Near-Optimal Dynamic Regret for Adversarial Linear Mixture MDPs

We study episodic linear mixture MDPs with the unknown transition and adversarial rewards under full-information feedback, employing *dynamic regret* as the performance measure. We start with in-depth analyses of the strengths and limitations of the two most popular methods: occupancy-measure-based and policy-based methods. We observe that while the occupancy-measure-based method is effective in addressing non-stationary environments, it encounters difficulties with the unknown transition. In contrast, the policy-based method can deal with the unknown transition effectively but faces challenges in handling non-stationary environments. Building on this, we propose a novel algorithm that combines the benefits of both methods. Specifically, it employs (i) an *occupancy-measure-based global optimization* with a two-layer structure to handle non-stationary environments; and (ii) a *policy-based variance-aware value-targeted regression* to tackle the unknown transition.