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.
In this paper, we aim to utilize only offline trajectory data to train a policy for multi-objective RL. We extend the offline policy-regularized method, a widely-adopted approach for single-objective offline RL problems, into the multi-objective setting in order to achieve the above goal. However, such methods face a new challenge in offline MORL settings, namely the preference-inconsistent demonstration problem. We propose two solutions to this problem: 1) filtering out preference-inconsistent demonstrations via approximating behavior preferences, and 2) adopting regularization techniques with high policy expressiveness. Moreover, we integrate the preference-conditioned scalarized update method into policy-regularized offline RL, in order to simultaneously learn a set of policies using a single policy network, thus reducing the computational cost induced by the training of a large number of individual policies for various preferences. Finally, we introduce Regularization Weight Adaptation to dynamically determine appropriate regularization weights for arbitrary target preferences during deployment. Empirical results on various multi-objective datasets demonstrate the capability of our approach in solving offline MORL problems.
Customizing robotic behaviors to be aligned with diverse human preferences is an underexplored challenge in the field of embodied AI. In this paper, we present Promptable Behaviors, a novel framework that facilitates efficient personalization of robotic agents to diverse human preferences in complex environments. We use multi-objective reinforcement learning to train a single policy adaptable to a broad spectrum of preferences. We introduce three distinct methods to infer human preferences by leveraging different types of interactions: (1) human demonstrations, (2) preference feedback on trajectory comparisons, and (3) language instructions. We evaluate the proposed method in personalized object-goal navigation and flee navigation tasks in ProcTHOR and RoboTHOR, demonstrating the ability to prompt agent behaviors to satisfy human preferences in various scenarios. Project page: https://promptable-behaviors.github.io
A central challenge of the clean energy transition is the development of catalysts for low-emissions technologies. Recent advances in Machine Learning for quantum chemistry drastically accelerate the computation of catalytic activity descriptors such as adsorption energies. Here we introduce AdsorbRL, a Deep Reinforcement Learning agent aiming to identify potential catalysts given a multi-objective binding energy target, trained using offline learning on the Open Catalyst 2020 and Materials Project data sets. We experiment with Deep Q-Network agents to traverse the space of all ~160,000 possible unary, binary and ternary compounds of 55 chemical elements, with very sparse rewards based on adsorption energy known for only between 2,000 and 3,000 catalysts per adsorbate. To constrain the actions space, we introduce Random Edge Traversal and train a single-objective DQN agent on the known states subgraph, which we find strengthens target binding energy by an average of 4.1 eV. We extend this approach to multi-objective, goal-conditioned learning, and train a DQN agent to identify materials with the highest (respectively lowest) adsorption energies for multiple simultaneous target adsorbates. We experiment with Objective Sub-Sampling, a novel training scheme aimed at encouraging exploration in the multi-objective setup, and demonstrate simultaneous adsorption energy improvement across all target adsorbates, by an average of 0.8 eV. Overall, our results suggest strong potential for Deep Reinforcement Learning applied to the inverse catalysts design problem.
Multi-objective reinforcement learning (MORL) extends traditional RL by seeking policies making different compromises among conflicting objectives. The recent surge of interest in MORL has led to diverse studies and solving methods, often drawing from existing knowledge in multi-objective optimization based on decomposition (MOO/D). Yet, a clear categorization based on both RL and MOO/D is lacking in the existing literature. Consequently, MORL researchers face difficulties when trying to classify contributions within a broader context due to the absence of a standardized taxonomy. To tackle such an issue, this paper introduces multi-objective reinforcement learning based on decomposition (MORL/D), a novel methodology bridging the literature of RL and MOO. A comprehensive taxonomy for MORL/D is presented, providing a structured foundation for categorizing existing and potential MORL works. The introduced taxonomy is then used to scrutinize MORL research, enhancing clarity and conciseness through well-defined categorization. Moreover, a flexible framework derived from the taxonomy is introduced. This framework accommodates diverse instantiations using tools from both RL and MOO/D. Its versatility is demonstrated by implementing it in different configurations and assessing it on contrasting benchmark problems. Results indicate MORL/D instantiations achieve comparable performance to current state-of-the-art approaches on the studied problems. By presenting the taxonomy and framework, this paper offers a comprehensive perspective and a unified vocabulary for MORL. This not only facilitates the identification of algorithmic contributions but also lays the groundwork for novel research avenues in MORL.
