Structure Matters: Dynamic Policy Gradient
This addresses convergence issues in reinforcement learning for researchers, offering a novel method that improves theoretical guarantees but is incremental in combining existing techniques.
The paper tackles the problem of policy gradient methods in infinite-horizon tabular MDPs by introducing the dynamic policy gradient (DynPG) framework, which integrates dynamic programming to decompose the MDP into contextual bandit problems and achieves a polynomial convergence rate in the effective horizon, contrasting with exponential lower bounds for vanilla methods.
In this work, we study $γ$-discounted infinite-horizon tabular Markov decision processes (MDPs) and introduce a framework called dynamic policy gradient (DynPG). The framework directly integrates dynamic programming with (any) policy gradient method, explicitly leveraging the Markovian property of the environment. DynPG dynamically adjusts the problem horizon during training, decomposing the original infinite-horizon MDP into a sequence of contextual bandit problems. By iteratively solving these contextual bandits, DynPG converges to the stationary optimal policy of the infinite-horizon MDP. To demonstrate the power of DynPG, we establish its non-asymptotic global convergence rate under the tabular softmax parametrization, focusing on the dependencies on salient but essential parameters of the MDP. By combining classical arguments from dynamic programming with more recent convergence arguments of policy gradient schemes, we prove that softmax DynPG scales polynomially in the effective horizon $(1-γ)^{-1}$. Our findings contrast recent exponential lower bound examples for vanilla policy gradient.