The time allocation problem in multi-function cognitive radar systems focuses on the trade-off between scanning for newly emerging targets and tracking the previously detected targets. We formulate this as a multi-objective optimization problem and employ deep reinforcement learning to find Pareto-optimal solutions and compare deep deterministic policy gradient (DDPG) and soft actor-critic (SAC) algorithms. Our results demonstrate the effectiveness of both algorithms in adapting to various scenarios, with SAC showing improved stability and sample efficiency compared to DDPG. We further employ the NSGA-II algorithm to estimate an upper bound on the Pareto front of the considered problem. This work contributes to the development of more efficient and adaptive cognitive radar systems capable of balancing multiple competing objectives in dynamic environments.
An internet network service provider manages its network with multiple objectives, such as high quality of service (QoS) and minimum computing resource usage. To achieve these objectives, a reinforcement learning-based (RL) algorithm has been proposed to train its network management agent. Usually, their algorithms optimize their agents with respect to a single static reward formulation consisting of multiple objectives with fixed importance factors, which we call preferences. However, in practice, the preference could vary according to network status, external concerns and so on. For example, when a server shuts down and it can cause other servers' traffic overloads leading to additional shutdowns, it is plausible to reduce the preference of QoS while increasing the preference of minimum computing resource usages. In this paper, we propose new RL-based network management agents that can select actions based on both states and preferences. With our proposed approach, we expect a single agent to generalize on various states and preferences. Furthermore, we propose a numerical method that can estimate the distribution of preference that is advantageous for unbiased training. Our experiment results show that the RL agents trained based on our proposed approach significantly generalize better with various preferences than the previous RL approaches, which assume static preference during training. Moreover, we demonstrate several analyses that show the advantages of our numerical estimation method.
Multi-objective reinforcement learning (MORL) aims to optimize policies in the presence of conflicting objectives, where linear scalarization is commonly used to reduce vector-valued returns into scalar signals. While effective for certain preferences, this approach cannot capture fairness-oriented goals such as Nash social welfare or max-min fairness, which require nonlinear and non-additive trade-offs. Although several online algorithms have been proposed for specific fairness objectives, a unified approach for optimizing nonlinear welfare criteria in the offline setting-where learning must proceed from a fixed dataset-remains unexplored. In this work, we present FairDICE, the first offline MORL framework that directly optimizes nonlinear welfare objective. FairDICE leverages distribution correction estimation to jointly account for welfare maximization and distributional regularization, enabling stable and sample-efficient learning without requiring explicit preference weights or exhaustive weight search. Across multiple offline benchmarks, FairDICE demonstrates strong fairness-aware performance compared to existing baselines.
Recent advances in language models have enabled framing molecule generation as sequence modeling. However, existing approaches often rely on single-objective reinforcement learning, limiting their applicability to real-world drug design, where multiple competing properties must be optimized. Traditional multi-objective reinforcement learning (MORL) methods require costly retraining for each new objective combination, making rapid exploration of trade-offs impractical. To overcome these limitations, we introduce Mol-MoE, a mixture-of-experts (MoE) architecture that enables efficient test-time steering of molecule generation without retraining. Central to our approach is a preference-based router training objective that incentivizes the router to combine experts in a way that aligns with user-specified trade-offs. This provides improved flexibility in exploring the chemical property space at test time, facilitating rapid trade-off exploration. Benchmarking against state-of-the-art methods, we show that Mol-MoE achieves superior sample quality and steerability.
Multi-objective reinforcement learning (MORL) addresses the challenge of simultaneously optimizing multiple, often conflicting, rewards, moving beyond the single-reward focus of conventional reinforcement learning (RL). This approach is essential for applications where agents must balance trade-offs between diverse goals, such as speed, energy efficiency, or stability, as a series of sequential decisions. This paper investigates the applicability and limitations of multi-objective evolutionary algorithms (MOEAs) in solving complex MORL problems. We assess whether these algorithms can effectively address the unique challenges posed by MORL and how MORL instances can serve as benchmarks to evaluate and improve MOEA performance. In particular, we propose a framework to characterize the features influencing MORL instance complexity, select representative MORL problems from the literature, and benchmark a suite of MOEAs alongside single-objective EAs using scalarized MORL formulations. Additionally, we evaluate the utility of existing multi-objective quality indicators in MORL scenarios, such as hypervolume conducting a comparison of the algorithms supported by statistical analysis. Our findings provide insights into the interplay between MORL problem characteristics and algorithmic effectiveness, highlighting opportunities for advancing both MORL research and the design of evolutionary algorithms.
