Effective Exploration Based on the Structural Information Principles

TL;DR

This work tackles the challenge of exploration in high-dimensional, sparse-reward reinforcement learning by introducing SI2E, a framework built on structural information principles. It defines structural mutual information $I^{SI}(X;Y)$ to capture dynamics-relevant relationships between state-action representations and subsequent states, and employs a 2-layer encoding-tree approach to minimize structural entropy and reveal hierarchical state-action communities. SI2E combines a dynamics-focused representation learning objective with a maximum structural entropy exploration strategy, using a policy-induced hierarchy to generate an intrinsic reward via a $k$-NN estimator, ultimately improving final performance and sample efficiency across MiniGrid, MetaWorld, and DMControl benchmarks. Theoretical connections to traditional mutual information and entropy reinforce the method’s rationale, while extensive experiments demonstrate substantial gains over state-of-the-art baselines, with notable improvements in both final performance and learning efficiency.

Abstract

Traditional information theory provides a valuable foundation for Reinforcement Learning, particularly through representation learning and entropy maximization for agent exploration. However, existing methods primarily concentrate on modeling the uncertainty associated with RL's random variables, neglecting the inherent structure within the state and action spaces. In this paper, we propose a novel Structural Information principles-based Effective Exploration framework, namely SI2E. Structural mutual information between two variables is defined to address the single-variable limitation in structural information, and an innovative embedding principle is presented to capture dynamics-relevant state-action representations. The SI2E analyzes value differences in the agent's policy between state-action pairs and minimizes structural entropy to derive the hierarchical state-action structure, referred to as the encoding tree. Under this tree structure, value-conditional structural entropy is defined and maximized to design an intrinsic reward mechanism that avoids redundant transitions and promotes enhanced coverage in the state-action space. Theoretical connections are established between SI2E and classical information-theoretic methodologies, highlighting our framework's rationality and advantage. Comprehensive evaluations in the MiniGrid, MetaWorld, and DeepMind Control Suite benchmarks demonstrate that SI2E significantly outperforms state-of-the-art exploration baselines regarding final performance and sample efficiency, with maximum improvements of 37.63% and 60.25%, respectively.

Figures (15)

• Figure 1: By incorporating the inherent state-action structure, we simplify the original six-state Markov Decision Process (MDP) with four actions to a five-state MDP with two actions, effectively reducing the size of state-action space from $24 (6\times4)$ to $10 (5\times2)$. Here, $s_2^\prime$ and $a_0^\prime$ represent vertex communities $\{s_2,s_5\}$ and $\{a_0,a_1\}$, respectively. In this scenario, a policy maximizing state-action Shannon entropy would encompass all possible transitions (blue color). In contrast, a policy maximizing structural entropy would selectively focus on crucial transitions (red color), avoiding redundant transitions between $s_2$ and $s_5$.
• Figure 2: The SI2E's overview architecture, including state-action representation learning and maximum structural entropy exploration.
• Figure 3: Learning curves across MetaWorld and DMControl tasks for ablation studies.
• Figure 4: Stretch operation on sibling nodes within the encoding tree.
• Figure 5: Illustration from a joint distribution to $2$-layer approximate binary trees: a) Bipartite distribution graph, b) Optimal encoding tree, c) Resulting encoding tree via a $1$-transformation.

Theorems & Definitions (11)

• Proposition 3.1
• Definition 3.2
• Definition 3.3
• Theorem 3.4
• Theorem 4.1
• Proposition 4.2
• Theorem 4.3
• proof
• proof
• proof