and compare two learning algorithms, Bayesian optimization and HyperNEAT. The results of the experiments in simulation show that both methods successfully learn good controllers, but Bayesian optimization is more effective and efficient. We validate the best learned controllers by constructing three robots from the test suite in the real world and observe their fitness and actual trajectories. The obtained results indicate a reality gap that depends on the controllers and the shape of the robots, but overall the trajectories are adequate and follow the target directions successfully.

Roxana Rădulescu, Patrick Mannion, Yijie Zhang et al.

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.

Eugenio Bargiacchi, Timothy Verstraeten, Diederik M. Roijers et al.

We present a new model-based reinforcement learning algorithm, Cooperative Prioritized Sweeping, for efficient learning in multi-agent Markov decision processes. The algorithm allows for sample-efficient learning on large problems by exploiting a factorization to approximate the value function. Our approach only requires knowledge about the structure of the problem in the form of a dynamic decision network. Using this information, our method learns a model of the environment and performs temporal difference updates which affect multiple joint states and actions at once. Batch updates are additionally performed which efficiently back-propagate knowledge throughout the factored Q-function. Our method outperforms the state-of-the-art algorithm sparse cooperative Q-learning algorithm, both on the well-known SysAdmin benchmark and randomized environments.

Roxana Rădulescu, Patrick Mannion, Diederik M. Roijers et al.

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.

Hélène Plisnier, Denis Steckelmacher, Diederik M. Roijers et al.

Actor-critic algorithms learn an explicit policy (actor), and an accompanying value function (critic). The actor performs actions in the environment, while the critic evaluates the actor's current policy. However, despite their stability and promising convergence properties, current actor-critic algorithms do not outperform critic-only ones in practice. We believe that the fact that the critic learns Q^pi, instead of the optimal Q-function Q*, prevents state-of-the-art robust and sample-efficient off-policy learning algorithms from being used. In this paper, we propose an elegant solution, the Actor-Advisor architecture, in which a Policy Gradient actor learns from unbiased Monte-Carlo returns, while being shaped (or advised) by the Softmax policy arising from an off-policy critic. The critic can be learned independently from the actor, using any state-of-the-art algorithm. Being advised by a high-quality critic, the actor quickly and robustly learns the task, while its use of the Monte-Carlo return helps overcome any bias the critic may have. In addition to a new Actor-Critic formulation, the Actor-Advisor, a method that allows an external advisory policy to shape a Policy Gradient actor, can be applied to many other domains. By varying the source of advice, we demonstrate the wide applicability of the Actor-Advisor to three other important subfields of RL: safe RL with backup policies, efficient leverage of domain knowledge, and transfer learning in RL. Our experimental results demonstrate the benefits of the Actor-Advisor compared to state-of-the-art actor-critic methods, illustrate its applicability to the three other application scenarios listed above, and show that many important challenges of RL can now be solved using a single elegant solution.

Axel Abels, Diederik M. Roijers, Tom Lenaerts et al.

Many real-world decision problems are characterized by multiple conflicting objectives which must be balanced based on their relative importance. In the dynamic weights setting the relative importance changes over time and specialized algorithms that deal with such change, such as a tabular Reinforcement Learning (RL) algorithm by Natarajan and Tadepalli (2005), are required. However, this earlier work is not feasible for RL settings that necessitate the use of function approximators. We generalize across weight changes and high-dimensional inputs by proposing a multi-objective Q-network whose outputs are conditioned on the relative importance of objectives and we introduce Diverse Experience Replay (DER) to counter the inherent non-stationarity of the Dynamic Weights setting. We perform an extensive experimental evaluation and compare our methods to adapted algorithms from Deep Multi-Task/Multi-Objective Reinforcement Learning and show that our proposed network in combination with DER dominates these adapted algorithms across weight change scenarios and problem domains.

Hélène Plisnier, Denis Steckelmacher, Tim Brys et al.

Many currently deployed Reinforcement Learning agents work in an environment shared with humans, be them co-workers, users or clients. It is desirable that these agents adjust to people's preferences, learn faster thanks to their help, and act safely around them. We argue that most current approaches that learn from human feedback are unsafe: rewarding or punishing the agent a-posteriori cannot immediately prevent it from wrong-doing. In this paper, we extend Policy Gradient to make it robust to external directives, that would otherwise break the fundamentally on-policy nature of Policy Gradient. Our technique, Directed Policy Gradient (DPG), allows a teacher or backup policy to override the agent before it acts undesirably, while allowing the agent to leverage human advice or directives to learn faster. Our experiments demonstrate that DPG makes the agent learn much faster than reward-based approaches, while requiring an order of magnitude less advice.

