Conformal Q-Learning

What is Conformal Q-Learning?

Conformal Q-Learning is a novel approach that combines conformal prediction with actor-critic methods to provide finite-sample uncertainty guarantees for Q-value estimates in offline reinforcement learning. It constructs prediction intervals around learned Q-values to ensure that true values lie within these intervals with high probability, using interval width as a regularizer to mitigate overestimation and stabilize policy learning.

Key Components

1. Conformal Prediction Integration

Conformal prediction is used to generate uncertainty estimates for Q-values. This is crucial in offline RL to avoid overconfident estimates for out-of-distribution actions. The algorithm maintains a calibration set and periodically updates conformal intervals to ensure reliable uncertainty quantification.

2. Actor-Critic Framework

Conformal Q-Learning builds upon the actor-critic architecture, where a critic (Q-function) estimates action-values and an actor (policy) selects actions. The conformal intervals are incorporated into both the critic updates and policy improvement steps.

3. Offline Learning Mechanism

The algorithm is designed to learn from static datasets without interacting with the environment during training. It uses techniques like conformal regularization to mitigate the challenges of offline RL, such as extrapolation error and distributional shift.

How Conformal Q-Learning Works

1. Initialization

The algorithm initializes a Q-network, policy network, and a calibration dataset. It also sets up learning rates and thresholds for conformal prediction.

2. Training Loop

During training, Conformal Q-Learning:

• Samples batches from the offline dataset
• Calibrates conformal intervals using the calibration set
• Updates the Q-network (critic) using the Bellman equation and conformal regularization
• Updates the policy network (actor) incorporating the conformal intervals

3. Conformal Interval Calibration

The algorithm computes nonconformity scores and determines the conformal threshold (q_α) based on the calibration dataset. This threshold is used to construct prediction intervals for Q-values.

Theoretical Guarantees

Conformal Coverage

Conformal Q-Learning provides a theoretical guarantee on the coverage of its prediction intervals. With high probability, the true Q-values lie within the constructed intervals, ensuring reliable uncertainty quantification.

Group-Conditional Coverage

The algorithm extends to group-conditional coverage, allowing for more fine-grained uncertainty estimates across different subsets of the state-action space.

Comparison with CQL

Theoretical analysis shows that Conformal Q-Learning is more optimistic than Conservative Q-Learning (CQL) while still maintaining conservative bounds, potentially leading to improved performance in practice.

Experimental Results

Experiments on standard RL benchmarks, including CartPole-v1, demonstrate that Conformal Q-Learning:

• Improves policy stability and reduces uncertainty over training
• Enhances robustness against out-of-distribution (OOD) actions
• Achieves comparable or better performance than baseline methods like DQN and CQL

Conclusion

Conformal Q-Learning represents a significant advancement in offline reinforcement learning by providing theoretically grounded uncertainty estimates. By integrating conformal prediction into the actor-critic framework, it addresses key challenges in offline RL, such as extrapolation error and policy stability. The method's success in both theoretical analysis and empirical evaluations makes it a promising approach for reliable offline RL in safety-critical and resource-constrained environments.