Reward-Aware Proto-Representations in Reinforcement Learning (2505.16217v1)

Abstract: In recent years, the successor representation (SR) has attracted increasing attention in reinforcement learning (RL), and it has been used to address some of its key challenges, such as exploration, credit assignment, and generalization. The SR can be seen as representing the underlying credit assignment structure of the environment by implicitly encoding its induced transition dynamics. However, the SR is reward-agnostic. In this paper, we discuss a similar representation that also takes into account the reward dynamics of the problem. We study the default representation (DR), a recently proposed representation with limited theoretical (and empirical) analysis. Here, we lay some of the theoretical foundation underlying the DR in the tabular case by (1) deriving dynamic programming and (2) temporal-difference methods to learn the DR, (3) characterizing the basis for the vector space of the DR, and (4) formally extending the DR to the function approximation case through default features. Empirically, we analyze the benefits of the DR in many of the settings in which the SR has been applied, including (1) reward shaping, (2) option discovery, (3) exploration, and (4) transfer learning. Our results show that, compared to the SR, the DR gives rise to qualitatively different, reward-aware behaviour and quantitatively better performance in several settings.

Reward-Aware Proto-Representations in Reinforcement Learning

The paper "Reward-Aware Proto-Representations in Reinforcement Learning" presents advancements in the domain of reinforcement learning (RL), specifically focusing on improving representation learning through the introduction of reward-aware proto-representations. The paper builds upon the foundational work related to successor representations (SR), which have been pivotal in addressing challenges such as exploration, credit assignment, and generalization within RL.

Summary of Contributions

The authors of this paper propose and analyze the default representation (DR), a novel representation that incorporates the reward dynamics of the environment, thereby extending the capabilities of the successor representation, which is inherently reward-agnostic. There are several notable theoretical and empirical contributions made by the authors:

1. Learning Methods: The paper introduces dynamic programming (DP) and temporal-difference (TD) learning methods for the DR. These methods are essential for the incremental, online learning of DR with linear computational cost, akin to existing methods for SR.
2. Theoretical Characterization: The authors lay the theoretical groundwork for DR, delineating the basis for its vector space and comparing it with SR, especially focusing on their eigenspectra. They demonstrate conditions under which DR and SR have equivalent eigenvectors, highlighting the DR’s reward-awareness in settings with varying rewards across states.
3. Function Approximation: A significant extension is made to apply DR within function approximation frameworks, introducing the concept of default features (DFs). This extension is particularly useful in enabling efficient transfer learning when rewards change at terminal states, without requiring access to transition dynamics—a key limitation of current DR applications.
4. Maximum Entropy RL Framework: The paper also explores the generalization of representation frameworks to the maximum entropy reinforcement learning framework, proposing the maximum entropy representation (MER).

Empirical Evaluation

The empirical analysis is thorough and demonstrates the practical benefits of DR across a variety of settings commonly utilized for SR:

• Reward Shaping: In environments where avoiding low-reward regions is crucial, DR-based shaping outperforms SR, guiding agents effectively to avoid sub-optimal paths.
• Option Discovery: By utilizing DR’s top eigenvectors, the authors propose a novel algorithm for option discovery, enabling reward-aware exploration, thus, outperforming traditional SR-based methods in terms of risk-sensitive exploration.
• Count-Based Exploration: The norm of DR, similar to SR's, provides effective pseudocounts for exploration, yielding substantial improvements over naive exploration strategies.
• Transfer Learning: The introduction of DFs allows for direct computation of optimal policies amidst new reward configurations, achieving transfer learning objectives efficiently, unlike existing methods that rely heavily on access to transition dynamics.

Implications and Future Directions

The implications of enhancing proto-representations with reward dynamics are multi-fold. Practically, this enables RL agents to balance exploration and exploitation more effectively, especially in environments with heterogeneous reward structures. Theoretical insights into the vector spaces of these representations open avenues for richer understanding and modeling of agent behavior.

Future research directions might include scaling DR to more complex environments through deep learning methodologies similar to those already explored for SR. Furthermore, exploring the distinct characteristics and applications of MER in more diverse RL settings would be valuable.

In conclusion, this paper represents a significant step forward in representation learning, bridging gaps between reward-agnostic and reward-sensitive paradigms in reinforcement learning. The DR could potentially serve as an effective compromise between these approaches, offering nuanced control over agent decision-making processes.