Computing an approximately optimal policy with high probability in this case is known as PAC RL with a generative model.

In this section we discuss how to adapt existing linear bandit results (mostly in the regret setting) to sample complexity results.

Leveraging themodel-based nature ofDisCo,wecanalso readily compute anε/cmin-optimal policy for any cost-sensitive shortest-path problem defined on theL-controllable states with minimum costcmin.

Model combination is a powerful approach to achieve superior performance with a set of models than by just selecting any single one. We study both theoretically and empirically the effectiveness of ensembles of Multi-Frequency Echo State Networks (MFESNs), which have been shown to achieve state-of-the-art macroeconomic time series forecasting results (Ballarin et al., 2024a). Hedge and Follow-the-Leader schemes are discussed, and their online learning guarantees are extended to the case of dependent data. In applications, our proposed Ensemble Echo State Networks show significantly improved predictive performance compared to individual MFESN models.

In contrast to the independent sampling assumed in classical matrix completion literature, the observed entries, which arise from past matching data, are constrained by matching capacity. This matching-induced dependence poses new challenges for both estimation and inference in the matrix completion framework. We propose a non-convex algorithm based on Grassmannian gradient descent and establish near-optimal entrywise convergence rates for three canonical mechanisms, i.e., one-to-one matching, one-to-many matching with one-sided random arrival, and two-sided random arrival. To facilitate valid uncertainty quantification and hypothesis testing on matching decisions, we further develop a general debiasing and projection framework for arbitrary linear forms of the reward matrix, deriving asymptotic normality with finite-sample guarantees under matching-induced dependent sampling. Our empirical experiments demonstrate that the proposed approach provides accurate estimation, valid confidence intervals, and efficient evaluation of matching policies.