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We introduce efficient algorithms which achieve nearly optimal regrets forthe problem of stochastic online shortest path routing with end-to-endfeedback. The setting is a natural application of the combinatorial stochasticbandits problem, a special case of the linear stochastic bandits problem. Weshow how the difficulties posed by the large scale action set can be overcomeby the networked structure of the action set. Our approach presents a novelconnection between bandit learning and shortest path algorithms. Our maincontribution is an adaptive exploration algorithm with nearly optimalinstance-dependent regret for any directed acyclic network. We then modify itso that nearly optimal worst case regret is achieved simultaneously. Driven bythe carefully designed Top-Two Comparison (TTC) technique, the algorithms areefficiently implementable. We further conduct extensive numerical experimentsto show that our proposed algorithms not only achieve superior regretperformances, but also reduce the runtime drastically.

Learning to Route Efficiently with End-to-End Feedback: The Value of Networked Structure