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Suppose that we observe a short time series where each time-t-specificdata-structure consists of many slightly dependent data indexed by a and thatwe want to estimate a feature of the law of the experiment that depends neitheron t nor on a. We develop and study an algorithm to learn sequentially whichbase algorithm in a user-supplied collection best carries out the estimationtask in terms of excess risk and oracular inequalities. The analysis, whichuses dependency graph to model the amount of conditional independence withineach t-specific data-structure and a concentration inequality by Janson [2004],leverages a large ratio of the number of distinct a's to the degree of thedependency graph in the face of a small number of t-specific data-structures.The so-called one-step ahead Super Learner is applied to the motivating examplewhere the challenge is to anticipate the cost of natural disasters in France.

One-step ahead sequential Super Learning from short times series of many slightly dependent data, and anticipating the cost of natural disasters