Ann Nowé

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.

Glenn Ceusters, Luis Ramirez Camargo, Rüdiger Franke et al.

Reinforcement learning (RL) is a promising optimal control technique for multi-energy management systems. It does not require a model a priori - reducing the upfront and ongoing project-specific engineering effort and is capable of learning better representations of the underlying system dynamics. However, vanilla RL does not provide constraint satisfaction guarantees - resulting in various potentially unsafe interactions within its safety-critical environment. In this paper, we present two novel safe RL methods, namely SafeFallback and GiveSafe, where the safety constraint formulation is decoupled from the RL formulation. These provide hard-constraint, rather than soft- and chance-constraint, satisfaction guarantees both during training a (near) optimal policy (which involves exploratory and exploitative, i.e. greedy, steps) as well as during deployment of any policy (e.g. random agents or offline trained RL agents). This without the need of solving a mathematical program, resulting in less computational power requirements and a more flexible constraint function formulation (no derivative information is required). In a simulated multi-energy systems case study we have shown that both methods start with a significantly higher utility (i.e. useful policy) compared to a vanilla RL benchmark and Optlayer benchmark (94,6% and 82,8% compared to 35,5% and 77,8%) and that the proposed SafeFallback method even can outperform the vanilla RL benchmark (102,9% to 100%). We conclude that both methods are viably safety constraint handling techniques applicable beyond RL, as demonstrated with random policies while still providing hard-constraint guarantees.

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.

Alexandra Cimpean, Timothy Verstraeten, Lander Willem et al.

Individual-based epidemiological models support the study of fine-grained preventive measures, such as tailored vaccine allocation policies, in silico. As individual-based models are computationally intensive, it is pivotal to identify optimal strategies within a reasonable computational budget. Moreover, due to the high societal impact associated with the implementation of preventive strategies, uncertainty regarding decisions should be communicated to policy makers, which is naturally embedded in a Bayesian approach. We present a novel technique for evaluating vaccine allocation strategies using a multi-armed bandit framework in combination with a Bayesian anytime $m$-top exploration algorithm. $m$-top exploration allows the algorithm to learn $m$ policies for which it expects the highest utility, enabling experts to inspect this small set of alternative strategies, along with their quantified uncertainty. The anytime component provides policy advisors with flexibility regarding the computation time and the desired confidence, which is important as it is difficult to make this trade-off beforehand. We consider the Belgian COVID-19 epidemic using the individual-based model STRIDE, where we learn a set of vaccination policies that minimize the number of infections and hospitalisations. Through experiments we show that our method can efficiently identify the $m$-top policies, which is validated in a scenario where the ground truth is available. Finally, we explore how vaccination policies can best be organised under different contact reduction schemes and we investigate the impact of vaccine uptake proportions (i.e., the proportion of individuals that will comply with the strategy and take the vaccine).

Glenn Ceusters, Muhammad Andy Putratama, Rüdiger Franke et al.

Safe reinforcement learning (RL) with hard constraint guarantees is a promising optimal control direction for multi-energy management systems. It only requires the environment-specific constraint functions itself a priori and not a complete model. The project-specific upfront and ongoing engineering efforts are therefore still reduced, better representations of the underlying system dynamics can still be learnt, and modelling bias is kept to a minimum. However, even the constraint functions alone are not always trivial to accurately provide in advance, leading to potentially unsafe behaviour. In this paper, we present two novel advancements: (I) combining the OptLayer and SafeFallback method, named OptLayerPolicy, to increase the initial utility while keeping a high sample efficiency and the possibility to formulate equality constraints. (II) introducing self-improving hard constraints, to increase the accuracy of the constraint functions as more and new data becomes available so that better policies can be learnt. Both advancements keep the constraint formulation decoupled from the RL formulation, so new (presumably better) RL algorithms can act as drop-in replacements. We have shown that, in a simulated multi-energy system case study, the initial utility is increased to 92.4% (OptLayerPolicy) compared to 86.1% (OptLayer) and that the policy after training is increased to 104.9% (GreyOptLayerPolicy) compared to 103.4% (OptLayer) - all relative to a vanilla RL benchmark. Although introducing surrogate functions into the optimisation problem requires special attention, we conclude that the newly presented GreyOptLayerPolicy method is the most advantageous.

