[Paper Review] Hierarchical State Abstraction Based on Structural Information Principles

Xianghua Zeng, Hao Peng+4 more|arXiv (Cornell University)|Apr 24, 2023

Neural dynamics and brain functionNeuroscience3 citations

TL;DR

This paper proposes SISA, a novel hierarchical state abstraction framework based on structural information principles to improve sample efficiency and performance in reinforcement learning with high-dimensional observations. By leveraging unsupervised hierarchical clustering, a learnable aggregation function weighted by structural entropy, and conditional structural entropy to mitigate information loss, SISA achieves up to 18.98% higher mean episode reward and 44.44% better sample efficiency than SOTA baselines on challenging continuous control benchmarks.

ABSTRACT

State abstraction optimizes decision-making by ignoring irrelevant environmental information in reinforcement learning with rich observations. Nevertheless, recent approaches focus on adequate representational capacities resulting in essential information loss, affecting their performances on challenging tasks. In this article, we propose a novel mathematical Structural Information principles-based State Abstraction framework, namely SISA, from the information-theoretic perspective. Specifically, an unsupervised, adaptive hierarchical state clustering method without requiring manual assistance is presented, and meanwhile, an optimal encoding tree is generated. On each non-root tree node, a new aggregation function and condition structural entropy are designed to achieve hierarchical state abstraction and compensate for sampling-induced essential information loss in state abstraction. Empirical evaluations on a visual gridworld domain and six continuous control benchmarks demonstrate that, compared with five SOTA state abstraction approaches, SISA significantly improves mean episode reward and sample efficiency up to 18.98 and 44.44%, respectively. Besides, we experimentally show that SISA is a general framework that can be flexibly integrated with different representation-learning objectives to improve their performances further.

Motivation & Objective

• To address the critical challenge of balancing irrelevant and essential information in state abstraction for high-dimensional, noisy observations in reinforcement learning.
• To eliminate reliance on manual hyperparameter tuning by developing an unsupervised, adaptive hierarchical clustering method for state abstraction.
• To mitigate sampling-induced information loss in state abstraction, especially in Markov abstraction, through a novel conditional structural entropy mechanism.
• To design a generalizable framework that can be flexibly integrated with existing representation learning objectives to further improve performance.
• To achieve superior sample efficiency and final performance on complex decision-making tasks without sacrificing task dynamics or reward structure.

Proposed method

• An unsupervised, adaptive hierarchical state clustering method is proposed using structuralization, sparsification, and optimization modules to construct an optimal encoding tree without manual intervention.
• A novel aggregation function is defined at each non-root tree node, using assigned structural entropy as weights to enable hierarchical abstraction from leaf to root.
• Conditional structural entropy is introduced to reconstruct state relations and compensate for essential information lost during sampling and compression.
• An autoencoder-based structure with representation-learning objectives is employed to refine state embeddings and support hierarchical clustering.
• The framework is designed to be general and integrable with existing abstraction methods such as Markov abstraction and SAC-AE for performance enhancement.
• The optimal encoding tree is learned end-to-end, enabling automatic abstraction that progressively ignores irrelevant details while preserving task-critical dynamics.

Experimental results

Research questions

• RQ1 Can a hierarchical state abstraction framework be developed that is both unsupervised and adaptive, eliminating the need for manual hyperparameter tuning?
• RQ2 How can structural information principles be leveraged to minimize information loss during state abstraction in reinforcement learning?
• RQ3 To what extent can conditional structural entropy reconstruct lost state relations and improve abstraction fidelity in sampled environments?
• RQ4 Can the proposed framework be generalized and integrated with existing representation learning objectives to further boost performance?
• RQ5 Does the hierarchical abstraction process on an optimal encoding tree lead to significant gains in sample efficiency and final performance on complex control tasks?

Key findings

• SISA achieves up to 18.98% higher mean episode reward compared to the best SOTA baseline across six DMControl environments.
• SISA improves sample efficiency by up to 44.44%, reducing the number of environment steps required to reach a target performance from 45k to 25k in the ball_in_cup-catch task.
• The ablation study confirms that both the fine-tune and abstract stages are essential, with SISA outperforming variants lacking either stage in final performance, sample efficiency, and training stability.
• Integration of SISA with Markov abstraction (Markov-SISA) and SAC-AE (SAC-SISA) yields higher final performance and sample efficiency than the original methods in both ball_in_cup-catch and cartpole-swingup tasks.
• The hierarchical abstraction process on the optimal encoding tree effectively preserves essential dynamics and rewards, enabling superior performance on challenging tasks with rich observations.
• SISA demonstrates strong generalization, achieving state-of-the-art results in both online and offline settings across visual gridworld and DMControl benchmarks.