This paper studies the adversarial graphical contextual bandits, a variant of multi-armed bandits that leverage two categories most common side information: contexts and observations. In this setting, learning agent repeatedly chooses from set K actions after being presented with d-dimensional context vector. The not only incurs observes loss chosen action, but also losses its neighboring in ob...

Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrary planar graph to index the decomposition. We prove that every graph that excludes a fixed graph as a minor has a planar decomposition with bounded width and a linear number of bags. The crossing number of a graph is ...

We develop nearly-linear time algorithms for approximately solving sparse symmetric diagonally-dominant linear systems. In particular, we present a linear-system solver that, given an n-by-n symmetric diagonally-dominant matrix A with m non-zero entries and an n-vector b, produces a vector x̃ satisfying ‖x̃ − x‖A ≤ ǫ, where x is the solution to Ax = b, in time m log m+O (m log(1/ǫ)) + n2 √ log n ...

In recent years different genetic programming (GP) structures have emerged. Today, the basic forms of representation for genetic programs are tree, linear and graph structures. In this contribution we introduce a new kind of GP structure which we call linear-graph. This is a further development to the linear-tree structure that we developed earlier. We describe the linear-graph structure, as we...