Precision agriculture, enhanced by artificial intelligence (AI), offers promising tools such as remote sensing, intelligent irrigation, fertilization management, and crop simulation to improve agricultural efficiency and sustainability. Reinforcement learning (RL), in particular, has outperformed traditional methods in optimizing yields and resource management. However, widespread AI adoption is limited by gaps between algorithmic recommendations and farmers' practical experience, local knowledge, and traditional practices. To address this, our study emphasizes Human-AI Interaction (HAII), focusing on transparency, usability, and trust in RL-based farm management. We employ a well-established trust framework - comprising ability, benevolence, and integrity - to develop a novel mathematical model quantifying farmers' confidence in AI-based fertilization strategies. Surveys conducted with farmers for this research reveal critical misalignments, which are integrated into our trust model and incorporated into a multi-objective RL framework. Unlike prior methods, our approach embeds trust directly into policy optimization, ensuring AI recommendations are technically robust, economically feasible, context-aware, and socially acceptable. By aligning technical performance with human-centered trust, this research supports broader AI adoption in agriculture.
Industrial automation increasingly demands energy-efficient control strategies to balance performance with environmental and cost constraints. In this work, we present a multi-objective reinforcement learning (MORL) framework for energy-efficient control of the Quanser Aero 2 testbed in its one-degree-of-freedom configuration. We design a composite reward function that simultaneously penalizes tracking error and electrical power consumption. Preliminary experiments explore the influence of varying the Energy penalty weight, alpha, on the trade-off between pitch tracking and energy savings. Our results reveal a marked performance shift for alpha values between 0.0 and 0.25, with non-Pareto optimal solutions emerging at lower alpha values, on both the simulation and the real system. We hypothesize that these effects may be attributed to artifacts introduced by the adaptive behavior of the Adam optimizer, which could bias the learning process and favor bang-bang control strategies. Future work will focus on automating alpha selection through Gaussian Process-based Pareto front modeling and transitioning the approach from simulation to real-world deployment.
Human drivers exhibit individual preferences regarding driving style. Adapting autonomous vehicles to these preferences is essential for user trust and satisfaction. However, existing end-to-end driving approaches often rely on predefined driving styles or require continuous user feedback for adaptation, limiting their ability to support dynamic, context-dependent preferences. We propose a novel approach using multi-objective reinforcement learning (MORL) with preference-driven optimization for end-to-end autonomous driving that enables runtime adaptation to driving style preferences. Preferences are encoded as continuous weight vectors to modulate behavior along interpretable style objectives$\unicode{x2013}$including efficiency, comfort, speed, and aggressiveness$\unicode{x2013}$without requiring policy retraining. Our single-policy agent integrates vision-based perception in complex mixed-traffic scenarios and is evaluated in diverse urban environments using the CARLA simulator. Experimental results demonstrate that the agent dynamically adapts its driving behavior according to changing preferences while maintaining performance in terms of collision avoidance and route completion.
