Multi-Objective Reinforcement Learning

Humanoid robots often need to balance competing objectives, such as maximizing speed while minimizing energy consumption. While current reinforcement learning (RL) methods can master complex skills like fall recovery and perceptive locomotion, they are constrained by fixed weighting strategies that produce a single suboptimal policy, rather than providing a diverse set of solutions for sophisticated multi-objective control. In this paper, we propose a novel framework leveraging Multi-Objective Reinforcement Learning (MORL) to achieve Preference-Conditioned Humanoid Control (PCHC). Unlike conventional methods that require training a series of policies to approximate the Pareto front, our framework enables a single, preference-conditioned policy to exhibit a wide spectrum of diverse behaviors. To effectively integrate these requirements, we introduce a Beta distribution-based alignment mechanism based on preference vectors modulating a Mixture-of-Experts (MoE) module. We validated our approach on two representative humanoid tasks. Extensive simulations and real-world experiments demonstrate that the proposed framework allows the robot to adaptively shift its objective priorities in real-time based on the input preference condition.

Humans often juggle multiple, sometimes conflicting objectives and shift their priorities as circumstances change, rather than following a fixed objective function. In contrast, most computational decision-making and multi-objective RL methods assume static preference weights or a known scalar reward. In this work, we study sequential decision-making problem when these preference weights are unobserved latent variables that drift with context. Specifically, we propose Dynamic Preference Inference (DPI), a cognitively inspired framework in which an agent maintains a probabilistic belief over preference weights, updates this belief from recent interaction, and conditions its policy on inferred preferences. We instantiate DPI as a variational preference inference module trained jointly with a preference-conditioned actor-critic, using vector-valued returns as evidence about latent trade-offs. In queueing, maze, and multi-objective continuous-control environments with event-driven changes in objectives, DPI adapts its inferred preferences to new regimes and achieves higher post-shift performance than fixed-weight and heuristic envelope baselines.

Reinforcement Learning (RL) has demonstrated its ability to solve complex decision-making problems in a variety of domains, by optimizing reward signals obtained through interaction with an environment. However, many real-world scenarios involve multiple, potentially conflicting objectives that cannot be easily represented by a single scalar reward. Multi-Objective Reinforcement Learning (MORL) addresses this limitation by enabling agents to optimize several objectives simultaneously, explicitly reasoning about trade-offs between them. However, the ``black box" nature of the RL models makes the decision process behind chosen objective trade-offs unclear. Current Explainable Reinforcement Learning (XRL) methods are typically designed for single scalar rewards and do not account for explanations with respect to distinct objectives or user preferences. To address this gap, in this paper we propose TREX, a Trajectory based Explainability framework to explain Multi-objective Reinforcement Learning policies, based on trajectory attribution. TREX generates trajectories directly from the learned expert policy, across different user preferences and clusters them into semantically meaningful temporal segments. We quantify the influence of these behavioural segments on the Pareto trade-off by training complementary policies that exclude specific clusters, measuring the resulting relative deviation on the observed rewards and actions compared to the original expert policy. Experiments on multi-objective MuJoCo environments - HalfCheetah, Ant and Swimmer, demonstrate the framework's ability to isolate and quantify the specific behavioural patterns.

Multi-objective reinforcement learning (MORL) provides an effective solution for decision-making problems involving conflicting objectives. However, achieving high-quality approximations to the Pareto policy set remains challenging, especially in complex tasks with continuous or high-dimensional state-action space. In this paper, we propose the Pareto Ascent Directional Decomposition based Multi-Objective Reinforcement Learning (PA2D-MORL) method, which constructs an efficient scheme for multi-objective problem decomposition and policy improvement, leading to a superior approximation of Pareto policy set. The proposed method leverages Pareto ascent direction to select the scalarization weights and computes the multi-objective policy gradient, which determines the policy optimization direction and ensures joint improvement on all objectives. Meanwhile, multiple policies are selectively optimized under an evolutionary framework to approximate the Pareto frontier from different directions. Additionally, a Pareto adaptive fine-tuning approach is applied to enhance the density and spread of the Pareto frontier approximation. Experiments on various multi-objective robot control tasks show that the proposed method clearly outperforms the current state-of-the-art algorithm in terms of both quality and stability of the outcomes.