Pieter Libin, Timothy Verstraeten, Diederik M. Roijers et al.

Pandemic influenza has the epidemic potential to kill millions of people. While various preventive measures exist (i.a., vaccination and school closures), deciding on strategies that lead to their most effective and efficient use remains challenging. To this end, individual-based epidemiological models are essential to assist decision makers in determining the best strategy to curb epidemic spread. However, individual-based models are computationally intensive and it is therefore pivotal to identify the optimal strategy using a minimal amount of model evaluations. Additionally, as epidemiological modeling experiments need to be planned, a computational budget needs to be specified a priori. Consequently, we present a new sampling technique to optimize the evaluation of preventive strategies using fixed budget best-arm identification algorithms. We use epidemiological modeling theory to derive knowledge about the reward distribution which we exploit using Bayesian best-arm identification algorithms (i.e., Top-two Thompson sampling and BayesGap). We evaluate these algorithms in a realistic experimental setting and demonstrate that it is possible to identify the optimal strategy using only a limited number of model evaluations, i.e., 2-to-3 times faster compared to the uniform sampling method, the predominant technique used for epidemiological decision making in the literature. Finally, we contribute and evaluate a statistic for Top-two Thompson sampling to inform the decision makers about the confidence of an arm recommendation.

Denis Steckelmacher, Diederik M. Roijers, Anna Harutyunyan et al.

Many real-world reinforcement learning problems have a hierarchical nature, and often exhibit some degree of partial observability. While hierarchy and partial observability are usually tackled separately (for instance by combining recurrent neural networks and options), we show that addressing both problems simultaneously is simpler and more efficient in many cases. More specifically, we make the initiation set of options conditional on the previously-executed option, and show that options with such Option-Observation Initiation Sets (OOIs) are at least as expressive as Finite State Controllers (FSCs), a state-of-the-art approach for learning in POMDPs. OOIs are easy to design based on an intuitive description of the task, lead to explainable policies and keep the top-level and option policies memoryless. Our experiments show that OOIs allow agents to learn optimal policies in challenging POMDPs, while being much more sample-efficient than a recurrent neural network over options.

Hossam Mossalam, Yannis M. Assael, Diederik M. Roijers et al.

We propose Deep Optimistic Linear Support Learning (DOL) to solve high-dimensional multi-objective decision problems where the relative importances of the objectives are not known a priori. Using features from the high-dimensional inputs, DOL computes the convex coverage set containing all potential optimal solutions of the convex combinations of the objectives. To our knowledge, this is the first time that deep reinforcement learning has succeeded in learning multi-objective policies. In addition, we provide a testbed with two experiments to be used as a benchmark for deep multi-objective reinforcement learning.

Auke J. Wiggers, Frans A. Oliehoek, Diederik M. Roijers

Zero-sum stochastic games provide a rich model for competitive decision making. However, under general forms of state uncertainty as considered in the Partially Observable Stochastic Game (POSG), such decision making problems are still not very well understood. This paper makes a contribution to the theory of zero-sum POSGs by characterizing structure in their value function. In particular, we introduce a new formulation of the value function for zs-POSGs as a function of the "plan-time sufficient statistics" (roughly speaking the information distribution in the POSG), which has the potential to enable generalization over such information distributions. We further delineate this generalization capability by proving a structural result on the shape of value function: it exhibits concavity and convexity with respect to appropriately chosen marginals of the statistic space. This result is a key pre-cursor for developing solution methods that may be able to exploit such structure. Finally, we show how these results allow us to reduce a zs-POSG to a "centralized" model with shared observations, thereby transferring results for the latter, narrower class, to games with individual (private) observations.

Joris Scharpff, Diederik M. Roijers, Frans A. Oliehoek et al.

In cooperative multi-agent sequential decision making under uncertainty, agents must coordinate to find an optimal joint policy that maximises joint value. Typical algorithms exploit additive structure in the value function, but in the fully-observable multi-agent MDP setting (MMDP) such structure is not present. We propose a new optimal solver for transition-independent MMDPs, in which agents can only affect their own state but their reward depends on joint transitions. We represent these dependencies compactly in conditional return graphs (CRGs). Using CRGs the value of a joint policy and the bounds on partially specified joint policies can be efficiently computed. We propose CoRe, a novel branch-and-bound policy search algorithm building on CRGs. CoRe typically requires less runtime than the available alternatives and finds solutions to problems previously unsolvable.