A Theoretical Analysis of Optimistic Proximal Policy Optimization in Linear Markov Decision Processes

• URL: http://arxiv.org/abs/2305.08841v2
• Date: Thu, 8 Jun 2023 11:53:51 GMT
• Title: A Theoretical Analysis of Optimistic Proximal Policy Optimization in Linear Markov Decision Processes
• Authors: Han Zhong, Tong Zhang
• Abstract summary: We propose an optimistic variant of PPO for episodic adversarial linear MDPs with full-information feedback. Compared with existing policy-based algorithms, we achieve the state-of-the-art regret bound in both linear MDPs and adversarial linear MDPs with full information.
• Score: 13.466249082564213
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The proximal policy optimization (PPO) algorithm stands as one of the most prosperous methods in the field of reinforcement learning (RL). Despite its success, the theoretical understanding of PPO remains deficient. Specifically, it is unclear whether PPO or its optimistic variants can effectively solve linear Markov decision processes (MDPs), which are arguably the simplest models in RL with function approximation. To bridge this gap, we propose an optimistic variant of PPO for episodic adversarial linear MDPs with full-information feedback, and establish a $\tilde{\mathcal{O}}(d^{3/4}H^2K^{3/4})$ regret for it. Here $d$ is the ambient dimension of linear MDPs, $H$ is the length of each episode, and $K$ is the number of episodes. Compared with existing policy-based algorithms, we achieve the state-of-the-art regret bound in both stochastic linear MDPs and adversarial linear MDPs with full information. Additionally, our algorithm design features a novel multi-batched updating mechanism and the theoretical analysis utilizes a new covering number argument of value and policy classes, which might be of independent interest.

Related papers

• Efficient Learning of POMDPs with Known Observation Model in Average-Reward Setting [56.92178753201331]
  We propose the Observation-Aware Spectral (OAS) estimation technique, which enables the POMDP parameters to be learned from samples collected using a belief-based policy. We show the consistency of the OAS procedure, and we prove a regret guarantee of order $mathcalO(sqrtT log(T)$ for the proposed OAS-UCRL algorithm.
  arXiv  Detail & Related papers  (2024-10-02T08:46:34Z)
• Narrowing the Gap between Adversarial and Stochastic MDPs via Policy Optimization [11.11876897168701]
  We propose an algorithm that achieves a regret bound of order $tildemathcalO(mathrmpoly(H)sqrtSAT)$. The proposed algorithm and analysis completely avoid the typical tool given by occupancy measures.
  arXiv  Detail & Related papers  (2024-07-08T08:06:45Z)
• Offline Primal-Dual Reinforcement Learning for Linear MDPs [16.782625445546273]
  Offline Reinforcement Learning (RL) aims to learn a near-optimal policy from a fixed dataset of transitions collected by another policy. This paper proposes a primal-dual optimization method based on the linear programming formulation of RL.
  arXiv  Detail & Related papers  (2023-05-22T11:45:23Z)
• Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes [80.89852729380425]
  We propose the first computationally efficient algorithm that achieves the nearly minimax optimal regret $tilde O(dsqrtH3K)$. Our work provides a complete answer to optimal RL with linear MDPs, and the developed algorithm and theoretical tools may be of independent interest.
  arXiv  Detail & Related papers  (2022-12-12T18:58:59Z)
• 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)
• 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)
• Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processes [99.26864533035454]
  We study offline reinforcement learning (RL) in partially observable Markov decision processes. We propose the underlineProxy variable underlinePessimistic underlinePolicy underlineOptimization (textttP3O) algorithm. textttP3O is the first provably efficient offline RL algorithm for POMDPs with a confounded dataset.
  arXiv  Detail & Related papers  (2022-05-26T19:13:55Z)
• Human-in-the-loop: Provably Efficient Preference-based Reinforcement Learning with General Function Approximation [107.54516740713969]
  We study human-in-the-loop reinforcement learning (RL) with trajectory preferences. Instead of receiving a numeric reward at each step, the agent only receives preferences over trajectory pairs from a human overseer. We propose the first optimistic model-based algorithm for PbRL with general function approximation.
  arXiv  Detail & Related papers  (2022-05-23T09:03:24Z)
• Optimistic Policy Optimization is Provably Efficient in Non-stationary MDPs [45.6318149525364]
  We study episodic reinforcement learning (RL) in non-stationary linear kernel Markov decision processes (MDPs) We propose the $underlinetextp$eriodically $underlinetextr$estarted $underlinetexto$ptimistic $underlinetextp$olicy $underlinetexto$ptimization algorithm (PROPO)
  arXiv  Detail & Related papers  (2021-10-18T02:33:20Z)
• Provably Efficient Exploration in Policy Optimization [117.09887790160406]
  This paper proposes an Optimistic variant of the Proximal Policy Optimization algorithm (OPPO) OPPO achieves $tildeO(sqrtd2 H3 T )$ regret. To the best of our knowledge, OPPO is the first provably efficient policy optimization algorithm that explores.
  arXiv  Detail & Related papers  (2019-12-12T08:40:02Z)

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.