Qingshuang Sun, Denis Steckelmacher, Yuan Yao et al.

Communication plays a vital role in multi-agent systems, fostering collaboration and coordination. However, in real-world scenarios where communication is bandwidth-limited, existing multi-agent reinforcement learning (MARL) algorithms often provide agents with a binary choice: either transmitting a fixed number of bytes or no information at all. This limitation hinders the ability to effectively utilize the available bandwidth. To overcome this challenge, we present the Dynamic Size Message Scheduling (DSMS) method, which introduces a finer-grained approach to scheduling by considering the actual size of the information to be exchanged. Our contribution lies in adaptively adjusting message sizes using Fourier transform-based compression techniques, enabling agents to tailor their messages to match the allocated bandwidth while striking a balance between information loss and transmission efficiency. Receiving agents can reliably decompress the messages using the inverse Fourier transform. Experimental results demonstrate that DSMS significantly improves performance in multi-agent cooperative tasks by optimizing the utilization of bandwidth and effectively balancing information value.

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.

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.

Mathieu Reymond, Eugenio Bargiacchi, Ann Nowé

In multi-objective optimization, learning all the policies that reach Pareto-efficient solutions is an expensive process. The set of optimal policies can grow exponentially with the number of objectives, and recovering all solutions requires an exhaustive exploration of the entire state space. We propose Pareto Conditioned Networks (PCN), a method that uses a single neural network to encompass all non-dominated policies. PCN associates every past transition with its episode's return. It trains the network such that, when conditioned on this same return, it should reenact said transition. In doing so we transform the optimization problem into a classification problem. We recover a concrete policy by conditioning the network on the desired Pareto-efficient solution. Our method is stable as it learns in a supervised fashion, thus avoiding moving target issues. Moreover, by using a single network, PCN scales efficiently with the number of objectives. Finally, it makes minimal assumptions on the shape of the Pareto front, which makes it suitable to a wider range of problems than previous state-of-the-art multi-objective reinforcement learning algorithms.

Hélène Plisnier, Denis Steckelmacher, Jeroen Willems et al.

Many instances of similar or almost-identical industrial machines or tools are often deployed at once, or in quick succession. For instance, a particular model of air compressor may be installed at hundreds of customers. Because these tools perform distinct but highly similar tasks, it is interesting to be able to quickly produce a high-quality controller for machine $N+1$ given the controllers already produced for machines $1..N$. This is even more important when the controllers are learned through Reinforcement Learning, as training takes time, energy and other resources. In this paper, we apply Policy Intersection, a Policy Shaping method, to help a Reinforcement Learning agent learn to solve a new variant of a compressors control problem faster, by transferring knowledge from several previously learned controllers. We show that our approach outperforms loading an old controller, and significantly improves performance in the long run.

Max Bruninx, Diederik van Binsbergen, Timothy Verstraeten et al.

Accurate production forecasts are essential to continue facilitating the integration of renewable energy sources into the power grid. This paper illustrates how to obtain probabilistic day-ahead forecasts of wind power generation via gradient boosting trees using an ensemble of weather forecasts. To this end, we perform a comparative analysis across three state-of-the-art probabilistic prediction methods-conformalised quantile regression, natural gradient boosting and conditional diffusion models-all of which can be combined with tree-based machine learning. The methods are validated using four years of data for all wind farms present within the Belgian offshore zone. Additionally, the point forecasts are benchmarked against deterministic engineering methods, using either the power curve or an advanced approach incorporating a calibrated analytical wake model. The experimental results show that the machine learning methods improve the mean absolute error by up to 53% and 33% compared to the power curve and the calibrated wake model. Considering the three probabilistic prediction methods, the conditional diffusion model is found to yield the best overall probabilistic and point estimate of wind power generation. Moreover, the findings suggest that the use of an ensemble of weather forecasts can improve point forecast accuracy by up to 23%.

