Provably Efficient Exploration in Policy Optimization for Markov Decision Processes with Linear Function Approximation and Adversarial Rewards

Core Concepts

The paper proposes an Optimistic variant of the Proximal Policy Optimization (OPPO) algorithm that incorporates exploration in a principled manner, and proves that it achieves a √d²H³T-regret in episodic Markov decision processes with linear function approximation and adversarial rewards.

Abstract

The paper addresses the challenge of designing a provably efficient policy optimization algorithm that incorporates exploration, which remains elusive compared to the theoretical understanding of value-based reinforcement learning. Key highlights: The paper proposes the Optimistic Proximal Policy Optimization (OPPO) algorithm, which follows an "optimistic version" of the policy gradient direction. OPPO solves a KL-regularized policy optimization subproblem at each update, where the linear component of the objective is defined using an estimated action-value function augmented with an exploration bonus. The exploration bonus quantifies the uncertainty in estimating the action-value function based on finite historical data, ensuring conservative optimism in the face of uncertainty and adversary. The paper proves that OPPO achieves a √d²H³T-regret (up to logarithmic factors) in episodic Markov decision processes with linear function approximation and adversarial rewards, without requiring access to a simulator or finite concentrability coefficients. This is the first provably sample-efficient policy optimization algorithm that incorporates exploration, complementing the existing computational efficiency guarantees of policy optimization algorithms.

Stats

The paper does not provide specific numerical metrics or figures to support the key claims. The analysis is focused on establishing theoretical regret bounds.

Quotes

None.

Key Insights Distilled From

Provably Efficient Exploration in Policy Optimization

by Qi Cai,Zhuor... at arxiv.org 04-02-2024

https://arxiv.org/pdf/1912.05830.pdf

Deeper Inquiries

How can the exploration bonus in OPPO be extended to handle more general function approximation settings beyond linear MDPs

In OPPO, the exploration bonus is explicitly incorporated into the action-value function to encourage exploration. This bonus function quantifies the uncertainty that arises from observing only finite historical data, leading to a conservative optimism in the policy updates. To extend this exploration bonus to more general function approximation settings beyond linear MDPs, one approach could be to adapt the bonus function to account for the specific characteristics of the function approximators used. For example, in settings with non-linear function approximators like neural networks, the bonus function could be designed to capture the uncertainty in the network's predictions or gradients. By incorporating this uncertainty into the action-value function, the algorithm can maintain a balance between exploration and exploitation in a more complex function approximation setting.

Can the conservative optimism principle in OPPO be applied to other policy optimization algorithms beyond proximal policy optimization

The conservative optimism principle in OPPO, which ensures that the updated policy remains optimistic in the face of uncertainty, can be applied to other policy optimization algorithms beyond proximal policy optimization. By incorporating a bonus function that quantifies uncertainty and encourages exploration, other algorithms can also benefit from the sample-efficient and robust properties of conservative optimism. For example, algorithms like Trust Region Policy Optimization (TRPO) or Natural Policy Gradient (NPG) could be modified to include a similar exploration bonus, leading to improved performance in challenging environments with unknown dynamics or adversarial rewards.

What are the potential connections between the optimistic exploration in OPPO and the intrinsic motivation or curiosity-driven exploration studied in the reinforcement learning literature

The optimistic exploration in OPPO aligns with the concept of intrinsic motivation or curiosity-driven exploration in the reinforcement learning literature. Both approaches emphasize the importance of exploring the environment to discover new information and improve learning performance. The exploration bonus in OPPO encourages the agent to take actions that lead to higher uncertainty or novelty, similar to how intrinsic motivation drives agents to seek out new experiences or states. By incorporating the principles of optimistic exploration into the design of reinforcement learning algorithms, researchers can enhance the agent's ability to learn efficiently and adapt to complex environments.