Despite the superior diagnostic capability of Magnetic Resonance Imaging (MRI), its use as a Point-of-Care (PoC) device remains limited by high cost and complexity. To enable such a future by reducing the magnetic field strength, one key approach will be to improve sampling strategies. Previous work has shown that it is possible to make diagnostic decisions directly from k-space with fewer samples. Such work shows that single diagnostic decisions can be made, but if we aspire to see MRI as a true PoC, multiple and sequential decisions are necessary while minimizing the number of samples acquired. We present a novel multi-objective reinforcement learning framework enabling comprehensive, sequential, diagnostic evaluation from undersampled k-space data. Our approach during inference actively adapts to sequential decisions to optimally sample. To achieve this, we introduce a training methodology that identifies the samples that contribute the best to each diagnostic objective using a step-wise weighting reward function. We evaluate our approach in two sequential knee pathology assessment tasks: ACL sprain detection and cartilage thickness loss assessment. Our framework achieves diagnostic performance competitive with various policy-based benchmarks on disease detection, severity quantification, and overall sequential diagnosis, while substantially saving k-space samples. Our approach paves the way for the future of MRI as a comprehensive and affordable PoC device. Our code is publicly available at https://github.com/vios-s/MRI_Sequential_Active_Sampling
Recent advances in reinforcement learning (RL) for large language model (LLM) fine-tuning show promise in addressing multi-objective tasks but still face significant challenges, including complex objective balancing, low training efficiency, poor scalability, and limited explainability. Leveraging ensemble learning principles, we introduce an Ensemble Multi-Objective RL (EMORL) framework that fine-tunes multiple models with individual objectives while optimizing their aggregation after the training to improve efficiency and flexibility. Our method is the first to aggregate the last hidden states of individual models, incorporating contextual information from multiple objectives. This approach is supported by a hierarchical grid search algorithm that identifies optimal weighted combinations. We evaluate EMORL on counselor reflection generation tasks, using text-scoring LLMs to evaluate the generations and provide rewards during RL fine-tuning. Through comprehensive experiments on the PAIR and Psych8k datasets, we demonstrate the advantages of EMORL against existing baselines: significantly lower and more stable training consumption ($17,529\pm 1,650$ data points and $6,573\pm 147.43$ seconds), improved scalability and explainability, and comparable performance across multiple objectives.
In practical application, the pursuit-evasion game (PEG) often involves multiple complex and conflicting objectives. The single-objective reinforcement learning (RL) usually focuses on a single optimization objective, and it is difficult to find the optimal balance among multiple objectives. This paper proposes a three-objective RL algorithm based on fuzzy Q-learning (FQL) to solve the PEG with different optimization objectives. First, the multi-objective FQL algorithm is introduced, which uses the reward function to represent three optimization objectives: evading pursuit, reaching target, and avoiding obstacle. Second, a multi-objective evaluation method and action selection strategy based on three-dimensional hypervolume are designed, which solved the dilemma of exploration-exploitation. By sampling the Pareto front, the update rule of the global strategy is obtained. The proposed algorithm reduces computational load while ensuring exploration ability. Finally, the performance of the algorithm is verified by simulation results.
Practitioners designing reinforcement learning policies face a fundamental challenge: translating intended behavioral objectives into representative reward functions. This challenge stems from behavioral intent requiring simultaneous achievement of multiple competing objectives, typically addressed through labor-intensive linear reward composition that yields brittle results. Consider the ubiquitous robotics scenario where performance maximization directly conflicts with energy conservation. Such competitive dynamics are resistant to simple linear reward combinations. In this paper, we present the concept of objective fulfillment upon which we build Fulfillment Priority Logic (FPL). FPL allows practitioners to define logical formula representing their intentions and priorities within multi-objective reinforcement learning. Our novel Balanced Policy Gradient algorithm leverages FPL specifications to achieve up to 500\% better sample efficiency compared to Soft Actor Critic. Notably, this work constitutes the first implementation of non-linear utility scalarization design, specifically for continuous control problems.
Real-world sequential decision-making tasks often require balancing trade-offs between multiple conflicting objectives, making Multi-Objective Reinforcement Learning (MORL) an increasingly prominent field of research. Despite recent advances, existing MORL literature has narrowly focused on performance within static environments, neglecting the importance of generalizing across diverse settings. Conversely, existing research on generalization in RL has always assumed scalar rewards, overlooking the inherent multi-objectivity of real-world problems. Generalization in the multi-objective context is fundamentally more challenging, as it requires learning a Pareto set of policies addressing varying preferences across multiple objectives. In this paper, we formalize the concept of generalization in MORL and how it can be evaluated. We then contribute a novel benchmark featuring diverse multi-objective domains with parameterized environment configurations to facilitate future studies in this area. Our baseline evaluations of state-of-the-art MORL algorithms on this benchmark reveals limited generalization capabilities, suggesting significant room for improvement. Our empirical findings also expose limitations in the expressivity of scalar rewards, emphasizing the need for multi-objective specifications to achieve effective generalization. We further analyzed the algorithmic complexities within current MORL approaches that could impede the transfer in performance from the single- to multiple-environment settings. This work fills a critical gap and lays the groundwork for future research that brings together two key areas in reinforcement learning: solving multi-objective decision-making problems and generalizing across diverse environments. We make our code available at https://github.com/JaydenTeoh/MORL-Generalization.