Cloud-native container orchestration requires resource schedulers capable of balancing infrastructure expenditure, fault resilience, and node utilisation. Conventional reinforcement learning approaches typically rely on monolithic single-agent models that suffer from gradient interference and reward dilution when mapping conflicting operational goals into a single scalar reward. We present Agentic-Kube, a cooperative multi-agent reinforcement learning framework designed for real-time Kubernetes pod placement. The architecture decomposes multi-objective scheduling into a tripartite optimisation space managed by dedicated sub-agents for cost minimisation, anti-affinity fault tolerance, and vector resource balancing. Agentic-Kube integrates a bipartite Graph Convolutional Network to capture dynamic host-pod dependencies, a two-stage monotonic QMIX value factorisation network to maintain joint action value coherence, and a plurality voting consensus mechanism with action feasibility masking against allocatable node predicates. We evaluate the framework across live heterogeneous Google Kubernetes Engine deployments and macro-scale cluster environments spanning 50 to 1,000 nodes under empirical Alibaba trace data, diurnal microservice variations, and flash-crowd bursts. Across physical and simulated evaluations, Agentic-Kube consistently achieves Pareto-efficient placements. In diurnal microservice workloads, it reduces anti-affinity service collisions to 7.11%, representing a 53.0% relative reduction compared to the default Kubernetes scheduler. Under Alibaba traces, the policy achieves a 65.15% spot instance allocation ratio, while macro-scale benchmarks demonstrate scaling up to 1,000 nodes with mean decision latencies under 17ms and 99th-percentile latencies under 31ms, executing without container restart failures and operating well within standard scheduling admission timeouts.

Multi-objective reinforcement learning (MORL) is a powerful tool to learn Pareto-optimal policy families across conflicting objectives. However, unlike traditional RL algorithms, existing MORL algorithms do not effectively leverage large-scale parallelization to concurrently simulate thousands of environments, thus facing vastly increased computation time. Ultimately, this has limited the application of MORL towards complex multi-objective robotics problems. To address these challenges, we present 1) MORLAX, a new GPU-native, fast MORL algorithm, and 2) MO-Playground, a pip-installable playground of GPU-accelerated multi-objective environments. Together, MORLAX and MO-Playground approximate Pareto sets within minutes, offering 26-271x speed-ups compared to legacy CPU-based approaches and up to 19x speed-ups over prior GPU-based approaches whilst learning superior Pareto front hypervolumes. We demonstrate MO-Playground's versatility by implementing a custom BRUCE humanoid robot environment and learning Pareto-optimal locomotion policies across 6 practical objectives in simulation, such as smoothness, efficiency and arm swinging. Our toolbox is available at https://dynamicmobility.github.io/moplayground/.

While standard reinforcement learning optimizes a single reward signal, many applications require optimizing a nonlinear utility $f(J_1^π,\dots,J_M^π)$ over multiple objectives, where each $J_m^π$ denotes the expected discounted return of a distinct reward function. A common approach is concave scalarization, which captures important trade-offs such as fairness and risk sensitivity. However, nonlinear scalarization introduces a fundamental challenge for policy gradient methods: the gradient depends on $\partial f(J^π)$, while in practice only empirical return estimates $\hat J$ are available. Because $f$ is nonlinear, the plug-in estimator is biased ($\mathbb{E}[\partial f(\hat J)] \neq \partial f(\mathbb{E}[\hat J])$), leading to persistent gradient bias that degrades sample complexity. In this work we identify and overcome this bias barrier in concave-scalarized multi-objective reinforcement learning. We show that existing policy-gradient methods suffer an intrinsic $\widetilde{\mathcal{O}}(ε^{-4})$ sample complexity due to this bias. To address this issue, we develop a Natural Policy Gradient (NPG) algorithm equipped with a multi-level Monte Carlo (MLMC) estimator that controls the bias of the scalarization gradient while maintaining low sampling cost. We prove that this approach achieves the optimal $\widetilde{\mathcal{O}}(ε^{-2})$ sample complexity for computing an $ε$-optimal policy. Furthermore, we show that when the scalarization function is second-order smooth, the first-order bias cancels automatically, allowing vanilla NPG to achieve the same $\widetilde{\mathcal{O}}(ε^{-2})$ rate without MLMC. Our results provide the first optimal sample complexity guarantees for concave multi-objective reinforcement learning under policy-gradient methods.

