Provably Efficient Maximum Entropy Exploration (1812.02690v2)

Abstract: Suppose an agent is in a (possibly unknown) Markov Decision Process in the absence of a reward signal, what might we hope that an agent can efficiently learn to do? This work studies a broad class of objectives that are defined solely as functions of the state-visitation frequencies that are induced by how the agent behaves. For example, one natural, intrinsically defined, objective problem is for the agent to learn a policy which induces a distribution over state space that is as uniform as possible, which can be measured in an entropic sense. We provide an efficient algorithm to optimize such such intrinsically defined objectives, when given access to a black box planning oracle (which is robust to function approximation). Furthermore, when restricted to the tabular setting where we have sample based access to the MDP, our proposed algorithm is provably efficient, both in terms of its sample and computational complexities. Key to our algorithmic methodology is utilizing the conditional gradient method (a.k.a. the Frank-Wolfe algorithm) which utilizes an approximate MDP solver.

• The paper introduces a novel algorithm leveraging the Frank-Wolfe method to maximize state entropy for effective exploration in MDPs.
• The paper establishes rigorous sample and computational efficiency bounds in tabular environments, confirming theoretical effectiveness.
• The paper validates its approach with experiments in environments like MountainCar, demonstrating improved uniform state visitation.

An Overview of "Provably Efficient Maximum Entropy Exploration"

The paper "Provably Efficient Maximum Entropy Exploration" tackles a critical problem in reinforcement learning (RL)—exploring state spaces in a Markov Decision Process (MDP) without explicit reward signals. The authors, Elad Hazan, Sham M. Kakade, Karan Singh, and Abby Van Soest, present a method to efficiently explore an MDP by optimizing a concave objective function over the state-visitation frequencies. The work is characterized by its focus on algorithms that seek to maximize the entropy of the state distribution, leading to an exploration strategy that aims for uniform state coverage.

Core Contributions

The paper proposes a novel approach for maximum entropy exploration using the Frank-Wolfe algorithm (conditional gradient method). Key contributions include:

1. Algorithm Development: The paper introduces an efficient algorithm for maximizing entropy in MDPs using an approximate planning oracle that is robust to function approximation. The approach utilizes a sequence of reward signals that directs the agent towards a maximum entropy state distribution.
2. Theoretical Guarantees: The authors provide rigorous proofs of the algorithm’s sample and computational efficiency in the tabular case, demonstrating provable efficiency both in learning and exploration.
3. Oracle-based Framework: The use of two primary oracles—an approximate planning oracle and a state distribution estimation oracle—underpins the proposed methodology. These oracles serve to guide the agent efficiently in environments with unknown dynamics.
4. Smoothness Constraints and Approximation Guarantees: The smoothness of the objective function is addressed, allowing the authors to derive theoretical bounds on the performance of their algorithm relative to the maximum achievable entropy.

Numerical and Empirical Validation

The paper supports its theoretical findings with proof-of-concept experiments in established RL environments such as MountainCar, Pendulum, and Ant. The MaxEnt agent's exploration strategy is shown to effectively increase the visitation entropy over time, thus validating the approach's ability to sample diverse states uniformly. The experiments make use of different types of neural network-based planning oracles, showcasing the adaptability of the method to different function approximations.

Implications and Future Directions

This work has significant implications for RL, especially in settings where external rewards are sparse or entirely absent. Maximizing state distribution entropy as an objective not only aids in thorough environment exploration but also lays groundwork for intrinsic motivation strategies. By successfully proving the efficiency of their approach, the authors contribute a substantial tool for tasks demanding high exploration efficiency, such as autonomous exploration and unsupervised skill discovery.

In terms of future research directions, the challenge of scaling these methods to environments with continuous or exceedingly large state spaces remains. The promising results in tabular settings call for extensions and adaptations to function approximation techniques that can further scale this approach. Additionally, research into integrating maximum entropy exploration with multi-task learning or transfer learning paradigms could unlock broader applications.

In summary, this paper offers a robust exploration strategy in the absence of reward signals by formulating the problem as one of maximizing the entropy of state distributive frequencies. Its contributions are both theoretical and practical, providing clear pathways for advancing exploration techniques in reinforcement learning.