We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said change, and study how restrictions on this budget impact achievable performance. We identify sharp conditions under which it is possible to achieve long-run avera...

We propose non-stationary spectral kernels for Gaussian process regression. Wepropose to model the spectral density of a non-stationary kernel function as amixture of input-dependent Gaussian process frequency density surfaces. Wesolve the generalised Fourier transform with such a model, and present a familyof non-stationary and non-monotonic kernels that can learn input-depende...

This paper studies repeated interactions between an agent and an unknown opponent that changes its strategy over time. We propose a framework for learning switching nonstationary strategies. The approach uses decision trees to learn the most up to date opponent’s strategy. Then, the agent’s strategy is computed by transforming the tree into a Markov Decision Process (MDP), whose solution dictat...

Analyzing datasets, such as sea-level records, pose a challenging statistical problem for reasons including non-stationarity, non-uniformly smooth spatial boundaries, and sparsity in the data. In this paper, we propose a framework to estimate the non-stationary covariance function by employing intrinsic statistics on the local covariates. These local covariates represent the underlying local co...