Learning to route efficiently with end-to-end feedback : the value of (identifiable) networked structure

Abstract

In this thesis, we introduce efficient algorithms which achieve nearly optimal instance-dependent and worst case regrets for the problem of stochastic online shortest path routing with end-to-end feedback. The setting is a natural application of the combinatorial stochastic bandits problem, a special case of the linear stochastic bandits problem. We show how the difficulties posed by the large scale action set can be overcome by the networked structure of the action set. Our approach presents a novel connection between bandit learning and shortest path algorithms. Our main contribution is a series of adaptive exploration algorithms that achieves nearly optimal O ((d²ln(T)+d³) [delta]max=[delta]²min) instance-dependent regret and Õ(d [square root]T) worst case regret at the same time. Driven by the carefully designed Top-Two Comparison (TTC) technique, the algorithms are efficiently implementable. We also conduct extensive numerical experiments to show that our proposed algorithms not only achieve superior regret performances, but also reduce the runtime drastically.