Information-Theoretic Opacity-Enforcement in Markov Decision Processes

Abstract

Although previous studies have applied diffusion models to time series forecasting, these efforts have struggled to preserve the intrinsic temporal correlations within the series, leading to suboptimal predictive outcomes. This failure primarily results from the introduction of independent, identically distributed (i.i.d.) noise. In the forward process, the addition of i.i.d. noise to the time series gradually diminishes these temporal correlations. The reverse process starts with i.i.d. noise and lacks priors related to temporal correlations, which can result in directional biases during sampling. From a frequency-domain perspective, noise disrupts the low-frequency-dominated structure of trend components, making it difficult for the model to learn long-term temporal dependencies. To address these limitations, we introduce a decomposition prediction framework to complement the novel Temporal Correlation-Empowered Diffusion Model. Overall, We decompose the time series into trend and residual components, predict them using a base model and a diffusion model, and then combine the results. Specifically, a frequency-domain MLP model was adopted as the base model due to its not distorting the original sequence, and better the capture of long-range temporal dependencies. The diffusion model incorporates two key modules to capture short- and mid-range temporal correlations: the Maintaining Temporal Correlation Module and the Redesigned Initial Module. Extensive experiments across multiple datasets demonstrate that the proposed method significantly outperforms related strong baselines.