We introduce a new algorithm for multi-objective reinforcement learning (MORL) with linear preferences, with the goal of enabling few-shot adaptation to new tasks. In MORL, the aim is to learn policies over multiple competing objectives whose relative importance (preferences) is unknown to the agent. While this alleviates dependence on scalar reward design, the expected return of a policy can change significantly with varying preferences, making it challenging to learn a single model to produce optimal policies under different preference conditions. We propose a generalized version of the Bellman equation to learn a single parametric representation for optimal policies over the space of all possible preferences. After an initial learning phase, our agent can execute the optimal policy under any given preference, or automatically infer an underlying preference with very few samples. Experiments across four different domains demonstrate the effectiveness of our approach.

Multi-objective reinforcement learning algorithms (MORL) extend standard reinforcement learning (RL) to scenarios where agents must optimize multiple---potentially conflicting---objectives, each represented by a distinct reward function. To facilitate and accelerate research and benchmarking in multi-objective RL problems, we introduce a comprehensive collection of software libraries that includes: (i) MO-Gymnasium, an easy-to-use and flexible API enabling the rapid construction of novel MORL environments. It also includes more than 20 environments under this API. This allows researchers to effortlessly evaluate any algorithms on any existing domains; (ii) MORL-Baselines, a collection of reliable and efficient implementations of state-of-the-art MORL algorithms, designed to provide a solid foundation for advancing research. Notably, all algorithms are inherently compatible with MO-Gymnasium; and(iii) a thorough and robust set of benchmark results and comparisons of MORL-Baselines algorithms, tested across various challenging MO-Gymnasium environments. These benchmarks were constructed to serve as guidelines for the research community, underscoring the properties, advantages, and limitations of each particular state-of-the-art method.

In this paper we consider multi-objective reinforcement learning where the objectives are balanced using preferences. In practice, the preferences are often given in an adversarial manner, e.g., customers can be picky in many applications. We formalize this problem as an episodic learning problem on a Markov decision process, where transitions are unknown and a reward function is the inner product of a preference vector with pre-specified multi-objective reward functions.

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 critical care settings such as the Intensive Care Unit, clinicians face the complex challenge of balancing conflicting objectives, primarily maximizing patient survival while minimizing resource utilization (e.g., length of stay). Single-objective Reinforcement Learning approaches typically address this by optimizing a fixed scalarized reward function, resulting in rigid policies that fail to adapt to varying clinical priorities. Multi-objective Reinforcement Learning (MORL) offers a solution by learning a set of optimal policies along the Pareto Frontier, allowing for dynamic preference selection at test time. However, applying MORL in healthcare necessitates strict offline learning from historical data. In this paper, we benchmark three offline MORL algorithms, Conditioned Conservative Pareto Q-Learning (CPQL), Adaptive CPQL, and a modified Pareto Efficient Decision Agent (PEDA) Decision Transformer (PEDA DT), against three scalarized single-objective baselines (BC, CQL, and DDQN) on the MIMIC-IV dataset. Using Off-Policy Evaluation (OPE) metrics, we demonstrate that PEDA DT algorithm offers superior flexibility compared to static scalarized baselines. Notably, our results extend previous findings on single-objective Decision Transformers in healthcare, confirming that sequence modeling architectures remain robust and effective when scaled to multi-objective conditioned generation. These findings suggest that offline MORL is a promising framework for enabling personalized, adjustable decision-making in critical care without the need for retraining.

Many real-world problems (e.g., resource management, autonomous driving, drug discovery) require optimizing multiple, conflicting objectives. Multi-objective reinforcement learning (MORL) extends classic reinforcement learning to handle multiple objectives simultaneously, yielding a set of policies that capture various trade-offs. However, the MORL field lacks complex, realistic environments and benchmarks. We introduce a water resource (Nile river basin) management case study and model it as a MORL environment. We then benchmark existing MORL algorithms on this task. Our results show that specialized water management methods outperform state-of-the-art MORL approaches, underscoring the scalability challenges MORL algorithms face in real-world scenarios.

Consequently, MORL's primary aim is to learn a variety of

In practical multi-agent systems, agents often have diverse objectives, which makes the system more complex, as each agent's performance across multiple criteria depends on the joint actions of all agents, creating intricate strategic trade-offs. To address this, we introduce the Multi-Objective Markov Game (MOMG), a framework for multi-agent reinforcement learning with multiple objectives. We propose the Pareto-Nash Equilibrium (PNE) as the primary solution concept, where no agent can unilaterally improve one objective without sacrificing performance on another. We prove existence of PNE, and establish an equivalence between the PNE and the set of Nash Equilibria of MOMG's corresponding linearly scalarized games, enabling solutions of MOMG by transferring to a standard single-objective Markov game. However, we note that computing a PNE is theoretically and computationally challenging, thus we propose and study weaker but more tractable solution concepts. Building on these foundations, we develop online learning algorithm that identify a single solution to MOMGs. Furthermore, we propose a two-phase, preference-free algorithm that decouples exploration from planning. Our algorithm enables computation of a PNE for any given preference profile without collecting new samples, providing an efficient methodological characterization of the entire Pareto-Nash front.

Multi-Objective Reinforcement Learning (MORL) presents significant challenges and opportunities for optimizing multiple objectives in Large Language Models (LLMs). We introduce a MORL taxonomy and examine the advantages and limitations of various MORL methods when applied to LLM optimization, identifying the need for efficient and flexible approaches that accommodate personalization functionality and inherent complexities in LLMs and RL. We propose a vision for a MORL benchmarking framework that addresses the effects of different methods on diverse objective relationships. As future research directions, we focus on meta-policy MORL development that can improve efficiency and flexibility through its bi-level learning paradigm, highlighting key research questions and potential solutions for improving LLM performance.