Autonomous vehicles (AVs) make driving decisions without human intervention. Therefore, ensuring AVs' dependability is critical. Despite significant research and development in AV development, their dependability assurance remains a significant challenge due to the complexity and unpredictability of their operating environments. Scenario-based testing evaluates AVs under various driving scenarios, but the unlimited number of potential scenarios highlights the importance of identifying critical scenarios that can violate safety or functional requirements. Such requirements are inherently interdependent and need to be tested simultaneously. To this end, we propose MOEQT, a novel multi-objective reinforcement learning (MORL)-based approach to generate critical scenarios that simultaneously test interdependent safety and functional requirements. MOEQT adapts Envelope Q-learning as the MORL algorithm, which dynamically adapts multi-objective weights to balance the relative importance between multiple objectives. MOEQT generates critical scenarios to violate multiple requirements through dynamically interacting with the AV environment, ensuring comprehensive AV testing. We evaluate MOEQT using an advanced end-to-end AV controller and a high-fidelity simulator and compare MOEQT with two baselines: a random strategy and a single-objective RL with a weighted reward function. Our evaluation results show that MOEQT achieved an overall better performance in identifying critical scenarios for violating multiple requirements than the baselines.
User information needs are often highly diverse and varied. A key challenge in current research is how to achieve controllable multi-objective generation while enabling rapid adaptation to accommodate diverse user demands during test time. Existing solutions, such as Rewarded Soup, focus on merging language models individually tuned on single objectives. While easy to implement and widely used, these approaches face limitations in achieving optimal performance due to their disregard for the impacts of competing objectives on model tuning. To address this issue, we propose Bone Soup, a novel model merging approach that first seeks a series of backbone models by considering the impacts of multiple objectives and then makes the soup (i.e., merge the backbone models). Specifically, Bone Soup begins by training multiple backbone models for different objectives using multi-objective reinforcement learning. Each backbone model is guided by a combination of backbone reward signals. To ensure that these models are optimal for the Pareto front, the backbone rewards are crafted by combining standard reward functions into basis vectors, which can then be modified through a rule-based construction method. Bone Soup leverages a symmetric circulant matrix mapping to generate the merging coefficients, which are used to merge the backbone models according to user preferences. Extensive experimental results demonstrate that Bone Soup exhibits strong controllability and Pareto optimality in controllable multi-objective generation, providing a more effective and efficient approach to addressing diverse user needs at test time.
Unmanned aerial vehicles (UAVs) have emerged as the potential aerial base stations (BSs) to improve terrestrial communications. However, the limited onboard energy and antenna power of a UAV restrict its communication range and transmission capability. To address these limitations, this work employs collaborative beamforming through a UAV-enabled virtual antenna array to improve transmission performance from the UAV to terrestrial mobile users, under interference from non-associated BSs and dynamic channel conditions. Specifically, we introduce a memory-based random walk model to more accurately depict the mobility patterns of terrestrial mobile users. Following this, we formulate a multi-objective optimization problem (MOP) focused on maximizing the transmission rate while minimizing the flight energy consumption of the UAV swarm. Given the NP-hard nature of the formulated MOP and the highly dynamic environment, we transform this problem into a multi-objective Markov decision process and propose an improved evolutionary multi-objective reinforcement learning algorithm. Specifically, this algorithm introduces an evolutionary learning approach to obtain the approximate Pareto set for the formulated MOP. Moreover, the algorithm incorporates a long short-term memory network and hyper-sphere-based task selection method to discern the movement patterns of terrestrial mobile users and improve the diversity of the obtained Pareto set. Simulation results demonstrate that the proposed method effectively generates a diverse range of non-dominated policies and outperforms existing methods. Additional simulations demonstrate the scalability and robustness of the proposed CB-based method under different system parameters and various unexpected circumstances.
