On the Global Convergence Rates of Softmax Policy Gradient Methods

• URL: http://arxiv.org/abs/2005.06392v3
• Date: Thu, 2 Jun 2022 06:16:17 GMT
• Title: On the Global Convergence Rates of Softmax Policy Gradient Methods
• Authors: Jincheng Mei, Chenjun Xiao, Csaba Szepesvari, Dale Schuurmans
• Abstract summary: We show that with the true gradient, policy gradient with a softmax parametrization converges at a $O(e-c cdot t)$ rate. Second, we analyze entropy regularized policy gradient and show that it enjoys a significantly faster linear convergence rate. Third, we explain how entropy regularization improves policy optimization, even with the true gradient.
• Score: 45.1868906130788
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We make three contributions toward better understanding policy gradient methods in the tabular setting. First, we show that with the true gradient, policy gradient with a softmax parametrization converges at a $O(1/t)$ rate, with constants depending on the problem and initialization. This result significantly expands the recent asymptotic convergence results. The analysis relies on two findings: that the softmax policy gradient satisfies a \L{}ojasiewicz inequality, and the minimum probability of an optimal action during optimization can be bounded in terms of its initial value. Second, we analyze entropy regularized policy gradient and show that it enjoys a significantly faster linear convergence rate $O(e^{-c \cdot t})$ toward softmax optimal policy $(c > 0)$. This result resolves an open question in the recent literature. Finally, combining the above two results and additional new $\Omega(1/t)$ lower bound results, we explain how entropy regularization improves policy optimization, even with the true gradient, from the perspective of convergence rate. The separation of rates is further explained using the notion of non-uniform \L{}ojasiewicz degree. These results provide a theoretical understanding of the impact of entropy and corroborate existing empirical studies.

Related papers

• Methods for Convex $(L_0,L_1)$-Smooth Optimization: Clipping, Acceleration, and Adaptivity [50.25258834153574]
  We focus on the class of (strongly) convex $(L0)$-smooth functions and derive new convergence guarantees for several existing methods. In particular, we derive improved convergence rates for Gradient Descent with smoothnessed Gradient Clipping and for Gradient Descent with Polyak Stepsizes.
  arXiv  Detail & Related papers  (2024-09-23T13:11:37Z)
• Differential Private Stochastic Optimization with Heavy-tailed Data: Towards Optimal Rates [15.27596975662702]
  We explore algorithms achieving optimal rates of DP optimization with heavy-tailed gradients. Our results match the minimax lower bound in citekamath2022, indicating that the theoretical limit of convex optimization under DP is achievable.
  arXiv  Detail & Related papers  (2024-08-19T11:07:05Z)
• Provable Policy Gradient Methods for Average-Reward Markov Potential Games [15.136494705127564]
  We study Markov potential games under the infinite horizon average reward criterion. We prove that both algorithms based on independent policy gradient and independent natural policy gradient converge globally to a Nash equilibrium for the average reward criterion.
  arXiv  Detail & Related papers  (2024-03-09T00:20:33Z)
• The Role of Baselines in Policy Gradient Optimization [83.42050606055822]
  We show that the emphstate value baseline allows on-policy. emphnatural policy gradient (NPG) to converge to a globally optimal. policy at an $O (1/t) rate gradient. We find that the primary effect of the value baseline is to textbfreduce the aggressiveness of the updates rather than their variance.
  arXiv  Detail & Related papers  (2023-01-16T06:28:00Z)
• Min-Max Optimization Made Simple: Approximating the Proximal Point Method via Contraction Maps [77.8999425439444]
  We present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems. Our work is based on the fact that the update rule of the Proximal Point method can be approximated up to accuracy.
  arXiv  Detail & Related papers  (2023-01-10T12:18:47Z)
• Homotopic Policy Mirror Descent: Policy Convergence, Implicit Regularization, and Improved Sample Complexity [40.2022466644885]
  homotopic policy mirror descent (HPMD) method for solving discounted, infinite horizon MDPs with finite state and action space. We report three properties that seem to be new in the literature of policy gradient methods.
  arXiv  Detail & Related papers  (2022-01-24T04:54:58Z)
• A Two-Time-Scale Stochastic Optimization Framework with Applications in Control and Reinforcement Learning [13.908826484332282]
  We study a new two-time-scale gradient method for solving optimization problems. Our first contribution is to characterize the finite-time complexity of the proposed two-time-scale gradient algorithm. We apply our framework to gradient-based policy evaluation algorithms in reinforcement learning.
  arXiv  Detail & Related papers  (2021-09-29T23:15:23Z)
• Softmax Policy Gradient Methods Can Take Exponential Time to Converge [60.98700344526674]
  The softmax policy gradient (PG) method is arguably one of the de facto implementations of policy optimization in modern reinforcement learning. We demonstrate that softmax PG methods can take exponential time -- in terms of $mathcalS|$ and $frac11-gamma$ -- to converge.
  arXiv  Detail & Related papers  (2021-02-22T18:56:26Z)
• On the Convergence and Sample Efficiency of Variance-Reduced Policy Gradient Method [38.34416337932712]
  Policy gives rise to a rich class of reinforcement learning (RL) methods, for example the REINFORCE. Yet the best known sample complexity result for such methods to find an $epsilon$-optimal policy is $mathcalO(epsilon-3)$, which is suboptimal. We study the fundamental convergence properties and sample efficiency of first-order policy optimization method.
  arXiv  Detail & Related papers  (2021-02-17T07:06:19Z)
• Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets [71.05306664267832]
  Adaptive algorithms perform gradient updates using the history of gradients and are ubiquitous in training deep neural networks. In this paper we analyze a variant of OptimisticOA algorithm for nonconcave minmax problems. Our experiments show that adaptive GAN non-adaptive gradient algorithms can be observed empirically.
  arXiv  Detail & Related papers  (2019-12-26T22:10:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.