Linear Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximation

• URL: http://arxiv.org/abs/2106.04096v4
• Date: Thu, 8 Feb 2024 11:02:15 GMT
• Title: Linear Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximation
• Authors: Semih Cayci, Niao He, R. Srikant
• Abstract summary: We establish finite-time convergence analyses of entropy-regularized NPG with linear function approximation. We prove that entropy-regularized NPG exhibits emphlinear convergence up to a function approximation error.
• Score: 30.02577720946978
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Natural policy gradient (NPG) methods with entropy regularization achieve impressive empirical success in reinforcement learning problems with large state-action spaces. However, their convergence properties and the impact of entropy regularization remain elusive in the function approximation regime. In this paper, we establish finite-time convergence analyses of entropy-regularized NPG with linear function approximation under softmax parameterization. In particular, we prove that entropy-regularized NPG with averaging satisfies the \emph{persistence of excitation} condition, and achieves a fast convergence rate of $\tilde{O}(1/T)$ up to a function approximation error in regularized Markov decision processes. This convergence result does not require any a priori assumptions on the policies. Furthermore, under mild regularity conditions on the concentrability coefficient and basis vectors, we prove that entropy-regularized NPG exhibits \emph{linear convergence} up to a function approximation error.

Related papers

• Deterministic Policy Gradient Primal-Dual Methods for Continuous-Space Constrained MDPs [82.34567890576423]
  We develop a deterministic policy gradient primal-dual method to find an optimal deterministic policy with non-asymptotic convergence. We prove that the primal-dual iterates of D-PGPD converge at a sub-linear rate to an optimal regularized primal-dual pair. To the best of our knowledge, this appears to be the first work that proposes a deterministic policy search method for continuous-space constrained MDPs.
  arXiv  Detail & Related papers  (2024-08-19T14:11:04Z)
• Entropy annealing for policy mirror descent in continuous time and space [2.8255028200738455]
  We analyze a continuous-time policy mirror descent dynamics, which updates the policy based on the gradient of an entropy-regularized value function. We prove that with a fixed entropy level, the dynamics converges exponentially to the optimal solution of the regularized problem.
  arXiv  Detail & Related papers  (2024-05-30T17:02:18Z)
• Geometry and convergence of natural policy gradient methods [0.0]
  We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that the trajectories in state-action space are solutions of gradient flows with respect to Hessian geometries.
  arXiv  Detail & Related papers  (2022-11-03T19:16:15Z)
• Linear Convergence of Natural Policy Gradient Methods with Log-Linear Policies [115.86431674214282]
  We consider infinite-horizon discounted Markov decision processes and study the convergence rates of the natural policy gradient (NPG) and the Q-NPG methods with the log-linear policy class. We show that both methods attain linear convergence rates and $mathcalO (1/epsilon2)$ sample complexities using a simple, non-adaptive geometrically increasing step size.
  arXiv  Detail & Related papers  (2022-10-04T06:17:52Z)
• Convergence and sample complexity of natural policy gradient primal-dual methods for constrained MDPs [21.347689976296834]
  We employ the natural policy gradient method to solve the discounted optimal optimal rate problem. We also provide convergence and finite-sample guarantees for two sample-based NPG-PD algorithms.
  arXiv  Detail & Related papers  (2022-06-06T04:28:04Z)
• Nonconvex Stochastic Scaled-Gradient Descent and Generalized Eigenvector Problems [98.34292831923335]
  Motivated by the problem of online correlation analysis, we propose the emphStochastic Scaled-Gradient Descent (SSD) algorithm. We bring these ideas together in an application to online correlation analysis, deriving for the first time an optimal one-time-scale algorithm with an explicit rate of local convergence to normality.
  arXiv  Detail & Related papers  (2021-12-29T18:46:52Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Beyond Exact Gradients: Convergence of Stochastic Soft-Max Policy Gradient Methods with Entropy Regularization [20.651913793555163]
  We revisit the classical entropy regularized policy gradient methods with the soft-max policy parametrization. We establish a global optimality convergence result and a sample complexity of $widetildemathcalO(frac1epsilon2)$ for the proposed algorithm.
  arXiv  Detail & Related papers  (2021-10-19T17:21:09Z)
• On the Convergence of Stochastic Extragradient for Bilinear Games with Restarted Iteration Averaging [96.13485146617322]
  We present an analysis of the ExtraGradient (SEG) method with constant step size, and present variations of the method that yield favorable convergence. We prove that when augmented with averaging, SEG provably converges to the Nash equilibrium, and such a rate is provably accelerated by incorporating a scheduled restarting procedure.
  arXiv  Detail & Related papers  (2021-06-30T17:51:36Z)
• SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives [86.01677297601624]
  We propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior.
  arXiv  Detail & Related papers  (2020-03-05T14:33:20Z)
• Convergence and sample complexity of gradient methods for the model-free linear quadratic regulator problem [27.09339991866556]
  We show that ODE searches for optimal control for an unknown computation system by directly searching over the corresponding space of controllers. We take a step towards demystifying the performance and efficiency of such methods by focusing on the gradient-flow dynamics set of stabilizing feedback gains and a similar result holds for the forward disctization of the ODE.
  arXiv  Detail & Related papers  (2019-12-26T16:56:59Z)

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.