Reward-Free Exploration for Reinforcement Learning (2002.02794v1)

Abstract: Exploration is widely regarded as one of the most challenging aspects of reinforcement learning (RL), with many naive approaches succumbing to exponential sample complexity. To isolate the challenges of exploration, we propose a new "reward-free RL" framework. In the exploration phase, the agent first collects trajectories from an MDP $\mathcal{M}$ without a pre-specified reward function. After exploration, it is tasked with computing near-optimal policies under for $\mathcal{M}$ for a collection of given reward functions. This framework is particularly suitable when there are many reward functions of interest, or when the reward function is shaped by an external agent to elicit desired behavior. We give an efficient algorithm that conducts $\tilde{\mathcal{O}}(S^2A\mathrm{poly}(H)/\epsilon^2)$ episodes of exploration and returns $\epsilon$-suboptimal policies for an arbitrary number of reward functions. We achieve this by finding exploratory policies that visit each "significant" state with probability proportional to its maximum visitation probability under any possible policy. Moreover, our planning procedure can be instantiated by any black-box approximate planner, such as value iteration or natural policy gradient. We also give a nearly-matching $\Omega(S^2AH^2/\epsilon^2)$ lower bound, demonstrating the near-optimality of our algorithm in this setting.

• The paper introduces a reward-free exploration framework that decouples data collection from reward-based planning, facilitating efficient policy computation for multiple reward functions.
• The proposed algorithm leverages black-box RL techniques to achieve near-optimal sample complexity of O(S²A·poly(H)/ε²) by ensuring significant states are adequately visited.
• The analysis provides a rigorous theoretical foundation, establishing a near-tight lower bound of Ω(S²AH²/ε²) that underscores the method's practical and theoretical significance.

Reward-Free Exploration for Reinforcement Learning: A Rigorous Analysis

The paper "Reward-Free Exploration for Reinforcement Learning" introduces a novel framework for addressing one of the most challenging problems in reinforcement learning (RL): effective exploration without relying on reward information during the data collection phase. The authors propose a reward-free RL paradigm wherein the agent initially gathers trajectories from a Markov Decision Process (MDP) without a predetermined reward function. Subsequently, the agent must compute near-optimal policies for a set of given reward functions in a separate planning phase. This approach is notably practical in scenarios with multiple reward functions of interest or when the reward function needs to be designed iteratively.

Key Contributions:

1. Reward-Free Exploration Framework: The framework separates the exploration and planning phases: the agent first explores without reward information and later optimizes policies for any number of reward functions. This setup is particularly beneficial for environments where the reward functions are either shaped interactively to achieve desired behaviors or are numerous.
2. Algorithm Development: The authors propose an efficient algorithm that, with $O(S^2A\mathrm{poly}(H)/\epsilon^2)$ episodes, conducts exploration and returns $\epsilon$-suboptimal policies for any given reward functions. The exploration strategy is straightforward, leveraging existing RL algorithms as black-box components. Importantly, the technique involves visiting every significant state with a probability proportional to its maximum visitation probability under any possible policy in the MDP.
3. Theoretical Results: A near-tight analysis of the sample complexity for reward-free exploration is provided. The paper establishes a lower bound of $\Omega(S^2AH^2/\epsilon^2)$, showing that the algorithmic sample complexity is close to optimal. This lower bound highlights that ensuring comprehensive coverage over the set of possible states incurs an additional factor of $S$ compared to standard RL tasks where a single reward function is provided upfront.
4. Technical Insights: The analysis introduces the concept of “significant states”—states that are meaningfully reachable under some optimal policy. The exploration phase is designed to ensure these significant states are visited adequately, thus enabling effective policy computation during the planning phase.
5. Modular Planning: The planning phase is modular, allowing researchers to use various black-box approximate planners such as value iteration or natural policy gradient. This adaptability facilitates the application of the proposed exploration strategy in different practical RL implementations.
6. Broader Implications: The separation of exploration from planning not only enhances sample efficiency across diverse reward functions but also provides foundational insights into the design of RL algorithms, especially for scenarios where sample efficiency is a stringent requirement.

Implications and Future Directions:

The implications of this work are both practical and theoretical. Practically, the reward-free RL approach is poised to significantly improve sample efficiency in multi-reward environments and iterative reward design settings. Theoretically, the findings enrich the understanding of exploration's role and requirements, particularly the complexity introduced by reward-free settings.

For future research, several promising avenues emerge:

• Generalizing the reward-free framework to settings with function approximation presents an interesting challenge, as does extending the analysis to continuous state spaces.
• Investigating reward-free exploration with partially observable MDPs (POMDPs) could yield insights relevant to real-world applications where states are not fully observable.
• Exploring the scalability of the approach, particularly in high-dimensional and complex environments, remains another frontier.

In conclusion, this paper makes substantial contributions to the field of reinforcement learning by efficiently addressing the exploration challenge in a reward-agnostic manner, enabling more versatile and practical applications of RL to complex, real-world problems.