Florent Delgrange, Ann Nowé, Guillermo A. Pérez

Although deep reinforcement learning (DRL) has many success stories, the large-scale deployment of policies learned through these advanced techniques in safety-critical scenarios is hindered by their lack of formal guarantees. Variational Markov Decision Processes (VAE-MDPs) are discrete latent space models that provide a reliable framework for distilling formally verifiable controllers from any RL policy. While the related guarantees address relevant practical aspects such as the satisfaction of performance and safety properties, the VAE approach suffers from several learning flaws (posterior collapse, slow learning speed, poor dynamics estimates), primarily due to the absence of abstraction and representation guarantees to support latent optimization. We introduce the Wasserstein auto-encoded MDP (WAE-MDP), a latent space model that fixes those issues by minimizing a penalized form of the optimal transport between the behaviors of the agent executing the original policy and the distilled policy, for which the formal guarantees apply. Our approach yields bisimulation guarantees while learning the distilled policy, allowing concrete optimization of the abstraction and representation model quality. Our experiments show that, besides distilling policies up to 10 times faster, the latent model quality is indeed better in general. Moreover, we present experiments from a simple time-to-failure verification algorithm on the latent space. The fact that our approach enables such simple verification techniques highlights its applicability.

Senne Deproost, Denis Steckelmacher, Ann Nowé

Despite many successful attempts at explaining Deep Reinforcement Learning policies using distillation, it remains difficult to balance the performance-interpretability trade-off and select a fitting surrogate model. In addition to this, traditional distillation only minimizes the distance between the behavior of the original and the surrogate policy while other RL-specific components such as action value are disregarded. To solve this, we introduce a new model-agnostic method called Critic-Driven Voronoi State Partitioning, which partitions a black box control policy into regions where a simple class of model can be optimized using gradient descent. By exploiting the critic value network of the original policy, we iteratively introduce new subpolicies in regions with insufficient value, standing in for a measure of policy complexity. The partitioning, a Voronoi quantizer, uses nearest neighbor lookups to assign a linear function to each point in the state space resulting in a cell-like diagram. We validate our approach on several well known benchmarks and proof that this distillation approaches the original policy using a reasonable sized set of linear functions.

Senne Deproost, Mehrdad Asadi, Ann Nowé

We introduce State Vector Space Partitioning (SVSP), a novel method to mimic a black box reinforcement learning policy using a set of human-interpretable subpolicies. By partitioning a distillation dataset of state action pairs with linear support vector machine splits, SVSP constructs a compact and structured representation of the original policy. Our method improves mean return by +7.4\% over previous critic driven state partitioning attempts such as Voronoi State Partitioning (VSP) and +2.8\% over the original TD3 policy, while reducing the number of required subpolicies against VSP by 82.1\%. Our results pave the path towards a more flexible form of distillation where both the decision boundary and surrogate models can be chosen within a margin of the original black box behavior.

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.

Axel Abels, Elias Fernandez Domingos, Ann Nowé et al.

Individual and social biases undermine the effectiveness of human advisers by inducing judgment errors which can disadvantage protected groups. In this paper, we study the influence these biases can have in the pervasive problem of fake news by evaluating human participants' capacity to identify false headlines. By focusing on headlines involving sensitive characteristics, we gather a comprehensive dataset to explore how human responses are shaped by their biases. Our analysis reveals recurring individual biases and their permeation into collective decisions. We show that demographic factors, headline categories, and the manner in which information is presented significantly influence errors in human judgment. We then use our collected data as a benchmark problem on which we evaluate the efficacy of adaptive aggregation algorithms. In addition to their improved accuracy, our results highlight the interactions between the emergence of collective intelligence and the mitigation of participant biases.

Florent Delgrange, Guy Avni, Anna Lukina et al.