Reinforcement learning (RL) has emerged as a powerful approach for tackling complex problems. The recent introduction of multi-objective reinforcement learning (MORL) has further expanded the scope of RL by enabling agents to make trade-offs among multiple objectives. This advancement not only has broadened the range of problems that can be tackled but also created numerous opportunities for exploration and advancement. Yet, the effectiveness of RL agents heavily relies on appropriately setting their hyperparameters. In practice, this task often proves to be challenging, leading to unsuccessful deployments of these techniques in various instances. Hence, prior research has explored hyperparameter optimization in RL to address this concern. This paper presents an initial investigation into the challenge of hyperparameter optimization specifically for MORL. We formalize the problem, highlight its distinctive challenges, and propose a systematic methodology to address it. The proposed methodology is applied to a well-known environment using a state-of-the-art MORL algorithm, and preliminary results are reported. Our findings indicate that the proposed methodology can effectively provide hyperparameter configurations that significantly enhance the performance of MORL agents. Furthermore, this study identifies various future research opportunities to further advance the field of hyperparameter optimization for MORL.
While Reinforcement Learning from Human Feedback (RLHF) aligns Large Language Models (LLMs) with general, aggregate human preferences, it is suboptimal for learning diverse, individual perspectives. In this work, we study Reinforcement Learning from Personalized Human Feedback (RLPHF) problem, wherein LLMs are aligned to multiple (sometimes conflicting) preferences by modeling alignment as a Multi-Objective Reinforcement Learning (MORL) problem. Compared to strong single-objective baselines, we show that we can achieve personalized alignment by decomposing preferences into multiple dimensions. These dimensions are defined based on personalizations that are declared as desirable by the user. In this work, we show that they can be efficiently trained independently in a distributed manner and combined effectively post-hoc through parameter merging. The code is available at https://github.com/joeljang/RLPHF.
Computerized Adaptive Testing(CAT) refers to an online system that adaptively selects the best-suited question for students with various abilities based on their historical response records. Most CAT methods only focus on the quality objective of predicting the student ability accurately, but neglect concept diversity or question exposure control, which are important considerations in ensuring the performance and validity of CAT. Besides, the students' response records contain valuable relational information between questions and knowledge concepts. The previous methods ignore this relational information, resulting in the selection of sub-optimal test questions. To address these challenges, we propose a Graph-Enhanced Multi-Objective method for CAT (GMOCAT). Firstly, three objectives, namely quality, diversity and novelty, are introduced into the Scalarized Multi-Objective Reinforcement Learning framework of CAT, which respectively correspond to improving the prediction accuracy, increasing the concept diversity and reducing the question exposure. We use an Actor-Critic Recommender to select questions and optimize three objectives simultaneously by the scalarization function. Secondly, we utilize the graph neural network to learn relation-aware embeddings of questions and concepts. These embeddings are able to aggregate neighborhood information in the relation graphs between questions and concepts. We conduct experiments on three real-world educational datasets, and show that GMOCAT not only outperforms the state-of-the-art methods in the ability prediction, but also achieve superior performance in improving the concept diversity and alleviating the question exposure. Our code is available at https://github.com/justarter/GMOCAT.
The goal of multi-objective reinforcement learning (MORL) is to learn policies that simultaneously optimize multiple competing objectives. In practice, an agent's preferences over the objectives may not be known apriori, and hence, we require policies that can generalize to arbitrary preferences at test time. In this work, we propose a new data-driven setup for offline MORL, where we wish to learn a preference-agnostic policy agent using only a finite dataset of offline demonstrations of other agents and their preferences. The key contributions of this work are two-fold. First, we introduce D4MORL, (D)atasets for MORL that are specifically designed for offline settings. It contains 1.8 million annotated demonstrations obtained by rolling out reference policies that optimize for randomly sampled preferences on 6 MuJoCo environments with 2-3 objectives each. Second, we propose Pareto-Efficient Decision Agents (PEDA), a family of offline MORL algorithms that builds and extends Decision Transformers via a novel preference-and-return-conditioned policy. Empirically, we show that PEDA closely approximates the behavioral policy on the D4MORL benchmark and provides an excellent approximation of the Pareto-front with appropriate conditioning, as measured by the hypervolume and sparsity metrics.
