  The game of bridge consists of two stages: bidding and playing. While playing
is proved to be relatively easy for computer programs, bidding is very
challenging. During the bidding stage, each player knowing only his/her own
cards needs to exchange information with his/her partner and interfere with
opponents at the same time. Existing methods for solving perfect-information
games cannot be directly applied to bidding. Most bridge programs are based on
human-designed rules, which, however, cannot cover all situations and are
usually ambiguous and even conflicting with each other. In this paper, we, for
the first time, propose a competitive bidding system based on deep learning
techniques, which exhibits two novelties. First, we design a compact
representation to encode the private and public information available to a
player for bidding. Second, based on the analysis of the impact of other
players' unknown cards on one's final rewards, we design two neural networks to
deal with imperfect information, the first one inferring the cards of the
partner and the second one taking the outputs of the first one as part of its
input to select a bid. Experimental results show that our bidding system
outperforms the top rule-based program.