We propose a novel framework to controller design in environments with a two-level structure: a known high-level graph ("map") in which each vertex is populated by a Markov decision process, called a "room". The framework "separates concerns" by using different design techniques for low- and high-level tasks. We apply reactive synthesis for high-level tasks: given a specification as a logical formula over the high-level graph and a collection of low-level policies obtained together with "concise" latent structures, we construct a "planner" that selects which low-level policy to apply in each room. We develop a reinforcement learning procedure to train low-level policies on latent structures, which unlike previous approaches, circumvents a model distillation step. We pair the policy with probably approximately correct guarantees on its performance and on the abstraction quality, and lift these guarantees to the high-level task. These formal guarantees are the main advantage of the framework. Other advantages include scalability (rooms are large and their dynamics are unknown) and reusability of low-level policies. We demonstrate feasibility in challenging case studies where an agent navigates environments with moving obstacles and visual inputs.

Apurva Shah, Axel Abels, Ann Nowé et al.

Perpetual voting addresses fairness in sequential collective decision-making by evaluating representational equity over time. However, existing perpetual voting rules rely on full participation and complete approval information, assumptions that rarely hold in practice, where partial turnout is the norm. In this work, we study the integration of Artificial Delegates, preference-learning agents trained to represent absent voters, into perpetual voting systems. We examine how absenteeism affects fairness and representativeness under various voting methods and evaluate the extent to which Artificial Delegates can compensate for missing participation. Our findings indicate that while absenteeism significantly affects fairness, Artificial Delegates reliably mitigate these effects and enhance robustness across diverse scenarios.

Mehrdad Asadi, Roxana Rădulescu, Ann Nowé

Swarming systems, such as for example multi-drone networks, excel at cooperative tasks like monitoring, surveillance, or disaster assistance in critical environments, where autonomous agents make decentralized decisions in order to fulfill team-level objectives in a robust and efficient manner. Unfortunately, team-level coordinated strategies in the wild are vulnerable to data poisoning attacks, resulting in either inaccurate coordination or adversarial behavior among the agents. To address this challenge, we contribute a framework that investigates the effects of such data poisoning attacks, using explainable AI methods. We model the interaction among agents using evolutionary intelligence, where an optimal coalition strategically emerges to perform coordinated tasks. Then, through a rigorous evaluation, the swarm model is systematically poisoned using data manipulation attacks. We showcase the applicability of explainable AI methods to quantify the effects of poisoning on the team strategy and extract footprint characterizations that enable diagnosing. Our findings indicate that when the model is poisoned above 10%, non-optimal strategies resulting in inefficient cooperation can be identified.

Yannick Molinghen, Raphaël Avalos, Mark Van Achter et al.

We introduce the Laser Learning Environment (LLE), a collaborative multi-agent reinforcement learning environment in which coordination is central. In LLE, agents depend on each other to make progress (interdependence), must jointly take specific sequences of actions to succeed (perfect coordination), and accomplishing those joint actions does not yield any intermediate reward (zero-incentive dynamics). The challenge of such problems lies in the difficulty of escaping state space bottlenecks caused by interdependence steps since escaping those bottlenecks is not rewarded. We test multiple state-of-the-art value-based MARL algorithms against LLE and show that they consistently fail at the collaborative task because of their inability to escape state space bottlenecks, even though they successfully achieve perfect coordination. We show that Q-learning extensions such as prioritized experience replay and n-steps return hinder exploration in environments with zero-incentive dynamics, and find that intrinsic curiosity with random network distillation is not sufficient to escape those bottlenecks. We demonstrate the need for novel methods to solve this problem and the relevance of LLE as cooperative MARL benchmark.

Senne Deproost, Dennis Steckelmacher, Ann Nowé

Deep Reinforcement Learning is one of the state-of-the-art methods for producing near-optimal system controllers. However, deep RL algorithms train a deep neural network, that lacks transparency, which poses challenges when the controller has to meet regulations, or foster trust. To alleviate this, one could transfer the learned behaviour into a model that is human-readable by design using knowledge distilla- tion. Often this is done with a single model which mimics the original model on average but could struggle in more dynamic situations. A key challenge is that this simpler model should have the right balance be- tween flexibility and complexity or right balance between balance bias and accuracy. We propose a new model-agnostic method to divide the state space into regions where a simplified, human-understandable model can operate in. In this paper, we use Voronoi partitioning to find regions where linear models can achieve similar performance to the original con- troller. We evaluate our approach on a gridworld environment and a classic control task. We observe that our proposed distillation to locally- specialized linear models produces policies that are explainable and show that the distillation matches or even slightly outperforms the black-box policy they are distilled from.