We study a multi-objective multi-armed bandit problem in a dynamic environment. The problem portrays a decision-maker that sequentially selects an arm from a given set. If selected, each action produces a reward vector, where every element follows a piecewise-stationary Bernoulli distribution. The agent aims at choosing an arm among the Pareto optimal set of arms to minimize its regret. We propose a Pareto generic upper confidence bound (UCB)-based algorithm with change detection to solve this problem. By developing the essential inequalities for multi-dimensional spaces, we establish that our proposal guarantees a regret bound in the order of $\gamma_T\log(T/{\gamma_T})$ when the number of breakpoints $\gamma_T$ is known. Without this assumption, the regret bound of our algorithm is $\gamma_T\log(T)$. Finally, we formulate an energy-efficient waveform design problem in an integrated communication and sensing system as a toy example. Numerical experiments on the toy example and synthetic and real-world datasets demonstrate the efficiency of our policy compared to the current methods.
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 $\epsilon$-optimal solution (for a bounded $\epsilon$) 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.
In this work we introduce reinforcement learning techniques for solving lexicographic multi-objective problems. These are problems that involve multiple reward signals, and where the goal is to learn a policy that maximises the first reward signal, and subject to this constraint also maximises the second reward signal, and so on. We present a family of both action-value and policy gradient algorithms that can be used to solve such problems, and prove that they converge to policies that are lexicographically optimal. We evaluate the scalability and performance of these algorithms empirically, demonstrating their practical applicability. As a more specific application, we show how our algorithms can be used to impose safety constraints on the behaviour of an agent, and compare their performance in this context with that of other constrained reinforcement learning algorithms.
Many real-world continuous control problems are in the dilemma of weighing the pros and cons, multi-objective reinforcement learning (MORL) serves as a generic framework of learning control policies for different preferences over objectives. However, the existing MORL methods either rely on multiple passes of explicit search for finding the Pareto front and therefore are not sample-efficient, or utilizes a shared policy network for coarse knowledge sharing among policies. To boost the sample efficiency of MORL, we propose Q-Pensieve, a policy improvement scheme that stores a collection of Q-snapshots to jointly determine the policy update direction and thereby enables data sharing at the policy level. We show that Q-Pensieve can be naturally integrated with soft policy iteration with convergence guarantee. To substantiate this concept, we propose the technique of Q replay buffer, which stores the learned Q-networks from the past iterations, and arrive at a practical actor-critic implementation. Through extensive experiments and an ablation study, we demonstrate that with much fewer samples, the proposed algorithm can outperform the benchmark MORL methods on a variety of MORL benchmark tasks.
We study fair multi-objective reinforcement learning in which an agent must learn a policy that simultaneously achieves high reward on multiple dimensions of a vector-valued reward. Motivated by the fair resource allocation literature, we model this as an expected welfare maximization problem, for some nonlinear fair welfare function of the vector of long-term cumulative rewards. One canonical example of such a function is the Nash Social Welfare, or geometric mean, the log transform of which is also known as the Proportional Fairness objective. We show that even approximately optimal optimization of the expected Nash Social Welfare is computationally intractable even in the tabular case. Nevertheless, we provide a novel adaptation of Q-learning that combines nonlinear scalarized learning updates and non-stationary action selection to learn effective policies for optimizing nonlinear welfare functions. We show that our algorithm is provably convergent, and we demonstrate experimentally that our approach outperforms techniques based on linear scalarization, mixtures of optimal linear scalarizations, or stationary action selection for the Nash Social Welfare Objective.
