Batch Policy Learning under Constraints (1903.08738v1)

Abstract: When learning policies for real-world domains, two important questions arise: (i) how to efficiently use pre-collected off-policy, non-optimal behavior data; and (ii) how to mediate among different competing objectives and constraints. We thus study the problem of batch policy learning under multiple constraints, and offer a systematic solution. We first propose a flexible meta-algorithm that admits any batch reinforcement learning and online learning procedure as subroutines. We then present a specific algorithmic instantiation and provide performance guarantees for the main objective and all constraints. To certify constraint satisfaction, we propose a new and simple method for off-policy policy evaluation (OPE) and derive PAC-style bounds. Our algorithm achieves strong empirical results in different domains, including in a challenging problem of simulated car driving subject to multiple constraints such as lane keeping and smooth driving. We also show experimentally that our OPE method outperforms other popular OPE techniques on a standalone basis, especially in a high-dimensional setting.

• The paper presents a meta-algorithm that integrates batch reinforcement learning with no-regret online learning to optimize policies under multiple constraints.
• It achieves improved sample complexity by reducing bounds from O(n^4) to O(n^2), ensuring near-optimal performance within safety limits.
• Empirical results in domains like autonomous driving and robotics demonstrate enhanced efficiency and safety over baseline approaches.

Overview of Batch Policy Learning under Constraints

The paper "Batch Policy Learning under Constraints" addresses a critical issue in reinforcement learning: the optimization of sequential decision-making policies when faced with multiple constraints, using pre-collected, off-policy, non-optimal behavior data. This work is particularly relevant in practical scenarios where exploring the environment actively, as in standard reinforcement learning approaches, might be costly or unsafe. This paper presents a systematic approach to batch policy learning in constrained settings, introducing both a theoretical framework and an empirical validation.

Main Contribution

The primary contribution of this work is the formulation of a meta-algorithm that operates by integrating any batch reinforcement learning and online learning procedure as subroutines for policy optimization in constrained environments. The constraints considered in this formulation are general, with a penalty term incorporated into the learning objective to handle multiple objectives and trade-offs efficiently.

Key Algorithmic Strategy

1. Meta-algorithm: This is based on standard techniques in constrained optimization, mainly utilizing a Lagrangian approach to transform constrained optimization problems into a series of constrained forms. It employs a no-regret online learning algorithm for dual variables (Lagrangian multipliers) and a batch policy optimization technique for primal variables (policies).
2. Algorithm Instantiation: The authors instantiate their framework with Fitted Q Iteration (FQI) for policy learning and Fitted Q Evaluation (FQE) for off-policy policy evaluation (OPE). This combination allows for handling nonlinear function approximators under finite-sample conditions, making it adaptable to high-dimensional, complex environments.

Theoretical Guarantees

The paper provides strong theoretical guarantees for the proposed algorithms. Notably, they achieve a sample complexity bound of $O(n^2)$, indicating improved convergence rates compared to prior work offering $O(n^4)$ bounds. This is significant for practical applications, where sample efficiency is paramount due to the high cost of data collection.

In particular:

• Theoretical analysis demonstrates that the proposed method guarantees near-optimal policy performance while adhering to constraints when the assumptions of the inherent BeLLMan error are met.
• The authors leverage upper bounds on concentration coefficients, illustrating efficient mapping from behavior policies to the unknown target policy.

Empirical Results

The efficacy of the proposed method is validated through simulation results in challenging environments:

1. Frozen Lake Domain: This experiment demonstrates safe policy learning by ensuring agents avoid catastrophic failures with high probability, achieving better trade-offs between goal completion and safety constraints than baseline approaches.
2. Car Racing Domain: A higher-dimensional test case where the algorithm needed to balance fast driving with smoothness and lane-keeping constraints. Here, the method not only significantly improves performance with respect to baseline policies but also suggests practical applicability in automotive or robotic control scenarios.
3. OPE Evaluation: In high-dimensional settings, the FQE method developed in this paper shows superiority over common off-policy evaluation techniques like importance sampling and doubly robust methods, especially in terms of bias-variance trade-offs.

Implications and Future Directions

The implications of this work extend beyond theoretical reinforcement learning; practical applications in domains such as autonomous driving, robotics, and financial decision-making are evident. As constraint satisfaction becomes increasingly relevant in real-world applications, the proposed approach provides a method that is theoretically sound and empirically validated.

The challenge of verifying the satisfaction of constraints from off-policy data, particularly in high-dimensional settings, is addressed through innovative evaluation techniques, yet this remains an area ripe for further exploration. Future developments could explore extending these methods to incorporate online learning capacities or adaptive learning of constraints, thus enhancing the adaptability and robustness of the policy learning framework.

Overall, by facilitating safe and efficient learning in environments where data is pre-collected and exploration might be dangerous or expensive, this paper sets a cornerstone for future research in batch reinforcement learning under constraints.