Policy Mirror Descent with Lookahead

• URL: http://arxiv.org/abs/2403.14156v3
• Date: Wed, 06 Nov 2024 14:29:05 GMT
• Title: Policy Mirror Descent with Lookahead
• Authors: Kimon Protopapas, Anas Barakat,
• Abstract summary: Policy Mirror Descent (PMD) can be seen as a soft Policy It algorithm implementing regularized 1-step greedy policy improvement. We propose a new class of PMD algorithms called $h$-PMD which incorporates multi-step greedy policy improvement. We show that $h$-PMD enjoys a faster dimension-free $gammah$-linear convergence rate, contingent on the computation of multi-step greedy policies.
• Score: 0.46040036610482665
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Policy Mirror Descent (PMD) stands as a versatile algorithmic framework encompassing several seminal policy gradient algorithms such as natural policy gradient, with connections with state-of-the-art reinforcement learning (RL) algorithms such as TRPO and PPO. PMD can be seen as a soft Policy Iteration algorithm implementing regularized 1-step greedy policy improvement. However, 1-step greedy policies might not be the best choice and recent remarkable empirical successes in RL such as AlphaGo and AlphaZero have demonstrated that greedy approaches with respect to multiple steps outperform their 1-step counterpart. In this work, we propose a new class of PMD algorithms called $h$-PMD which incorporates multi-step greedy policy improvement with lookahead depth $h$ to the PMD update rule. To solve discounted infinite horizon Markov Decision Processes with discount factor $\gamma$, we show that $h$-PMD which generalizes the standard PMD enjoys a faster dimension-free $\gamma^h$-linear convergence rate, contingent on the computation of multi-step greedy policies. We propose an inexact version of $h$-PMD where lookahead action values are estimated. Under a generative model, we establish a sample complexity for $h$-PMD which improves over prior work. Finally, we extend our result to linear function approximation to scale to large state spaces. Under suitable assumptions, our sample complexity only involves dependence on the dimension of the feature map space instead of the state space size.

Related papers

• Model-Free, Regret-Optimal Best Policy Identification in Online CMDPs [17.62509045102346]
  This paper considers the best policy identification problem in online Constrained Markov Decision Processes (CMDPs) We are interested in algorithms that are model-free, have low regret, and identify an approximately optimal policy with a high probability. Existing model-free algorithms for online CMDPs with sublinear regret and constraint violation do not provide any convergence guarantee to an optimal policy.
  arXiv  Detail & Related papers  (2023-09-27T04:33:09Z)
• Last-Iterate Convergent Policy Gradient Primal-Dual Methods for Constrained MDPs [107.28031292946774]
  We study the problem of computing an optimal policy of an infinite-horizon discounted Markov decision process (constrained MDP) We develop two single-time-scale policy-based primal-dual algorithms with non-asymptotic convergence of their policy iterates to an optimal constrained policy. To the best of our knowledge, this work appears to be the first non-asymptotic policy last-iterate convergence result for single-time-scale algorithms in constrained MDPs.
  arXiv  Detail & Related papers  (2023-06-20T17:27:31Z)
• Optimal Convergence Rate for Exact Policy Mirror Descent in Discounted Markov Decision Processes [18.35462792871242]
  Policy Mirror Descent is a family of algorithms that covers a wide range of novel and fundamental methods in reinforcement learning. Motivated by the instability of policy iteration with inexact policy evaluation, PMD algorithmically regularises the policy improvement step of PI. We show that the dimension-free $gamma$-rate of PI can be achieved by the general family of unregularised PMD algorithms under an adaptive step-size.
  arXiv  Detail & Related papers  (2023-02-22T13:55:08Z)
• First-order Policy Optimization for Robust Markov Decision Process [40.2022466644885]
  We consider the problem of solving robust Markov decision process (MDP) MDP involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. For $(mathbfs,mathbfa)$-rectangular uncertainty sets, we establish several structural observations on the robust objective.
  arXiv  Detail & Related papers  (2022-09-21T18:10:28Z)
• Nearly Optimal Latent State Decoding in Block MDPs [74.51224067640717]
  In episodic Block MDPs, the decision maker has access to rich observations or contexts generated from a small number of latent states. We are first interested in estimating the latent state decoding function based on data generated under a fixed behavior policy. We then study the problem of learning near-optimal policies in the reward-free framework.
  arXiv  Detail & Related papers  (2022-08-17T18:49:53Z)
• Best Policy Identification in Linear MDPs [70.57916977441262]
  We investigate the problem of best identification in discounted linear Markov+Delta Decision in the fixed confidence setting under a generative model. The lower bound as the solution of an intricate non- optimization program can be used as the starting point to devise such algorithms.
  arXiv  Detail & Related papers  (2022-08-11T04:12:50Z)
• Efficient Policy Iteration for Robust Markov Decision Processes via Regularization [49.05403412954533]
  Robust decision processes (MDPs) provide a framework to model decision problems where the system dynamics are changing or only partially known. Recent work established the equivalence between texttts rectangular $L_p$ robust MDPs and regularized MDPs, and derived a regularized policy iteration scheme that enjoys the same level of efficiency as standard MDPs. In this work, we focus on the policy improvement step and derive concrete forms for the greedy policy and the optimal robust Bellman operators.
  arXiv  Detail & Related papers  (2022-05-28T04:05:20Z)
• Block Policy Mirror Descent [40.2022466644885]
  We present a new class of policy (PG) methods, namely the block policy mirror descent (BPMD) BPMD is used to solve a class of regularized reinforcement learning (RL) problems with strongly convex regularizers. This is the first time that block coordinate descent methods have been developed and analyzed for policy optimization in reinforcement learning.
  arXiv  Detail & Related papers  (2022-01-15T04:42:02Z)
• 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)
• Provably Efficient Safe Exploration via Primal-Dual Policy Optimization [105.7510838453122]
  We study the Safe Reinforcement Learning (SRL) problem using the Constrained Markov Decision Process (CMDP) formulation. We present an provably efficient online policy optimization algorithm for CMDP with safe exploration in the function approximation setting.
  arXiv  Detail & Related papers  (2020-03-01T17:47:03Z)

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.