Reinforcement learning (RL) has been widely applied to sequential decision making, where interpretability and performance are both critical for practical adoption. Current approaches typically focus on performance and rely on post hoc explanations to account for interpretability. Different from these approaches, we focus on designing an interpretability-oriented yet performance-enhanced RL approach. Specifically, we propose a spectral based linear RL method that extends the ridge regression-based approach through a spectral filter function. The proposed method clarifies the role of regularization in controlling estimation error and further enables the design of an adaptive regularization parameter selection strategy guided by the bias-variance trade-off principle. Theoretical analysis establishes near-optimal bounds for both parameter estimation and generalization error. Extensive experiments on simulated environments and real-world datasets from Kuaishou and Taobao demonstrate that our method either outperforms or matches existing baselines in decision quality. We also conduct interpretability analyses to illustrate how the learned policies make decisions, thereby enhancing user trust. These results highlight the potential of our approach to bridge the gap between RL theory and practical decision making, providing interpretability, accuracy, and adaptability in management contexts.

Conventional self-attention mechanisms exhibit quadratic complexity in sequence length, making them challenging to scale for long inputs. We present FFTNet, an adaptive spectral filtering framework that uses the Fast Fourier Transform (FFT) to achieve global token mixing in O(n log n) time. By mapping inputs into the frequency domain, FFTNet exploits orthogonality and energy preservation-- guaranteed by Parseval's theorem--to efficiently model long-range dependencies. Our main theoretical contributions include 1) An adaptive spectral filter that highlights salient frequency components, 2) A hybrid scheme combining local windowing with a global FFT branch, 3) Nonlinear feature transformations applied in both the frequency and token domains. Experiments on Long Range Arena and ImageNet validate our theoretical insights and demonstrate superior performance over fixed Fourier-based and standard attention models.