Andries Rosseau, Raphaël Avalos, Ann Nowé

The competitive and cooperative forces of natural selection have driven the evolution of intelligence for millions of years, culminating in nature's vast biodiversity and the complexity of human minds. Inspired by this process, we propose a novel multi-agent reinforcement learning framework where each agent is assigned a genotype and where reward functions are modelled after the concept of inclusive fitness. An agent's genetic material may be shared with other agents, and our inclusive reward function naturally accounts for this. We study the resulting social dynamics in two types of network games with prisoner's dilemmas and find that our results align with well-established principles from biology, such as Hamilton's rule. Furthermore, we outline how this framework can extend to more open-ended environments with spatial and temporal structure, finite resources, and evolving populations. We hypothesize the emergence of an arms race of strategies, where each new strategy is a gradual improvement over earlier adaptations of other agents, effectively producing a multi-agent autocurriculum analogous to biological evolution. In contrast to the binary team-based structures prevalent in earlier research, our gene-based reward structure introduces a spectrum of cooperation ranging from full adversity to full cooperativeness based on genetic similarity, enabling unique non team-based social dynamics. For example, one agent having a mutual cooperative relationship with two other agents, while the two other agents behave adversarially towards each other. We argue that incorporating inclusive fitness in agents provides a foundation for the emergence of more strategically advanced and socially intelligent agents.

Alexandra Cimpean, Nicole Orzan, Catholijn Jonker et al.

Equity in real-world sequential decision problems can be enforced using fairness-aware methods. Therefore, we require algorithms that can make suitable and transparent trade-offs between performance and the desired fairness notions. As the desired performance-fairness trade-off is hard to specify a priori, we propose a framework where multiple trade-offs can be explored. Insights provided by the reinforcement learning algorithm regarding the obtainable performance-fairness trade-offs can then guide stakeholders in selecting the most appropriate policy. To capture fairness, we propose an extended Markov decision process, $f$MDP, that explicitly encodes individuals and groups. Given this $f$MDP, we formalise fairness notions in the context of sequential decision problems and formulate a fairness framework that computes fairness measures over time. We evaluate our framework in two scenarios with distinct fairness requirements: job hiring, where strong teams must be composed while treating applicants equally, and fraud detection, where fraudulent transactions must be detected while ensuring the burden on customers is fairly distributed. We show that our framework learns policies that are more fair across multiple scenarios, with only minor loss in performance reward. Moreover, we observe that group and individual fairness notions do not necessarily imply one another, highlighting the benefit of our framework in settings where both fairness types are desired. Finally, we provide guidelines on how to apply this framework across different problem settings.

Senne Deproost, Denis Steckelmacher, Ann Nowé

With Deep Reinforcement Learning (DRL) being increasingly considered for the control of real-world systems, the lack of transparency of the neural network at the core of RL becomes a concern. Programmatic Reinforcement Learning (PRL) is able to to create representations of this black-box in the form of source code, not only increasing the explainability of the controller but also allowing for user adaptations. However, these methods focus on distilling a black-box policy into a program and do so after learning using the Mean Squared Error between produced and wanted behaviour, discarding other elements of the RL algorithm. The distilled policy may therefore perform significantly worse than the black-box learned policy. In this paper, we propose to directly learn a program as the policy of an RL agent. We build on TD3 and use its critics as the basis of the objective function of a genetic algorithm that syntheses the program. Our approach builds the program during training, as opposed to after the fact. This steers the program to actual high rewards, instead of a simple Mean Squared Error. Also, our approach leverages the TD3 critics to achieve high sample-efficiency, as opposed to pure genetic methods that rely on Monte-Carlo evaluations. Our experiments demonstrate the validity, explainability and sample-efficiency of our approach in a simple gridworld environment.

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.

