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We introduce algorithms for online, full-information prediction that arecompetitive with contextual tree experts of unknown complexity, in bothprobabilistic and adversarial settings. We show that by incorporating aprobabilistic framework of structural risk minimization into existing adaptivealgorithms, we can robustly learn not only the presence of stochastic structurewhen it exists (leading to constant as opposed to $\mathcal{O}(\sqrt{T})$regret), but also the correct model order. We thus obtain regret bounds thatare competitive with the regret of an optimal algorithm that possesses strongside information about both the complexity of the optimal contextual treeexpert and whether the process generating the data is stochastic oradversarial. These are the first constructive guarantees on simultaneousadaptivity to the model and the presence of stochasticity.

Best of many worlds: Robust model selection for online supervised learning