Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction (1906.00949v2)

Abstract: Off-policy reinforcement learning aims to leverage experience collected from prior policies for sample-efficient learning. However, in practice, commonly used off-policy approximate dynamic programming methods based on Q-learning and actor-critic methods are highly sensitive to the data distribution, and can make only limited progress without collecting additional on-policy data. As a step towards more robust off-policy algorithms, we study the setting where the off-policy experience is fixed and there is no further interaction with the environment. We identify bootstrapping error as a key source of instability in current methods. Bootstrapping error is due to bootstrapping from actions that lie outside of the training data distribution, and it accumulates via the BeLLMan backup operator. We theoretically analyze bootstrapping error, and demonstrate how carefully constraining action selection in the backup can mitigate it. Based on our analysis, we propose a practical algorithm, bootstrapping error accumulation reduction (BEAR). We demonstrate that BEAR is able to learn robustly from different off-policy distributions, including random and suboptimal demonstrations, on a range of continuous control tasks.

• The paper identifies bootstrapping error as a key instability source in off-policy Q-learning from static datasets.
• It presents a theoretical framework with a distribution-constrained Bellman operator and introduces metrics like the suboptimality constant.
• The BEAR algorithm consistently outperforms TD3, BCQ, and other methods across varied dataset qualities, ensuring stable Q-values.

Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction

The paper "Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction" investigates the challenges of off-policy reinforcement learning (RL) when learning from static datasets, which are prevalent in real-world applications like autonomous driving and recommender systems. The authors attribute a primary source of instability in off-policy learning to bootstrapping error, resulting from out-of-distribution (OOD) actions in the BeLLMan backup.

Key Contributions

1. Identification of Bootstrapping Error: The core issue examined is how bootstrapping error arises in Q-learning when actions being considered during BeLLMan backups do not lie within the distribution of the training data. This error compounds over iterations, leading to unstable learning.
2. Theoretical Analysis: The paper provides a theoretical framework to analyze this bootstrapping error. The authors introduce a distribution-constrained BeLLMan operator. They define a suboptimality constant and a concentrability coefficient to quantify the deviation from the optimal policy and the distributional shift, respectively.
3. Bootstrapping Error Accumulation Reduction (BEAR) Algorithm: The practical outcome of the analysis is BEAR, an algorithm designed to mitigate bootstrapping error by constraining the learned policy to actions supported by the training data distribution. The algorithm employs Maximum Mean Discrepancy (MMD) to ensure this constraint is maintained effectively.

Experimental Results

The experiments demonstrate BEAR's robustness across various scenarios, including random, mediocre, and optimal off-policy datasets. BEAR consistently outperforms traditional off-policy RL algorithms like TD3 and other state-of-the-art methods such as BCQ. The results are highlighted in three critical settings:

• Medium-Quality Data: When the training dataset is generated from a partially trained policy, BEAR shows significant performance improvements over BCQ and TD3, highlighting its ability to handle imperfect but informative datasets effectively.
• Random Data: BEAR is capable of extracting valuable policies even from random data, where naive RL often fails due to a lack of meaningful action sequences.
• Optimal Data: BEAR matches near-optimal performance when the dataset is derived from an optimal policy, showcasing its flexibility in leveraging high-quality data without diverging.

Detailed Analysis and Insights

In-depth analysis reveals that BEAR maintains stable Q-values by effectively constraining action selection during the backup process. This leads to a significant reduction in bootstrapping error compared to other methods. The concentration on support matching, rather than full distribution matching, provides a less conservative but sufficiently safe policy improvement, avoiding the pitfalls encountered by algorithms strictly adhering to the behavior policy.

Implications and Future Directions

The practical implications of this research are profound for the deployment of RL in real-world settings where on-policy data collection is expensive or infeasible. The theoretical underpinnings provided for bootstrapping error reduction open avenues for further refinements and applications to larger-scale problems in operations research and robotics.

Future developments could enhance BEAR by integrating state distribution constraints directly, which could provide a more streamlined approach to error mitigation. Additionally, refining kernels and divergence measures could offer improved performance in high-dimensional action spaces, addressing one of the current limitations noted in the paper.

Conclusion

The research in "Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction" addresses a critical obstacle in off-policy RL with a theoretically solid and empirically validated approach. BEAR effectively balances the need to leverage existing datasets with the necessity to maintain stable and convergent learning. This paper marks a significant step towards making off-policy RL more robust and applicable in complex, real-world tasks.