Revisiting Bisimulation Metric for Robust Representations in Reinforcement Learning

2025-07-24

AI Summary

Traditional bisimulation metrics suffer from two critical limitations: (1) imprecise reward discrepancy definitions, failing to capture discriminative scenarios; and (2) recursive updates relying on fixed, hand-crafted weights, hindering adaptation to dynamic shifts in reward scales and transition dynamics importance across training stages and tasks. To address these, we propose an adaptive bisimulation metric: first, we introduce a joint state-action measure to reformulate reward discrepancy computation; second, we design a learnable, dynamically weighted recursive update operator that adaptively balances the contributions of reward and transition terms. We provide theoretical convergence guarantees for the proposed metric. Empirical evaluation on DeepMind Control and Meta-World benchmarks demonstrates that representations learned under our metric exhibit superior discriminability, and downstream policies achieve significantly higher performance than those trained with existing bisimulation methods.

Technology Category

• Multiagent Systems: Adversarial Agents
• Search and Optimization: Sampling/Simulation-based Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Bisimulation metric has long been regarded as an effective control-related representation learning technique in various reinforcement learning tasks. However, in this paper, we identify two main issues with the conventional bisimulation metric: 1) an inability to represent certain distinctive scenarios, and 2) a reliance on predefined weights for differences in rewards and subsequent states during recursive updates. We find that the first issue arises from an imprecise definition of the reward gap, whereas the second issue stems from overlooking the varying importance of reward difference and next-state distinctions across different training stages and task settings. To address these issues, by introducing a measure for state-action pairs, we propose a revised bisimulation metric that features a more precise definition of reward gap and novel update operators with adaptive coefficient. We also offer theoretical guarantees of convergence for our proposed metric and its improved representation distinctiveness. In addition to our rigorous theoretical analysis, we conduct extensive experiments on two representative benchmarks, DeepMind Control and Meta-World, demonstrating the effectiveness of our approach.

Problem

• Improving bisimulation metric for better RL representation
• Addressing imprecise reward gap definition in current metric
• Adapting dynamic weights for reward and state differences

Innovation

• Revised bisimulation metric with precise reward gap
• Adaptive coefficient for dynamic importance adjustment
• Theoretical convergence and distinctiveness guarantees