Reusing Historical Trajectories in Natural Policy Gradient via Importance Sampling: Convergence and Convergence Rate

Belangrijkste concepten

The author explores the convergence and convergence rate of a natural policy gradient method with reusing historical trajectories via importance sampling, showing that it improves the convergence rate by an order of O(1/K).

Samenvatting

The content discusses the application of importance sampling in policy optimization algorithms, focusing on accelerating learning through historical trajectory reuse. Theoretical analysis and empirical studies demonstrate improved convergence rates.
The reinforcement learning framework is explored, emphasizing the significance of efficient data utilization for policy optimization. The proposed algorithm, RNPG, leverages historical trajectories to enhance convergence rates.
Importance sampling techniques are highlighted for off-policy evaluation and policy optimization in reinforcement learning. The study provides insights into bias reduction and variance improvement through reusing past trajectories.
Natural policy gradient methods are discussed for stable updates and smoother learning dynamics in policy optimization algorithms. Theoretical results are supported by empirical demonstrations on classical benchmarks.

Statistieken

Σ2(θ) = Σ′2(θ) - Σ1(θ)
limn→∞ αn = 0
limn→∞ θn = ¯θ w.p.1
|R(s, a)| ≤ Ur (Absolute value of reward bounded)
∇η(¯θ) = 0 (Optimal solution at limit point)
E[ c∇η(θ)] = 0 (Unbiased estimator assumption)
ω(ξi m, θn|θm) = dπθn (ξm)/dπθm (ξm)
FIM estimator bF(θn) = ϵId + 1/B ∑ PB i=1 S(ξi n, θn)

Citaten

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Reusing Historical Trajectories in Natural Policy Gradient via Importance Sampling

by Yifan Lin,Yu... om arxiv.org 03-04-2024

https://arxiv.org/pdf/2403.00675.pdf

Diepere vragen

How does the bias introduced by reusing historical trajectories impact the overall performance of the algorithm

The bias introduced by reusing historical trajectories in the algorithm can have a significant impact on its overall performance. This bias arises from the dependence between iterations when utilizing past data to estimate the gradient and Fisher information matrix. As shown in the study, this bias can affect the accuracy of these estimators, leading to deviations from the true values. In turn, this can influence the convergence properties of the algorithm and potentially slow down or hinder its ability to reach optimal solutions efficiently.

What are the practical implications of approximating likelihood ratios to improve computational efficiency

Approximating likelihood ratios is a practical strategy that can enhance computational efficiency in algorithms like RNPG. By replacing exact likelihood ratios with approximations based on current policy parameters, researchers can simplify calculations and reduce computational complexity. This approximation helps streamline the estimation process for key components such as gradients and FIMs, making it more feasible to implement complex reinforcement learning algorithms in real-world applications where computational resources may be limited.

How can the findings from this study be applied to real-world scenarios beyond classical benchmarks

The findings from this study hold valuable insights that extend beyond classical benchmarks into real-world scenarios involving reinforcement learning applications. By understanding how reusing historical trajectories impacts convergence rates and biases in natural policy gradient algorithms, practitioners can optimize their approaches for various domains such as robotics, healthcare systems optimization, autonomous driving technologies, and more. Implementing strategies like importance sampling with an awareness of biases introduced by historical trajectory reuse could lead to improved performance and faster convergence in practical reinforcement learning settings.