Robotic bin packing is widely deployed in warehouse automation, with current systems achieving robust performance through heuristic and learning-based strategies. These systems must balance compact placement with rapid execution, where selecting alternative items or reorienting them can improve space utilization but introduce additional time. We propose a selection-based formulation that explicitly reasons over this trade-off: at each step, the robot evaluates multiple candidate actions, weighing expected packing benefit against estimated operational time. This enables time-aware strategies that selectively accept increased operational time when it yields meaningful spatial improvements. Our method, STEP (Space-Time Efficient Packing), uses a preference-conditioned, Transformer-based reinforcement learning policy, and allows generalization across candidate set sizes and integration with standard placement modules. It achieves a 44% reduction in operational time without compromising packing density. Additional material is available at https://step-packing.github.io.

Patient no-shows disrupt outpatient clinic operations, reduce productivity, and may delay necessary care. Clinics often adopt overbooking or double-booking to mitigate these effects. However, poorly calibrated policies can increase congestion and waiting times. Most existing methods rely on fixed heuristics and fail to adapt to real-time scheduling conditions or patient-specific no-show risk. To address these limitations, we propose an adaptive outpatient double-booking framework that integrates individualized no-show prediction with multi-objective reinforcement learning. The scheduling problem is formulated as a Markov decision process, and patient-level no-show probabilities estimated by a Multi-Head Attention Soft Random Forest model are incorporated in the reinforcement learning state. We develop a Multi-Policy Proximal Policy Optimization method equipped with a Multi-Policy Co-Evolution Mechanism. Under this mechanism, we propose a novel τ rule based on Kullback-Leibler divergence that enables selective knowledge transfer among behaviorally similar policies, improving convergence and expanding the diversity of trade-offs. In addition, SHapley Additive exPlanations is used to interpret both the predicted no-show risk and the agent's scheduling decisions. The proposed framework determines when to single-book, double-book, or reject appointment requests, providing a dynamic and data-driven alternative to conventional outpatient scheduling policies.

Autonomous driving involves multiple, often conflicting objectives such as safety, efficiency, and comfort. In reinforcement learning (RL), these objectives are typically combined through weighted summation, which collapses their relative priorities and often yields policies that violate safety-critical constraints. To overcome this limitation, we introduce the Preordered Multi-Objective MDP (Pr-MOMDP), which augments standard MOMDPs with a preorder over reward components. This structure enables reasoning about actions with respect to a hierarchy of objectives rather than a scalar signal. To make this structure actionable, we extend distributional RL with a novel pairwise comparison metric, Quantile Dominance (QD), that evaluates action return distributions without reducing them into a single statistic. Building on QD, we propose an algorithm for extracting optimal subsets, the subset of actions that remain non-dominated under each objective, which allows precedence information to shape both decision-making and training targets. Our framework is instantiated with Implicit Quantile Networks (IQN), establishing a concrete implementation while preserving compatibility with a broad class of distributional RL methods. Experiments in Carla show improved success rates, fewer collisions and off-road events, and deliver statistically more robust policies than IQN and ensemble-IQN baselines. By ensuring policies respect rewards preorder, our work advances safer, more reliable autonomous driving systems.

Multi-objective reinforcement learning (MORL) is effective for multi-echelon combinatorial supply chain optimisation, where tasks involve high dimensionality, uncertainty, and competing objectives. However, its deployment in dynamic environments is hindered by the need for task-specific retraining and substantial computational cost. We introduce MIRACL (Meta multI-objective Reinforcement leArning with Composite Learning), a hierarchical Meta-MORL framework that allows for a few-shot generalisation across diverse tasks. MIRACL decomposes each task into structured subproblems for efficient policy adaptation and meta-learns a global policy across tasks using a Pareto-based adaptation strategy to encourage diversity in meta-training and fine-tuning. To our knowledge, this is the first integration of Meta-MORL with such mechanisms in combinatorial optimisation. Although validated in the supply chain domain, MIRACL is theoretically domain-agnostic and applicable to broader dynamic multi-objective decision-making problems. Empirical evaluations show that MIRACL outperforms conventional MORL baselines in simple to moderate tasks, achieving up to 10% higher hypervolume and 5% better expected utility. These results underscore the potential of MIRACL for robust, efficient adaptation in multi-objective problems.