Axel Abels, Tom Lenaerts, Vito Trianni et al.

Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such changes in depth and breadth of knowledge as a partitioning of the problem space into regions of differing expertise. We provide here new algorithms that explicitly consider and adapt to the relationship between problem instances and experts' knowledge. We first propose and highlight the drawbacks of a naive approach based on nearest neighbor queries. To address these drawbacks we then introduce a novel algorithm - expertise trees - that constructs decision trees enabling the learner to select appropriate models. We provide theoretical insights and empirically validate the improved performance of our novel approach on a range of problems for which existing methods proved to be inadequate.

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.

Florent Delgrange, Ann Nowé, Guillermo A. Pérez

We consider the challenge of policy simplification and verification in the context of policies learned through reinforcement learning (RL) in continuous environments. In well-behaved settings, RL algorithms have convergence guarantees in the limit. While these guarantees are valuable, they are insufficient for safety-critical applications. Furthermore, they are lost when applying advanced techniques such as deep-RL. To recover guarantees when applying advanced RL algorithms to more complex environments with (i) reachability, (ii) safety-constrained reachability, or (iii) discounted-reward objectives, we build upon the DeepMDP framework introduced by Gelada et al. to derive new bisimulation bounds between the unknown environment and a learned discrete latent model of it. Our bisimulation bounds enable the application of formal methods for Markov decision processes. Finally, we show how one can use a policy obtained via state-of-the-art RL to efficiently train a variational autoencoder that yields a discrete latent model with provably approximately correct bisimulation guarantees. Additionally, we obtain a distilled version of the policy for the latent model.

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.

Axel Abels, Tom Lenaerts, Vito Trianni et al.

Quite some real-world problems can be formulated as decision-making problems wherein one must repeatedly make an appropriate choice from a set of alternatives. Multiple expert judgements, whether human or artificial, can help in taking correct decisions, especially when exploration of alternative solutions is costly. As expert opinions might deviate, the problem of finding the right alternative can be approached as a collective decision making problem (CDM) via aggregation of independent judgements. Current state-of-the-art approaches focus on efficiently finding the optimal expert, and thus perform poorly if all experts are not qualified or if they are overly biased, thereby potentially derailing the decision-making process. In this paper, we propose a new algorithmic approach based on contextual multi-armed bandit problems (CMAB) to identify and counteract such biased expertise. We explore homogeneous, heterogeneous and polarised expert groups and show that this approach is able to effectively exploit the collective expertise, outperforming state-of-the-art methods, especially when the quality of the provided expertise degrades. Our novel CMAB-inspired approach achieves a higher final performance and does so while converging more rapidly than previous adaptive algorithms.

Youri Coppens, Denis Steckelmacher, Catholijn M. Jonker et al.

Today's advanced Reinforcement Learning algorithms produce black-box policies, that are often difficult to interpret and trust for a person. We introduce a policy distilling algorithm, building on the CN2 rule mining algorithm, that distills the policy into a rule-based decision system. At the core of our approach is the fact that an RL process does not just learn a policy, a mapping from states to actions, but also produces extra meta-information, such as action values indicating the quality of alternative actions. This meta-information can indicate whether more than one action is near-optimal for a certain state. We extend CN2 to make it able to leverage knowledge about equally-good actions to distill the policy into fewer rules, increasing its interpretability by a person. Then, to ensure that the rules explain a valid, non-degenerate policy, we introduce a refinement algorithm that fine-tunes the rules to obtain good performance when executed in the environment. We demonstrate the applicability of our algorithm on the Mario AI benchmark, a complex task that requires modern reinforcement learning algorithms including neural networks. The explanations we produce capture the learned policy in only a few rules, that allow a person to understand what the black-box agent learned. Source code: https://gitlab.ai.vub.ac.be/yocoppen/svcn2

Glenn Ceusters, Román Cantú Rodríguez, Alberte Bouso García et al.