Transmission grid congestion increases as the electrification of various sectors requires transmitting more power. Topology control, through substation reconfiguration, can reduce congestion but its potential remains under-exploited in operations. A challenge is modeling the topology control problem to align well with the objectives and constraints of operators. Addressing this challenge, this paper investigates the application of multi-objective reinforcement learning (MORL) to integrate multiple conflicting objectives for power grid topology control. We develop a MORL approach using deep optimistic linear support (DOL) and multi-objective proximal policy optimization (MOPPO) to generate a set of Pareto-optimal policies that balance objectives such as minimizing line loading, topological deviation, and switching frequency. Initial case studies show that the MORL approach can provide valuable insights into objective trade-offs and improve Pareto front approximation compared to a random search baseline. The generated multi-objective RL policies are 30% more successful in preventing grid failure under contingencies and 20% more effective when training budget is reduced - compared to the common single objective RL policy.
Power grid operators face increasing difficulties in the control room as the increase in energy demand and the shift to renewable energy introduce new complexities in managing congestion and maintaining a stable supply. Effective grid topology control requires advanced tools capable of handling multi-objective trade-offs. While Reinforcement Learning (RL) offers a promising framework for tackling such challenges, existing Multi-Objective Reinforcement Learning (MORL) approaches fail to scale to the large state and action spaces inherent in real-world grid operations. Here we present a two-phase, efficient and scalable Multi-Objective Optimisation (MOO) method designed for grid topology control, combining an efficient RL learning phase with a rapid planning phase to generate day-ahead plans for unseen scenarios. We validate our approach using historical data from TenneT, a European Transmission System Operator (TSO), demonstrating minimal deployment time, generating day-ahead plans within 4-7 minutes with strong performance. These results underline the potential of our scalable method to support real-world power grid management, offering a practical, computationally efficient, and time-effective tool for operational planning. Based on current congestion costs and inefficiencies in grid operations, adopting our approach by TSOs could potentially save millions of euros annually, providing a compelling economic incentive for its integration in the control room.
Multi-objective decision-making problems have emerged in numerous real-world scenarios, such as video games, navigation and robotics. Considering the clear advantages of Reinforcement Learning (RL) in optimizing decision-making processes, researchers have delved into the development of Multi-Objective RL (MORL) methods for solving multi-objective decision problems. However, previous methods either cannot obtain the entire Pareto front, or employ only a single policy network for all the preferences over multiple objectives, which may not produce personalized solutions for each preference. To address these limitations, we propose a novel decomposition-based framework for MORL, Pareto Set Learning for MORL (PSL-MORL), that harnesses the generation capability of hypernetwork to produce the parameters of the policy network for each decomposition weight, generating relatively distinct policies for various scalarized subproblems with high efficiency. PSL-MORL is a general framework, which is compatible for any RL algorithm. The theoretical result guarantees the superiority of the model capacity of PSL-MORL and the optimality of the obtained policy network. Through extensive experiments on diverse benchmarks, we demonstrate the effectiveness of PSL-MORL in achieving dense coverage of the Pareto front, significantly outperforming state-of-the-art MORL methods in the hypervolume and sparsity indicators.
Multi-objective optimization (MOO) lies at the core of many machine learning (ML) applications that involve multiple, potentially conflicting objectives (e.g., multi-task learning, multi-objective reinforcement learning, among many others). Despite the long history of MOO, recent years have witnessed a surge in interest within the ML community in the development of gradient manipulation algorithms for MOO, thanks to the availability of gradient information in many ML problems. However, existing gradient manipulation methods for MOO often suffer from long training times, primarily due to the need for computing dynamic weights by solving an additional optimization problem to determine a common descent direction that can decrease all objectives simultaneously. To address this challenge, we propose a new and efficient algorithm called Periodic Stochastic Multi-Gradient Descent (PSMGD) to accelerate MOO. PSMGD is motivated by the key observation that dynamic weights across objectives exhibit small changes under minor updates over short intervals during the optimization process. Consequently, our PSMGD algorithm is designed to periodically compute these dynamic weights and utilizes them repeatedly, thereby effectively reducing the computational overload. Theoretically, we prove that PSMGD can achieve state-of-the-art convergence rates for strongly-convex, general convex, and non-convex functions. Additionally, we introduce a new computational complexity measure, termed backpropagation complexity, and demonstrate that PSMGD could achieve an objective-independent backpropagation complexity. Through extensive experiments, we verify that PSMGD can provide comparable or superior performance to state-of-the-art MOO algorithms while significantly reducing training time.