We study the constant regret guarantees in reinforcement learning (RL). Our objective is to design an algorithm that incurs only finite regret over infinite episodes with high probability. We introduce an algorithm, Cert-LSVI-UCB, for misspec-ified linear Markov decision processes (MDPs) where both the transition kernel and the reward function can be approximated by some linear function up to mis-specification level ζ . At the core of Cert-LSVI-UCB is an innovative certified estimator, which facilitates a fine-grained concentration analysis for multi-phase value-targeted regression, enabling us to establish an instance-dependent regret bound that is constant w.r.t. the number of episodes.

Hybrid Reinforcement Learning (RL), where an agent learns from both an offline dataset and online explorations in an unknown environment, has garnered significant recent interest. A crucial question posed by Xie et al. (2022b) is whether hybrid RL can improve upon the existing lower bounds established for purely of-fline or online RL without requiring that the behavior policy visit every state and action the optimal policy does. While Li et al. (2023b) provided an affirmative answer for tabular P AC RL, the question remains unsettled for both the regret-minimizing and non-tabular cases. In this work, building upon recent advancements in offline RL and reward-agnostic exploration, we develop computationally efficient algorithms for both P AC and regret-minimizing RL with linear function approximation, without requiring concentrability on the entire state-action space. We demonstrate that these algorithms achieve sharper error or regret bounds that are no worse than, and can improve on, the optimal sample complexity in offline RL (the first algorithm, for P AC RL) and online RL (the second algorithm, for regret-minimizing RL) in linear Markov decision processes (MDPs), regardless of the quality of the behavior policy. To our knowledge, this work establishes the tightest theoretical guarantees currently available for hybrid RL in linear MDPs.

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.

As one of the most mainstream paradigms for sequential decision-making, RL has extensive applications in many real-world problems (Kober et al., 2013; Mnih et al.,

Differential privacy (DP) [Dwork et al., 2006] is a well-established definition of privacy with many

Our contributions are summarized as follows.