Multi-Objective Constraint Inference using Inverse reinforcement learning

Reinforcement Learning (RL) systems are typically trained using a single, well-specified scalar reward function. However, real-world decision-making tasks often involve multiple, competing objectives, such as performance versus efficiency, where ground-truth reward functions are difficult to specify or inaccessible. While Multi-Objective RL (MORL) addresses such trade-offs by modeling rewards as vectors, existing approaches typically assume access to a well-specified reward function for each objective, inheriting the same challenges faced by single-objective RL. Meanwhile, Preference-based RL (PbRL) has shown great potential in solving complex tasks without access to a pre-defined reward function through reward learning from human feedback, yet has largely been studied in single-objective settings. In this work, we bridge this gap with LEMUR: Learning to Align with Multi-Objective Reinforcement Learning with Preference feedback, a novel framework where an agent interactively learns from the preferences of multiple humans to learn optimal multi-objective policies. Our approach jointly learns policies and multiple objective-specific reward models from human feedback, enabling agents to effectively balance competing objectives during learning. We evaluate LEMUR on a variety of benchmark multi-objective tasks, and empirical results demonstrate its superior performance over baseline methods. Our method presents a promising direction for solving multi-objective decision-making tasks without pre-defined reward functions.

Multi-Objective Reinforcement Learning (MORL) extends standard RL by optimizing policies with respect to multiple, often conflicting, objectives. While max-min MORL has emerged as an effective approach for promoting fairness, its applicability remains limited, particularly when constraints must be incorporated. In this paper, we propose a MORL framework that integrates the max-min criterion with explicit constraint satisfaction. We establish a theoretical foundation for the proposed framework and validate the resulting algorithm through convergence analysis and experiments in tabular settings. We further demonstrate the practical relevance of our approach in simulated building thermal control, multi-objective locomotion control, and greenhouse-gas-emission-aware traffic management. Across these domains, our method effectively balances fairness and constraint satisfaction in multi-objective decision-making.

Ensuring safe behavior in reinforcement learning (RL) is challenging when safety constraints are implicit and cannot be densely measured. In many settings, supervision is limited to coarse approvals or rejections of whole trajectories (e.g., whether a rollout remained within an unknown safety threshold). We propose TraCeS (Trajectory-based Constraint Estimation for Safety), a method for learning per-timestep violation credit from such sparse trajectory-level labels. TraCeS trains a sequential violation estimator whose per-step credits factorize the predicted probability that a trajectory has not yet violated the constraint, and integrates this learned signal into constrained policy optimization. The method requires neither a known cost function nor a known threshold, and remains compatible with standard continuous-control algorithms. We provide a theoretical analysis of the approximation gap introduced by the learning objective, and demonstrate empirically that TraCeS improves constraint satisfaction and feedback efficiency over baselines across multiple continuous-control benchmarks, including long-horizon tasks and settings with noisy or inconsistent labels.