Convergence and Optimality of Policy Gradient Methods in Weakly Smooth Settings
Authors: Matthew S. Zhang, Murat A Erdogdu, Animesh Garg9066-9073
AAAI 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work, we establish explicit convergence rates of policy gradient methods, extending the convergence regime to weakly smooth policy classes with L2 integrable gradient. We provide intuitive examples to illustrate the insight behind these new conditions. Notably, our analysis also shows that convergence rates are achievable for both the standard policy gradient and the natural policy gradient algorithms under these assumptions. Lastly we provide performance guarantees for the converged policies. |
| Researcher Affiliation | Academia | Matthew S. Zhang1,3, Murat A. Erdogdu1,2,3, Animesh Garg1,3 1 Department of Computer Science at the University of Toronto, 2 Department of Statistical Sciences at the University of Toronto, 3 Vector Institute for Artificial Intelligence |
| Pseudocode | Yes | Algorithm 1: Policy Gradient for H older Smooth Objectives and Algorithm 2: Natural Policy Gradient for H older Smooth Objectives |
| Open Source Code | No | The paper mentions related works and their algorithms but does not include any statement about releasing its own source code or provide a link to a code repository for the methodology described. |
| Open Datasets | No | The paper mentions the 'Mountain Car environment' as an example and describes a 'single-state exploration problem' with a defined reward function for illustrative purposes. It does not refer to or provide access information for any standard public datasets used for training. |
| Dataset Splits | No | The paper is theoretical in nature and does not describe empirical experiments that would involve dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper does not provide any specific details regarding the hardware used for computations or experiments, such as CPU/GPU models, memory, or cloud instances. |
| Software Dependencies | No | The paper does not specify any software dependencies or their version numbers required to replicate the work. |
| Experiment Setup | Yes | We note two prominant applications of our assumptions: ... Example 1. (Generalized Gaussian Policy) If we choose the parameter κ (1, 2], we can choose the generalized Gaussian distribution to parameterize our policy: ... Figure 1: (a) Tail Growth: ... α = 0.1, for the [0, 0] state in the Mountain Car environment. ... (b) Exploration Performance: Comparing the performance of Generalized Gaussian and the standard Gaussian policy, with α = 0.7, for the reward function found in Equation (10), |θ θ| = 3.3. ... Learning Rates In the sequel, we consider the following learning rates: (i) constant ht = λ, (ii) dependent on the total number of steps β0 1 β0+1 , (iii) decaying ht = λt q, q [0, 1). and B σ2 (1 γ)2 and λβ0 1 γ C |