#### Authors

Yuandong Tian, Qucheng Gong, Yu Jiang

#### Abstract

To learn good joint policies for multi-agent collaboration with incomplete information remains a fundamental challenge. While for two-player zero-sum games, coordinate-ascent approaches (optimizing one agent's policy at a time, e.g., self-play) work with guarantees, in multi-agent cooperative setting they often converge to sub-optimal Nash equilibrium. On the other hand, directly modeling joint policy changes in incomplete information game is nontrivial due to complicated interplay of policies (e.g., upstream updates affect downstream state reachability). In this paper, we show global changes of game values can be decomposed to policy changes localized at each information set, with a novel term named \emph{policy-change density}. Based on this, we propose \emph{Joint Policy Search} (JPS) that iteratively improves joint policies of collaborative agents in incomplete information games, without re-evaluating the entire game. On multiple collaborative tabular games, JPS is proven to never worsen performance and can improve solutions provided by unilateral approaches (e.g, CFR), outperforming algorithms designed for collaborative policy learning (e.g. BAD). Furthermore, for real-world game whose states are too many to enumerate, \ours{} has an online form that naturally links with gradient updates. We test it to Contract Bridge, a 4-player imperfect-information game where a team of $2$ collaborates to compete against the other. In its bidding phase, players bid in turn to find a good contract through a limited information channel. Based on a strong baseline agent that bids competitive bridge purely through domain-agnostic self-play, JPS improves collaboration of team players and outperforms WBridge5, a championship-winning software, by $+0.63$ IMPs (International Matching Points) per board over $1000$ games, substantially better than previous SoTA ($+0.41$ IMPs/b against WBridge5). Note that $+0.1$ IMPs/b is regarded as a nontrivial improvement in Computer Bridge.