Core Concepts

The paper proposes a Gauss-Newton Temporal Difference (GNTD) learning method to solve the Q-learning problem with nonlinear function approximation. GNTD takes one Gauss-Newton step to optimize a variant of Mean-Squared Bellman Error, achieving improved sample complexity compared to existing temporal difference methods.

Abstract

The paper proposes the Gauss-Newton Temporal Difference (GNTD) learning algorithm to solve the Q-learning problem with nonlinear function approximation. The key highlights are:
GNTD takes one Gauss-Newton step to optimize a variant of Mean-Squared Bellman Error, where target networks are adopted to avoid double sampling.
GNTD achieves improved finite-sample convergence guarantees compared to existing temporal difference methods. For neural network parameterization with ReLU activation, GNTD achieves an improved sample complexity of Õ(ε^-1), as opposed to the O(ε^-2) sample complexity of existing neural TD methods.
An Õ(ε^-1.5) sample complexity of GNTD is also established for general smooth function approximations.
The paper designs an efficient implementation of GNTD using the Kronecker-factored Approximate Curvature (K-FAC) method, which demonstrates exceptional numerical performance across both continuous and discrete RL tasks, as well as offline and online settings.

Stats

The sample complexity of GNTD for neural network approximation is Õ(ε^-1), improving upon the O(ε^-2) sample complexity of existing neural TD methods.
The sample complexity of GNTD for general smooth function approximation is Õ(ε^-1.5).

Quotes

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Key Insights Distilled From

by Zhifa Ke,Jun... at **arxiv.org** 04-02-2024

Deeper Inquiries

The GNTD framework can be extended to other reinforcement learning settings beyond policy evaluation by incorporating it into actor-critic algorithms or off-policy learning methods. In actor-critic algorithms, the GNTD approach can be used to update the critic network, which estimates the value function, while the actor network determines the policy. By applying the GNTD updates to the critic network, the algorithm can learn more efficiently and effectively. Additionally, in off-policy learning, GNTD can be used to update the Q-values based on experiences collected from a different policy, allowing for more stable and robust learning.

One potential limitation of the GNTD approach compared to other RL algorithms is the computational complexity of the Gauss-Newton step, especially in large-scale problems with complex neural network architectures. This can lead to increased training times and resource requirements. To address this limitation, techniques such as parallelization, distributed computing, or optimization strategies specific to neural networks can be employed to improve the efficiency of the GNTD algorithm. Additionally, regularization methods can be used to prevent overfitting and improve generalization performance.

The improved sample complexity results of GNTD have significant implications for the broader field of reinforcement learning and function approximation. By achieving better sample complexity, GNTD can lead to faster and more efficient learning in RL tasks, reducing the amount of data required to converge to optimal solutions. This can have practical benefits in real-world applications where data collection may be costly or time-consuming. The improved sample complexity also opens up opportunities for applying GNTD in more challenging and complex environments, where data efficiency is crucial for successful learning.

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