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.

Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process.

The application of low-order decomposition results in considerable memory savings while preserving the features essential for learning, and also offers theoretical guarantees to convergence.

The collected data in recommender systems generally suffers selection bias. Considerable works are proposed to address selection bias induced by observed user and item features, but they fail when hidden features (e.g., user age or salary) that affect