Deep Reinforcement Learning is a promising tool for robotic control, yet practical application is often hindered by the difficulty of designing effective reward functions. Real-world tasks typically require optimizing multiple objectives simultaneously, necessitating precise tuning of their weights to learn a policy with the desired characteristics. To address this, we propose a two-stage reward curriculum where we decouple task-specific objectives from behavioral terms. In our method, we first train the agent on a simplified task-only reward function to ensure effective exploration before introducing the full reward that includes auxiliary behavior-related terms such as energy efficiency. Further, we analyze various transition strategies and demonstrate that reusing samples between phases is critical for training stability. We validate our approach on the DeepMind Control Suite, ManiSkill3, and a mobile robot environment, modified to include auxiliary behavioral objectives. Our method proves to be simple yet effective, substantially outperforming baselines trained directly on the full reward while exhibiting higher robustness to specific reward weightings.

Single-task RL agents are typically trained under a fixed reward function, which limits their robustness to reward misspecification and their ability to adapt to changing preferences. We introduce Reward-Conditioned Reinforcement Learning (RCRL), an off-policy method that conditions agents on reward parameterizations while collecting experience under a single nominal objective. By recomputing counterfactual rewards from shared replay data, RCRL exposes the agent to multiple reward objectives without additional environment interaction, connecting single-task RL with ideas from multi-objective and multi-task learning. Across single-task, multi-task, and vision-based benchmarks, RCRL improves sample efficiency under the nominal reward parameterization, enables efficient adaptation to new parameterizations, and supports zero-shot behavioral adjustment at deployment. Our results show that RCRL provides a scalable mechanism for learning robust, steerable policies without sacrificing the simplicity of single-task training.

Reinforcement Learning with Rubric Rewards (RLRR) is a framework that extends conventional reinforcement learning from human feedback (RLHF) and verifiable rewards (RLVR) by replacing scalar preference signals with structured, multi-dimensional, contextual rubric-based evaluations. However, existing approaches in RLRR are limited to linearly compressing vector rewards into a scalar reward with a fixed weightings, which is sensitive to artificial score design and fails to capture correlations among reward dimensions. To overcome the limitations of reward aggregation, this work proposes Alternating Reinforcement Learning with Rubric Rewards (ARL-RR), a framework that eliminates the need for a fixed scalarization by optimizing one semantic rubric meta-class at a time. Theoretically, we show that reward aggregation induces a variance contraction effect, which helps explain the performance gains. We further introduce a lightweight, search-based adaptation procedure that selects the next meta-class dynamically based on task performance, enabling the policy to emphasize critical objectives and thereby improve the model performance. Empirically, our experiments on the HealthBench dataset with experts annotations demonstrate that ARL-RR uniformly outperforms scalarized methods in both model performance and training efficiency across different model scales (1.7B, 4B, 8B, and 14B).

Offline Reinforcement Learning (RL) is an emerging field of RL in which policies are learned solely from demonstrations. Within offline RL, some environments involve balancing multiple objectives, but existing multi-objective offline RL algorithms do not provide an efficient way to find a fair compromise. FairDICE (see arXiv:2506.08062v2) seeks to fill this gap by adapting OptiDICE (an offline RL algorithm) to automatically learn weights for multiple objectives to e.g. incentivise fairness among objectives. As this would be a valuable contribution, this replication study examines the replicability of claims made regarding FairDICE. We find that many theoretical claims hold, but an error in the code reduces FairDICE to standard behaviour cloning in continuous environments, and many important hyperparameters were originally underspecified. After rectifying this, we show in experiments extending the original paper that FairDICE can scale to complex environments and high-dimensional rewards, though it can be reliant on (online) hyperparameter tuning. We conclude that FairDICE is a theoretically interesting method, but the experimental justification requires significant revision.