Multi-agent Reinforcement Learning (MARL) is a powerful tool for training autonomous agents acting independently in a common environment. However, it can lead to sub-optimal behavior when individual incentives and group incentives diverge. Humans are remarkably capable at solving these social dilemmas. It is an open problem in MARL to replicate such cooperative behaviors in selfish agents. In this work, we draw upon the idea of formal contracting from economics to overcome diverging incentives between agents in MARL. We propose an augmentation to a Markov game where agents voluntarily agree to binding transfers of reward, under pre-specified conditions. Our contributions are theoretical and empirical. First, we show that this augmentation makes all subgame-perfect equilibria of all Fully Observable Markov Games exhibit socially optimal behavior, given a sufficiently rich space of contracts. Next, we show that for general contract spaces, and even under partial observability, richer contract spaces lead to higher welfare. Hence, contract space design solves an exploration-exploitation tradeoff, sidestepping incentive issues. We complement our theoretical analysis with experiments. Issues of exploration in the contracting augmentation are mitigated using a training methodology inspired by multi-objective reinforcement learning: Multi-Objective Contract Augmentation Learning (MOCA). We test our methodology in static, single-move games, as well as dynamic domains that simulate traffic, pollution management and common pool resource management.
Multi-objective reinforcement learning (MORL) approaches have emerged to tackle many real-world problems with multiple conflicting objectives by maximizing a joint objective function weighted by a preference vector. These approaches find fixed customized policies corresponding to preference vectors specified during training. However, the design constraints and objectives typically change dynamically in real-life scenarios. Furthermore, storing a policy for each potential preference is not scalable. Hence, obtaining a set of Pareto front solutions for the entire preference space in a given domain with a single training is critical. To this end, we propose a novel MORL algorithm that trains a single universal network to cover the entire preference space scalable to continuous robotic tasks. The proposed approach, Preference-Driven MORL (PD-MORL), utilizes the preferences as guidance to update the network parameters. It also employs a novel parallelization approach to increase sample efficiency. We show that PD-MORL achieves up to 25% larger hypervolume for challenging continuous control tasks and uses an order of magnitude fewer trainable parameters compared to prior approaches.
We study policy optimization for Markov decision processes (MDPs) with multiple reward value functions, which are to be jointly optimized according to given criteria such as proportional fairness (smooth concave scalarization), hard constraints (constrained MDP), and max-min trade-off. We propose an Anchor-changing Regularized Natural Policy Gradient (ARNPG) framework, which can systematically incorporate ideas from well-performing first-order methods into the design of policy optimization algorithms for multi-objective MDP problems. Theoretically, the designed algorithms based on the ARNPG framework achieve $\tilde{O}(1/T)$ global convergence with exact gradients. Empirically, the ARNPG-guided algorithms also demonstrate superior performance compared to some existing policy gradient-based approaches in both exact gradients and sample-based scenarios.
In real-world decision optimization, often multiple competing objectives must be taken into account. Following classical reinforcement learning, these objectives have to be combined into a single reward function. In contrast, multi-objective reinforcement learning (MORL) methods learn from vectors of per-objective rewards instead. In the case of multi-policy MORL, sets of decision policies for various preferences regarding the conflicting objectives are optimized. This is especially important when target preferences are not known during training or when preferences change dynamically during application. While it is, in general, straightforward to extend a single-objective reinforcement learning method for MORL based on linear scalarization, solutions that are reachable by these methods are limited to convex regions of the Pareto front. Non-linear MORL methods like Thresholded Lexicographic Ordering (TLO) are designed to overcome this limitation. Generalized MORL methods utilize function approximation to generalize across objective preferences and thereby implicitly learn multiple policies in a data-efficient manner, even for complex decision problems with high-dimensional or continuous state spaces. In this work, we propose \textit{generalized Thresholded Lexicographic Ordering} (gTLO), a novel method that aims to combine non-linear MORL with the advantages of generalized MORL. We introduce a deep reinforcement learning realization of the algorithm and present promising results on a standard benchmark for non-linear MORL and a real-world application from the domain of manufacturing process control.
In this paper, the authors investigate the Deep Sea Treasure (DST) problem as proposed by Vamplew et al. Through a number of proofs, the authors show the original DST problem to be quite basic, and not always representative of practical Multi-Objective Optimization problems. In an attempt to bring theory closer to practice, the authors propose an alternative, improved version of the DST problem, and prove that some of the properties that simplify the original DST problem no longer hold. The authors also provide a reference implementation and perform a comparison between their implementation, and other existing open-source implementations of the problem. Finally, the authors also provide a complete Pareto-front for their new DST problem.
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.