Model-predictive-control (MPC) offers an optimal control technique to establish and ensure that the total operation cost of multi-energy systems remains at a minimum while fulfilling all system constraints. However, this method presumes an adequate model of the underlying system dynamics, which is prone to modelling errors and is not necessarily adaptive. This has an associated initial and ongoing project-specific engineering cost. In this paper, we present an on- and off-policy multi-objective reinforcement learning (RL) approach, that does not assume a model a priori, benchmarking this against a linear MPC (LMPC - to reflect current practice, though non-linear MPC performs better) - both derived from the general optimal control problem, highlighting their differences and similarities. In a simple multi-energy system (MES) configuration case study, we show that a twin delayed deep deterministic policy gradient (TD3) RL agent offers potential to match and outperform the perfect foresight LMPC benchmark (101.5%). This while the realistic LMPC, i.e. imperfect predictions, only achieves 98%. While in a more complex MES system configuration, the RL agent's performance is generally lower (94.6%), yet still better than the realistic LMPC (88.9%). In both case studies, the RL agents outperformed the realistic LMPC after a training period of 2 years using quarterly interactions with the environment. We conclude that reinforcement learning is a viable optimal control technique for multi-energy systems given adequate constraint handling and pre-training, to avoid unsafe interactions and long training periods, as is proposed in fundamental future work.

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.

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.

Pieter Libin, Arno Moonens, Timothy Verstraeten et al.

Epidemics of infectious diseases are an important threat to public health and global economies. Yet, the development of prevention strategies remains a challenging process, as epidemics are non-linear and complex processes. For this reason, we investigate a deep reinforcement learning approach to automatically learn prevention strategies in the context of pandemic influenza. Firstly, we construct a new epidemiological meta-population model, with 379 patches (one for each administrative district in Great Britain), that adequately captures the infection process of pandemic influenza. Our model balances complexity and computational efficiency such that the use of reinforcement learning techniques becomes attainable. Secondly, we set up a ground truth such that we can evaluate the performance of the 'Proximal Policy Optimization' algorithm to learn in a single district of this epidemiological model. Finally, we consider a large-scale problem, by conducting an experiment where we aim to learn a joint policy to control the districts in a community of 11 tightly coupled districts, for which no ground truth can be established. This experiment shows that deep reinforcement learning can be used to learn mitigation policies in complex epidemiological models with a large state space. Moreover, through this experiment, we demonstrate that there can be an advantage to consider collaboration between districts when designing prevention strategies.

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.

Timothy Verstraeten, Pieter JK Libin, Ann Nowé

In many settings, as for example wind farms, multiple machines are instantiated to perform the same task, which is called a fleet. The recent advances with respect to the Internet of Things allow control devices and/or machines to connect through cloud-based architectures in order to share information about their status and environment. Such an infrastructure allows seamless data sharing between fleet members, which could greatly improve the sample-efficiency of reinforcement learning techniques. However in practice, these machines, while almost identical in design, have small discrepancies due to production errors or degradation, preventing control algorithms to simply aggregate and employ all fleet data. We propose a novel reinforcement learning method that learns to transfer knowledge between similar fleet members and creates member-specific dynamics models for control. Our algorithm uses Gaussian processes to establish cross-member covariances. This is significantly different from standard transfer learning methods, as the focus is not on sharing information over tasks, but rather over system specifications. We demonstrate our approach on two benchmarks and a realistic wind farm setting. Our method significantly outperforms two baseline approaches, namely individual learning and joint learning where all samples are aggregated, in terms of the median and variance of the results.

Timothy Verstraeten, Eugenio Bargiacchi, Pieter JK Libin et al.

