A Cover Time Study of a non-Markovian Algorithm

Abstract: Given a traversal algorithm, cover time is the expected number of steps needed to visit all nodes in a given graph. A smaller cover time means a higher exploration efficiency of traversal algorithm. Although random walk algorithms have been studied extensively in the existing literature, there has been no cover time result for any non-Markovian method. In this work, we stand on a theoretical perspective and show that the negative feedback strategy (a count-based exploration method) is better than the naive random walk search. In particular, the former strategy can locally improve the search efficiency for an arbitrary graph. It also achieves smaller cover times for special but important graphs, including clique graphs, tree graphs, etc. Moreover, we make connections between our results and reinforcement learning literature to give new insights on why classical UCB and MCTS algorithms are so useful. Various numerical results corroborate our theoretical findings.