R), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which is updated based on confidence bounds.

In classical reinforcement learning agents accept arbitrary short term loss for long term gain when exploring their environment. This is infeasible for safety critical applications such as robotics, where even a single unsafe action may cause system failure or harm the environment. In this paper, we address the problem of safely exploring finite Markov decision processes (MDP). We define safety in terms of an a priori unknown safety constraint that depends on states and actions and satisfies certain regularity conditions expressed via a Gaussian process prior.

We consider the problem of variational inference in probabilistic models with both log-submodular and log-supermodular higher-order potentials. These models can represent arbitrary distributions over binary variables, and thus generalize the commonly used pairwise Markov random fields and models with log-supermodular potentials only, for which efficient approximate inference algorithms are known. While inference in the considered models is #P-hard in general, we present efficient approximate algorithms exploiting recent advances in the field of discrete optimization. We demonstrate the effectiveness of our approach in a large set of experiments, where our model allows reasoning about preferences over sets of items with complements and substitutes.

We study a rich family of distributions that capture variable interactions significantly more expressive than those representable with low-treewidth or pairwise graphical models, or log-supermodular models. We call these cooperative graphical models. Yet, this family retains structure, which we carefully exploit for efficient inference techniques. Our algorithms combine the polyhedral structure of submodular functions in new ways with variational inference methods to obtain both lower and upper bounds on the partition function. While our fully convex upper bound is minimized as an SDP or via tree-reweighted belief propagation, our lower bound is tightened via belief propagation or mean-field algorithms. The resulting algorithms are easy to implement and, as our experiments show, effectively obtain good bounds and marginals for synthetic and real-world examples.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Can we incorporate discrete optimization algorithms within modern machine learning models? For example, is it possible to incorporate in deep architectures a layer whose output is the minimal cut of a parametrized graph? Given that these models are trained end-to-end by leveraging gradient information, the introduction of such layers seems very challenging due to their non-continuous output. In this paper we focus on the problem of submodular minimization, for which we show that such layers are indeed possible. The key idea is that we can continuously relax the output without sacrificing guarantees. We provide an easily computable approximation to the Jacobian complemented with a complete theoretical analysis. Finally, these contributions let us experimentally learn probabilistic log-supermodular models via a bi-level variational inference formulation.