Agents in the real world must often balance multiple objectives, such as speed, stability, and energy efficiency in continuous control. To account for changing conditions and preferences, an agent must ideally learn a Pareto frontier of policies representing multiple optimal trade-offs. Recent advances in multi-policy multi-objective reinforcement learning (MORL) enable learning a Pareto front directly, but require full multi-objective consideration from the start of training. In practice, multi-objective preferences often arise after a policy has already been trained on a single specialised objective. Existing MORL methods cannot leverage these pre-trained `specialists' to learn Pareto fronts and avoid incurring the sample costs of retraining. We introduce Mixed Advantage Pareto Extraction (MAPEX), an offline MORL method that constructs a frontier of policies by reusing pre-trained specialist policies, critics, and replay buffers. MAPEX combines evaluations from specialist critics into a mixed advantage signal, and weights a behaviour cloning loss with it to train new policies that balance multiple objectives. MAPEX's post hoc Pareto front extraction preserves the simplicity of single-objective off-policy RL, and avoids retrofitting these algorithms into complex MORL frameworks. We formally describe the MAPEX procedure and evaluate MAPEX on five multi-objective MuJoCo environments. Given the same starting policies, MAPEX produces comparable fronts at $0.001\%$ the sample cost of established baselines.

Deep reinforcement learning (RL) has been applied extensively to solve complex decision-making problems. In many real-world scenarios, tasks often have several conflicting objectives and may require multiple agents to cooperate, which are the multi-objective multi-agent decision-making problems. However, only few works have been conducted on this intersection. Existing approaches are limited to separate fields and can only handle multi-agent decision-making with a single objective, or multi-objective decision-making with a single agent. In this paper, we propose MO-MIX to solve the multi-objective multi-agent reinforcement learning (MOMARL) problem. Our approach is based on the centralized training with decentralized execution (CTDE) framework. A weight vector representing preference over the objectives is fed into the decentralized agent network as a condition for local action-value function estimation, while a mixing network with parallel architecture is used to estimate the joint action-value function. In addition, an exploration guide approach is applied to improve the uniformity of the final non-dominated solutions. Experiments demonstrate that the proposed method can effectively solve the multi-objective multi-agent cooperative decision-making problem and generate an approximation of the Pareto set. Our approach not only significantly outperforms the baseline method in all four kinds of evaluation metrics, but also requires less computational cost.

Optimizing the consolidation process in container-based fulfillment centers requires trading off competing objectives such as processing speed, resource usage, and space utilization while adhering to a range of real-world operational constraints. This process involves moving items between containers via a combination of human and robotic workstations to free up space for inbound inventory and increase container utilization. We formulate this problem as a large-scale Multi-Objective Reinforcement Learning (MORL) task with high-dimensional state spaces and dynamic system behavior. Our method builds on recent theoretical advances in solving constrained RL problems via best-response and no-regret dynamics in zero-sum games, enabling principled minimax policy learning. Policy evaluation on realistic warehouse simulations shows that our approach effectively trades off objectives, and we empirically observe that it learns a single policy that simultaneously satisfies all constraints, even if this is not theoretically guaranteed. We further introduce a theoretical framework to handle the problem of error cancellation, where time-averaged solutions display oscillatory behavior. This method returns a single iterate whose Lagrangian value is close to the minimax value of the game. These results demonstrate the promise of MORL in solving complex, high-impact decision-making problems in large-scale industrial systems.

Reward design has been one of the central challenges for real world reinforcement learning (RL) deployment, especially in settings with multiple objectives. Preference-based RL offers an appealing alternative by learning from human preferences over pairs of behavioural outcomes. More recently, RL from AI feedback (RLAIF) has demonstrated that large language models (LLMs) can generate preference labels at scale, mitigating the reliance on human annotators. However, existing RLAIF work typically focuses only on single-objective tasks, leaving the open question of how RLAIF handles systems that involve multiple objectives. In such systems trade-offs among conflicting objectives are difficult to specify, and policies risk collapsing into optimizing for a dominant goal. In this paper, we explore the extension of the RLAIF paradigm to multi-objective self-adaptive systems. We show that multi-objective RLAIF can produce policies that yield balanced trade-offs reflecting different user priorities without laborious reward engineering. We argue that integrating RLAIF into multi-objective RL offers a scalable path toward user-aligned policy learning in domains with inherently conflicting objectives.

