  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.
