Off-Policy Maximum Entropy RL with Future State and Action Visitation Measures (2412.06655v1)

Abstract: We introduce a new maximum entropy reinforcement learning framework based on the distribution of states and actions visited by a policy. More precisely, an intrinsic reward function is added to the reward function of the Markov decision process that shall be controlled. For each state and action, this intrinsic reward is the relative entropy of the discounted distribution of states and actions (or features from these states and actions) visited during the next time steps. We first prove that an optimal exploration policy, which maximizes the expected discounted sum of intrinsic rewards, is also a policy that maximizes a lower bound on the state-action value function of the decision process under some assumptions. We also prove that the visitation distribution used in the intrinsic reward definition is the fixed point of a contraction operator. Following, we describe how to adapt existing algorithms to learn this fixed point and compute the intrinsic rewards to enhance exploration. A new practical off-policy maximum entropy reinforcement learning algorithm is finally introduced. Empirically, exploration policies have good state-action space coverage, and high-performing control policies are computed efficiently.

• The paper proposes a novel intrinsic reward based on the relative entropy of discounted future state-action visitation measures to enhance exploration in sparse-reward environments.
• The methodology leverages a contraction mapping property to guarantee policy convergence and outperforms benchmarks like SAC and OPAC+MV.
• Empirical evaluations demonstrate that the OPAC+CV algorithm consistently achieves higher returns and more comprehensive state-action coverage in complex navigation tasks.

Off-Policy Maximum Entropy Reinforcement Learning with Future State and Action Visitation Measures

This paper presents an innovative extension to the Maximum Entropy Reinforcement Learning (MaxEntRL) paradigm that integrates off-policy learning capabilities while offering a novel approach to intrinsic reward modeling. The fundamental proposition is the incorporation of a future state and action visitation measure that translates into an intrinsic reward, enhancing exploration efficiency in environments characterized by sparse or deceptive external reward signals.

Summary of Contributions

The authors introduce a MaxEntRL framework where each state-action pair is associated with a relative entropy-based intrinsic reward concerning the discounted distribution of future state-action pairs. This intrinsic reward is grounded on the conditional visitation distribution, effectively converging towards a fixed point of a contraction operator. The theoretical implications of this contraction property enable the adaptation of existing off-policy algorithms to optimize the intrinsic reward-driven exploration, ultimately yielding high-performing policies.

Key Theoretical Insights

1. Intrinsic Reward Functionality: The intrinsic reward for any state-action pair is defined by the relative entropy of the discounted visitation measure with respect to a predefined target distribution, allowing for flexible exploration strategies tailored to varying problem contexts.
2. Optimization via Contraction Mapping: The contraction mapping property of the intrinsic reward operator ensures the existence and uniqueness of a policy that optimizes the expected intrinsic rewards, scaling effectively across different state-action spaces.
3. Lower Bound on State-Action Value: The framework's design inherently enhances exploration by maximizing a lower bound on the conventional state-action value function, driving the policy towards more informative behaviors in environments with challenging reward structures.

Empirical Evaluation

The empirical part of the paper systematically demonstrates the efficacy of the proposed algorithm, termed Off-Policy Actor-Critic with Conditional Visitation Measures (OPAC+CV), against established baselines including Soft Actor-Critic (SAC) and Off-Policy Actor-Critic with Marginal Visitation Measures (OPAC+MV). The domains of evaluation include variations of grid-world tasks from the Minigrid suite, where challenges stem from sparse reward distributions and the necessity for complex navigation strategies.

• Exploration Efficiency: OPAC+CV achieves state-action space coverage that is competitive with or exceeds that of the compared algorithms. The intrinsic motivation model successfully drives the policy to explore diverse state-action paths, as evidenced by higher entropy in the visitation distributions in multiple configurations.
• Control Performance: When external reward optimization is invoked, OPAC+CV consistently finds policies with greater returns compared to SAC, particularly in larger and sparser scenarios where traditional algorithms struggle. This underscores the robustness of the framework in handling delayed or sparse feedback conditions effectively.

Implications and Future Directions

The introduction of future visitation measures in MaxEntRL opens several avenues for further research and potential applications:

1. Scalability and Generalization: While the paper indicates promising results in discrete, finite environments, extending this methodology to continuous state and action spaces remains a critical task, potentially leveraging advanced neural density estimation techniques.
2. Integration with Model-Based Approaches: Combining this framework with model-based RL could further leverage learned visitation distributions for forward planning and strategic decision-making, broadening its applicability in real-world complex systems.
3. Adaptive Feature Space Exploration: Adapting the feature space dynamically, perhaps incorporating learned representations that maximize expected return or reward-predictive features, could enhance the adaptability and efficiency of the exploration process across diverse tasks.

In conclusion, this paper provides a compelling advancement in the MaxEntRL landscape by enhancing intrinsic exploration capabilities through an off-policy, visitation measure-based approach. It sets a foundational basis for developing more robust RL algorithms that can adapt efficiently to complex environments where traditional exploration methods may falter.