This work studies heterogeneous Multi-Objective Reinforcement Learning (MORL), where objectives can differ sharply in temporal frequency. Such heterogeneity allows dense objectives to dominate learning, while sparse long-horizon rewards receive weak credit assignment, leading to poor sample efficiency. We propose a Parallel Reward Integration with Symmetry (PRISM) algorithm that enforces reflectional symmetry as an inductive bias in aligning reward channels. PRISM introduces ReSymNet, a theory-motivated model that reconciles temporal-frequency mismatches across objectives, using residual blocks to learn a scaled opportunity value that accelerates exploration while preserving the optimal policy. We also propose SymReg, a reflectional equivariance regulariser that enforces agent mirroring and constrains policy search to a reflection-equivariant subspace. This restriction provably reduces hypothesis complexity and improves generalisation. Across MuJoCo benchmarks, PRISM consistently outperforms both a sparse-reward baseline and an oracle trained with full dense rewards, improving Pareto coverage and distributional balance: it achieves hypervolume gains exceeding 100% over the baseline and up to 32% over the oracle. The code is at https://github.com/EVIEHub/PRISM.

Generative policies based on diffusion models and flow matching have shown strong promise for offline reinforcement learning (RL), but their applicability remains largely confined to continuous action spaces. To address a broader range of offline RL settings, we extend flow matching to a general framework that supports discrete action spaces with multiple objectives. Specifically, we replace continuous flows with continuous-time Markov chains, trained using a Q-weighted flow matching objective. We then extend our design to multi-agent settings, mitigating the exponential growth of joint action spaces via a factorized conditional path. We theoretically show that, under idealized conditions, optimizing this objective recovers the optimal policy. Extensive experiments further demonstrate that our method performs robustly across diverse settings and benchmarks, including high-dimensional control, multi-agent games, and dynamically changing preferences over multiple objectives, while outperforming traditional offline RL methods in practical multi-modal decision-making scenarios. Our discrete framework can also be applied to continuous-control problems through action quantization, providing a flexible trade-off between representational complexity and performance.

This paper addresses multi-objective conflicts and catastrophic forgetting in uncrewed aerial vehicle (UAV) networks across dynamic spatiotemporal environments. Conventional multi-agent reinforcement learning (MARL) algorithms suffer from severe policy degradation during sequential task transitions. We propose a spatiotemporal continual federated learning (SCFL) framework driven by the group-decoupled multi-agent proximal policy optimization (G-MAPPO) algorithm. SCFL incorporates a three-stage geometric alignment mechanism: it resolves local gradient conflicts via group-decoupled policy optimization (GDPO), mitigates spatial Non-Independent and Identically Distributed (non-IID) client drift through adaptive cosine aggregation, and suppresses inter-task interference via global temporal orthogonal projection without raw experience replay. Evaluations show that SCFL achieves superior robustness over federated baselines, maintaining spatial service reliability above 0.95 and a load balancing index of approximately 0.95 during non-stationary transitions. A longitudinal self-degradation analysis further shows that SCFL preserves historical knowledge with near-zero performance variation in spatial reliability and QoS under moderate loads from 40 to 120 users, while revealing its operating boundary under extreme congestion with 140 users due to hard projection constraints. The framework provides a scalable, communication-efficient approach for autonomous aerial network orchestration.

Preference-Conditioned Policy Learning (PCPL) in Multi-Objective Reinforcement Learning (MORL) approximates diverse Pareto-optimal solutions by conditioning a single policy on user-specified preferences, enabling run-time adaptation to arbitrary trade-offs without retraining. However, existing PCPL benchmarks are largely restricted to toy tasks and fixed environments, limiting their realism and scalability. To address this gap, we introduce GraphAllocBench, a flexible benchmark built on CityPlannerEnv, a novel graph-based resource allocation sandbox inspired by city management. GraphAllocBench provides a rich suite of problems with customizable objective functions, varying preference conditions, complex Pareto Fronts, and high-dimensional scalability. We further propose two supplementary metrics -- Proportion of Non-Dominated Solutions (PNDS) and Ordering Score (OS) -- that capture prediction reliability and preference consistency while complementing the widely used hypervolume metric. Through experiments with several state-of-the-art PCPL algorithms and our own MLP and graph-aware PCPL-PPO baseline, we show that GraphAllocBench exposes distinct failure modes that hypervolume alone does not capture but our supplementary metrics reveal, while motivating graph-based approaches such as Graph Neural Networks (GNNs) for scaling to complex, high-dimensional allocation tasks. By letting users freely vary objectives, preferences, and allocation rules, GraphAllocBench serves as a versatile and extensible testbed for advancing PCPL.

