Actor-critic multi-objective reinforcement learning for non-linear utility functions

Abstract 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. 

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Monte Carlo tree search algorithms for risk-aware and multi-objective reinforcement learning

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

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

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. Through these experiments, we show that the top policies follow a clear trend regarding the prioritised age groups and assigned vaccine type, which provides insights for future vaccination campaigns.

Evaluating COVID-19 vaccine allocation policies using Bayesian m-top exploration

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.

MOMAland: A Set of Benchmarks for Multi-Objective Multi-Agent Reinforcement Learning

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.

Pareto Conditioned Networks

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Pareto Conditioned Networks

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