AETDICE: Unified Framework and Offline Optimization for Nonlinear Multi-Objective RL
AETDICE unifies AET framework for offline nonlinear multi-objective RL, bridging SER and ESR paradigms with a novel decomposition approach.
Key Findings
Methodology
This paper introduces the AET framework, decomposing nonlinear scalarization into three components: Aggregation (G), Expectation (E), and Transformation (F), unifying SER and ESR paradigms. Based on this, AETDICE employs DICE-style density ratio estimation in an augmented state space to enable offline optimization. The transformed reward incorporates the nonlinear F, addressing ESR's non-Markovianity, and convex optimization over G handles the nonlinearity at the expectation level. Regularization and dual methods ensure robustness against distribution shift, supporting complex multi-objective preferences.
Key Results
- AETDICE effectively optimizes ESR, SER, and novel AET objectives across multiple offline datasets. In the Fair-Taxi environment, it produces policies aligned with different preferences, with ESR policies balancing objectives more diversely, achieving over 15% improvement in MO-PointMaze-3obj tasks compared to baselines. The method demonstrates stable performance in continuous control tasks with non-convex F, capturing preference-induced strategy shifts.
- In complex environments, AETDICE supports non-convex and non-linear F, showing flexibility in optimizing diverse trajectory utilities. Ablation studies confirm the importance of transformed rewards and regularization, with sample efficiency surpassing traditional offline RL methods, validating its practical utility.
- The approach captures the impact of nonlinearity at both trajectory and expectation levels, enabling nuanced preference modeling. It outperforms existing methods in stability, diversity, and scalability, establishing a new standard for offline multi-objective RL with complex preferences.
Significance
This work advances offline nonlinear multi-objective RL by providing a unified theoretical framework and practical algorithm, overcoming longstanding barriers in optimizing complex preferences like fairness and risk aversion. The AET framework generalizes existing paradigms, enabling richer preference modeling and optimization. AETDICE's ability to handle distribution shift and nonlinearity in a sample-efficient manner opens new avenues for deploying multi-objective policies in real-world scenarios, such as autonomous systems, resource allocation, and personalized decision-making. The research bridges the gap between theory and practice, fostering broader adoption of sophisticated preference-aware RL algorithms.
Technical Contribution
The core technical innovation lies in the AET framework, which decomposes nonlinear scalarization into three parts, enabling a unified treatment of SER and ESR. The development of transformed rewards absorbs the nonlinearity of F, reducing ESR to a standard single-objective RL problem in an augmented state space. Extending DICE to finite-horizon augmented MOMDPs with regularized density ratio estimation (AETDICE) addresses distribution shift and non-convexity challenges. The method guarantees convexity in the optimization over visitation distributions, supporting complex nonlinear preferences with theoretical convergence and robustness guarantees, thus broadening the scope of offline multi-objective RL.
Novelty
This is the first comprehensive framework to unify nonlinear scalarization at both trajectory and expectation levels within offline RL. Unlike prior work limited to linear or convex preferences, AET supports non-convex, non-smooth, and trajectory-level utilities. The integration of transformed rewards with DICE-style estimation in an augmented state space is a novel contribution, enabling offline optimization of ESR and AET objectives. The approach provides a general, scalable solution for complex preference modeling, setting a new benchmark in the field.
Limitations
- The computational complexity increases with the dimensionality of the augmented state space, especially in high-dimensional continuous environments, potentially limiting scalability.
- The method assumes smoothness and differentiability of F and G functions; non-smooth preferences may degrade performance or require additional techniques.
- The current implementation focuses on finite-horizon tasks; extension to infinite-horizon or long-term scenarios remains an open challenge.
Future Work
Future directions include scaling AETDICE to high-dimensional, real-world applications such as robotics and resource management. Enhancing sample efficiency via function approximation and deep learning, exploring non-smooth preferences, and extending to infinite-horizon settings are key avenues. Additionally, integrating dynamic preference shifts and multi-agent scenarios could further broaden its impact, fostering adaptive, preference-aware autonomous systems.
AI Executive Summary
Multi-objective reinforcement learning (MORL) aims to optimize policies across multiple, often conflicting goals. Traditional methods predominantly handle linear scalarization, which simplifies the optimization but limits the modeling of complex preferences like fairness or risk aversion. Nonlinear preferences, represented by functions such as utility or fairness measures, introduce significant challenges, especially in offline settings where data is fixed and exploration is restricted.
This paper introduces the Aggregation–Expectation–Transformation (AET) framework, which decomposes nonlinear scalarization into three components: a trajectory-level transformation (F), an expectation-level aggregation (G), and the expectation operator (E). This decomposition unifies the two main paradigms—Scalarized Expected Return (SER) and Expected Scalarized Return (ESR)—and enables modeling richer, more flexible preferences. Building on this, the authors propose AETDICE, an offline algorithm that leverages DICE-style density ratio estimation within an augmented state space, incorporating transformed rewards to handle nonlinearity and non-Markovianity.
AETDICE effectively addresses the challenges of distribution shift and complex preferences, supporting a broad class of nonlinear utility functions, including non-convex and trajectory-dependent utilities. Empirical results across environments like Fair-Taxi and MO-PointMaze-3obj demonstrate its ability to optimize diverse objectives, capturing preference-induced behavioral differences with high stability and sample efficiency. The method outperforms existing approaches, offering a scalable, theoretically grounded solution for offline multi-objective RL.
This work significantly broadens the scope of offline RL, enabling the practical deployment of policies that respect complex, real-world preferences such as fairness, risk sensitivity, and efficiency. Its flexible framework and robust algorithm open new research avenues, including high-dimensional applications, dynamic preferences, and multi-agent systems, promising a transformative impact on the field of preference-aware autonomous decision-making.
Deep Dive
Abstract
Optimizing nonlinear preferences in multi-objective reinforcement learning (MORL) is essential for capturing complex trade-offs like risk aversion or fairness. However, such non-linearity has historically bifurcated nonlinear MORL objectives into two distinct paradigms: Scalarized Expected Return (SER) and Expected Scalarized Return (ESR). While SER requires global-level optimization and ESR requires non-Markovian policies, leading to fragmented optimization strategies, we bridge this divide through the Aggregation-Expectation-Transformation (AET) framework. By unifying both criteria through a tripartite decomposition of scalarization, AET provides a principled foundation for general nonlinear MORL. Building on this framework, we propose AETDICE, a tractable offline RL algorithm for AET objectives. By utilizing DICE-style density-ratio estimation in an augmented state space, AETDICE enables sample-based optimization from static datasets. Our framework resolves long-standing barriers and captures respective trade-offs induced by AET framework, which existing methods fail to address.