A central difficulty in applying reinforcement learning to real-world applications such as autonomous driving is that conventional scalar reward formulations obtained by aggregating multiple often competing objectives may obscure the structure of their trade-offs. These challenges are particularly relevant to decision-making for heavy-duty vehicles, which requires balancing safety, efficiency, and operational costs under demanding commercial requirements. We present a preference-conditioned multi-objective reinforcement learning framework that explicitly represents these objectives and utilizes Generalized Policy Improvement and Proximal Policy Optimization to learn policies capturing different trade-offs between them. The proposed method approximates the Pareto front across three conflicting objectives: safety, quantified in terms of collisions and successful completion; energy efficiency, quantified using energy cost; and time efficiency, quantified using driver cost. We evaluate the framework in a scalable highway traffic simulation environment tailored for tactical decision making in heavy-duty trucks. It yields smooth and interpretable Pareto fronts, and evaluations across traffic densities and against an analytical baseline show that the learned policies capture meaningful trade-offs. The preference-conditioned policy enables transitions between different driving behaviors without retraining, demonstrating the potential of multi-objective reinforcement learning for adaptive decision making in autonomous heavy-duty vehicles.

Agents in many multi-agent systems must balance several, possibly conflicting, objectives, and the trade-offs an agent can achieve depend on how the other agents behave. We study this setting through the Multi-Objective Markov Game (MOMG), a Markov game in which each agent receives a vector of rewards, and adopt the Pareto-Nash Equilibrium (PNE) as the solution concept: at a PNE, no agent can unilaterally improve one of its objectives without sacrificing another. We show that PNEs always exist and coincide with the Nash equilibria of the linearly scalarized games with strictly positive weights, so standard single-objective Markov-game solvers suffice to compute them. We further define the Weak Pareto-Nash Equilibrium (WPNE), which excludes only unilateral deviations that strictly improve all objectives at once. The associated gap (WPNG) is zero exactly at WPNEs and never exceeds the Nash gap of any linearly scalarized game; hence an approximate Nash equilibrium of a scalarized game is also an approximate WPNE. When the preference profile is known in advance, learning in an MOMG therefore reduces to learning in a single scalarized Markov game, for which we provide a sample-efficient algorithm. When preferences are revealed only after data collection, we design a two-phase algorithm that first explores without any preference information; with high probability, every Nash equilibrium of the learned scalarized game is then an approximate WPNE for every queried preference profile, and the WPNG of any policy can be estimated accurately from the learned model. Experiments on tabular games and four multi-objective multi-agent environments illustrate the theory and show the effect of preference-free exploration.

Urban Air Mobility (UAM) envisions the widespread use of small aerial vehicles to transform transportation in dense urban environments. However, UAM faces critical operational challenges, particularly the balance between minimizing noise exposure and maintaining safe separation in low-altitude urban airspace, two potentially conflicting objectives that are often addressed separately. We propose a reinforcement learning (RL)-based air traffic management system that integrates both noise and safety considerations within a unified, decentralized framework. Under this scalable air traffic coordination solution, agents operate in a structured, multi-layered airspace and learn altitude adjustment policies to jointly manage noise impact and separation constraints. The system demonstrates strong performance across both objectives and reveals tradeoffs among separation, noise exposure, and energy efficiency under high traffic density. Among the three objectives, safe separation is accorded the highest priority, whereas the relative significance of noise and energy varies by location and is contingent upon financial and public policy considerations. The findings highlight the potential of RL and multi-objective coordination strategies in enhancing the safety, quietness, and efficiency of UAM operations.