Multi-agent coordination is prevalent in many real-world applications. However, such coordination is challenging due to its combinatorial nature. An important observation in this regard is that agents in the real world often only directly affect a limited set of neighbouring agents. Leveraging such loose couplings among agents is key to making coordination in multi-agent systems feasible. In this work, we focus on learning to coordinate. Specifically, we consider the multi-agent multi-armed bandit framework, in which fully cooperative loosely-coupled agents must learn to coordinate their decisions to optimize a common objective. We propose multi-agent Thompson sampling (MATS), a new Bayesian exploration-exploitation algorithm that leverages loose couplings. We provide a regret bound that is sublinear in time and low-order polynomial in the highest number of actions of a single agent for sparse coordination graphs. Additionally, we empirically show that MATS outperforms the state-of-the-art algorithm, MAUCE, on two synthetic benchmarks, and a novel benchmark with Poisson distributions. An example of a loosely-coupled multi-agent system is a wind farm. Coordination within the wind farm is necessary to maximize power production. As upstream wind turbines only affect nearby downstream turbines, we can use MATS to efficiently learn the optimal control mechanism for the farm. To demonstrate the benefits of our method toward applications we apply MATS to a realistic wind farm control task. In this task, wind turbines must coordinate their alignments with respect to the incoming wind vector in order to optimize power production. Our results show that MATS improves significantly upon state-of-the-art coordination methods in terms of performance, demonstrating the value of using MATS in practical applications with sparse neighbourhood structures.

Felipe Gomez Marulanda, Pieter Libin, Timothy Verstraeten et al.

Over the last decade, the demand for better segmentation and classification algorithms in 3D spaces has significantly grown due to the popularity of new 3D sensor technologies and advancements in the field of robotics. Point-clouds are one of the most popular representations to store a digital description of 3D shapes. However, point-clouds are stored in irregular and unordered structures, which limits the direct use of segmentation algorithms such as Convolutional Neural Networks. The objective of our work is twofold: First, we aim to provide a full analysis of the PointNet architecture to illustrate which features are being extracted from the point-clouds. Second, to propose a new network architecture called IPC-Net to improve the state-of-the-art point cloud architectures. We show that IPC-Net extracts a larger set of unique features allowing the model to produce more accurate segmentations compared to the PointNet architecture. In general, our approach outperforms PointNet on every family of 3D geometries on which the models were tested. A high generalisation improvement was observed on every 3D shape, especially on the rockets dataset. Our experiments demonstrate that our main contribution, inter-point activation on the network's layers, is essential to accurately segment 3D point-clouds.

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 Roijers et al.

For a robot to learn a good policy, it often requires expensive equipment (such as sophisticated sensors) and a prepared training environment conducive to learning. However, it is seldom possible to perfectly equip robots for economic reasons, nor to guarantee ideal learning conditions, when deployed in real-life environments. A solution would be to prepare the robot in the lab environment, when all necessary material is available to learn a good policy. After training in the lab, the robot should be able to get by without the expensive equipment that used to be available to it, and yet still be guaranteed to perform well on the field. The transition between the lab (source) and the real-world environment (target) is related to transfer learning, where the state-space between the source and target tasks differ. We tackle a simulated task with continuous states and discrete actions presenting this challenge, using Bootstrapped Dual Policy Iteration, a model-free actor-critic reinforcement learning algorithm, and Policy Shaping. Specifically, we train a BDPI agent, embodied by a virtual robot performing a task in the V-Rep simulator, sensing its environment through several proximity sensors. The resulting policy is then used by a second agent learning the same task in the same environment, but with camera images as input. The goal is to obtain a policy able to perform the task relying on merely camera images.

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.

Luisa M Zintgraf, Diederik M Roijers, Sjoerd Linders et al.

In multi-objective decision planning and learning, much attention is paid to producing optimal solution sets that contain an optimal policy for every possible user preference profile. We argue that the step that follows, i.e, determining which policy to execute by maximising the user's intrinsic utility function over this (possibly infinite) set, is under-studied. This paper aims to fill this gap. We build on previous work on Gaussian processes and pairwise comparisons for preference modelling, extend it to the multi-objective decision support scenario, and propose new ordered preference elicitation strategies based on ranking and clustering. Our main contribution is an in-depth evaluation of these strategies using computer and human-based experiments. We show that our proposed elicitation strategies outperform the currently used pairwise methods, and found that users prefer ranking most. Our experiments further show that utilising monotonicity information in GPs by using a linear prior mean at the start and virtual comparisons to the nadir and ideal points, increases performance. We demonstrate our decision support framework in a real-world study on traffic regulation, conducted with the city of Amsterdam.

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.