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On Generalization Across Environments In Multi-Objective Reinforcement Learning

Jayden Teoh, Pradeep Varakantham, Peter Vamplew

TL;DR

This work addresses the challenge of generalizing across diverse environments in Multi-Objective Reinforcement Learning (MORL) by formalizing a framework based on Multi-Objective Contextual MDPs (MOC-MDPs) and introducing the MORL-Generalization benchmark. It proposes the Normalized Hypervolume Generalization Ratio (NHGR) to quantify cross-context Pareto-front generalization and investigates both axiomatic and utility-based generalization channels, including context-observability considerations. Empirical results across six domains and eight MORL algorithms reveal substantial generalization gaps, with best context-appropriate NHGR values far from 1 and even zero-shot stages performing poorly, underscoring limitations of current approaches and of scalar rewards for generalization. The paper contributes a rigorous evaluation protocol, open-source software, and a concrete research direction toward integrating MORL with robust generalization for real-world, multi-objective decision-making.

Abstract

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.

On Generalization Across Environments In Multi-Objective Reinforcement Learning

TL;DR

This work addresses the challenge of generalizing across diverse environments in Multi-Objective Reinforcement Learning (MORL) by formalizing a framework based on Multi-Objective Contextual MDPs (MOC-MDPs) and introducing the MORL-Generalization benchmark. It proposes the Normalized Hypervolume Generalization Ratio (NHGR) to quantify cross-context Pareto-front generalization and investigates both axiomatic and utility-based generalization channels, including context-observability considerations. Empirical results across six domains and eight MORL algorithms reveal substantial generalization gaps, with best context-appropriate NHGR values far from 1 and even zero-shot stages performing poorly, underscoring limitations of current approaches and of scalar rewards for generalization. The paper contributes a rigorous evaluation protocol, open-source software, and a concrete research direction toward integrating MORL with robust generalization for real-world, multi-objective decision-making.

Abstract

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.

Paper Structure

This paper contains 35 sections, 17 equations, 13 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Multi-Objective Contextual Markov Decision Process
  4. Empirical Evaluation of MORL Generalization Performance
  5. MORL Generalization Benchmark
  6. Experiments
  7. MORL Generalization Results
  8. Scalar Reward is Not Enough for RL Generalization
  9. Related Work
  10. Discussion and Conclusion
  11. Analysis of Failure Modes in MORL Approaches
  12. Pareto Archival Methods
  13. Reliance on Linear Scalarization
  14. Value Function Interference
  15. Principle of Unchanged Pareto Optimality
  16. ...and 20 more sections

Figures (13)

  • Figure 1: NHGR visualized as the ratio between the hypervolume of the normalized generalist's and the optimal Pareto fronts (dashed and shaded areas).
  • Figure 2: Domains in the MORL Generalization benchmark. Top row from left to right: 1) MO-LunarLander, 2) MO-Hopper, 3) MO-Cheetah, 4) MO-Humanoid. Middle row: MO-LavaGrid (8 handcrafted evaluation environments). Bottom row: MO-SuperMarioBros (8 out of 32 stages).
  • Figure 3: Aggregate NHGR performance in all domains of the benchmark. Each algorithm is evaluated across 5 independent seeds and several evaluation environment configurations. Higher IQM and lower optimality gap scores are better. The best algorithm for each domain is bolded.
  • Figure 4: (a) MO-SuperMarioBros performances on 4 stages. Stage 3-3 in the rightmost column shares visual similarities with the other stages so it is excluded from training to evaluate for ZSG. (b) Heatmap of visited tiles for a specialist and generalist in the MO-LavaGrid "Room" environment. Each column's title shows the conditioned linear weights for the lava and time penalty objectives.
  • Figure 5: Single-objective return on 6 MO-Hopper testing environments during training. Each curve is measured across 5 seeds (mean and standard error).
  • ...and 8 more figures

Theorems & Definitions (5)

  • Definition 1: Multi-Objective Contextual MDP
  • Definition 2: Axiomatic Generalization
  • Definition 3: Utility-based Generalization
  • Definition 4: Normalized Hypervolume Generalization Ratio
  • Definition 5: Expected Utility Generalization Ratio