  This paper presents an algorithmic framework for the distributed on-line
source seeking, termed as 'DoSS', with a multi-robot system in an unknown
dynamical environment. Our algorithm, building on a novel concept called dummy
confidence upper bound (D-UCB), integrates both estimation of the unknown
environment and task planning for the multiple robots simultaneously, and as a
result, drives the team of robots to a steady state in which multiple sources
of interest are located. Unlike the standard UCB algorithm in the context of
multi-armed bandits, the introduction of D-UCB significantly reduces the
computational complexity in solving subproblems of the multi-robot task
planning. This also enables our 'DoSS' algorithm to be implementable in a
distributed on-line manner. The performance of the algorithm is theoretically
guaranteed by showing a sub-linear upper bound of the cumulative regret.
Numerical results on a real-world methane emission seeking problem are also
provided to demonstrate the effectiveness of the proposed algorithm.
