Identifying causal effects is a key problem of interest across many disciplines. The two long-standing approaches to estimate causal effects are observational and experimental (randomized) studies.

Causal inference, i.e., understanding the effect of an intervention in a stochastic system, is a key focus of research in statistics and machine learning [

Quantile (and, more generally, KL) regret bounds, such as those achieved by NormalHedge (Chaudhuri, Freund, and Hsu 2009) and its variants, relax the goal of competing against the best individual expert to only competing against a majority of experts on adversarial data.

Weargue that hedging is an activity that human and machine agents should engage in more broadly, even when the agent's value is not necessarily in monetary units.

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.

Our results improve upon recent work of Syrgkanis et al. [