Abstract In many real-world scenarios, the utility of a user is derived from a 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 work, we propose first-order stochastic dominance as a criterion to build solution sets to maximise expected utility. We also define 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. Additionally, we define a new solution concept called the ESR set, which is a set of policies that are ESR dominant. Finally, we present a new multi-objective tabular distributional reinforcement learning (MOTDRL) algorithm to learn the ESR set in multi-objective multi-armed bandit settings.

Infectious disease outbreaks can have a disruptive impact on public health and societal processes. As decision-making in the context of epidemic mitigation is multi-dimensional hence complex, reinforcement learning in combination with complex epidemic models provides a methodology to design refined prevention strategies. Current research focuses on optimizing policies with respect to a single objective, such as the pathogen’s attack rate. However, as the mitigation of epidemics involves distinct, and possibly conflicting, criteria (i.a., mortality, morbidity, economic cost, well-being), a multi-objective decision approach is warranted to obtain balanced policies. To enhance future decision-making, we propose a deep multi-objective reinforcement learning approach by building upon a state-of-the-art algorithm called Pareto Conditioned Networks (PCN) to obtain a set of solutions for distinct outcomes of the decision problem. We consider different deconfinement strategies after the first Belgian lockdown within the COVID-19 pandemic and aim to minimize both COVID-19 cases (i.e., infections and hospitalizations) and the societal burden induced by the mitigation measures. As such, we connected a multi-objective Markov decision process with a stochastic compartment model designed to approximate the Belgian COVID-19 waves and explore reactive strategies. 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 set that PCN returns, and observe that it explored the whole range of possible social restrictions, leading to high-quality trade-offs, as it captured the problem dynamics. In this work, we demonstrate that multi-objective reinforcement learning adds value to epidemiological modeling and provides essential insights to balance mitigation policies.

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.

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.

Abstract Real-world sequential 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.

Abstract 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, and provides a suitable basis for the creation of artificial general intelligence. 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, this type of reward is insufficient for the development of human-aligned artificial general intelligence due to unacceptable risks of unsafe or unethical behaviour.