  Auxiliary learning is an effective method for enhancing the generalization
capabilities of trained models, particularly when dealing with small datasets.
However, this approach may present several difficulties: (i) optimizing
multiple objectives can be more challenging, and (ii) how to balance the
auxiliary tasks to best assist the main task is unclear. In this work, we
propose a novel approach, named AuxiNash, for balancing tasks in auxiliary
learning by formalizing the problem as generalized bargaining game with
asymmetric task bargaining power. Furthermore, we describe an efficient
procedure for learning the bargaining power of tasks based on their
contribution to the performance of the main task and derive theoretical
guarantees for its convergence. Finally, we evaluate AuxiNash on multiple
multi-task benchmarks and find that it consistently outperforms competing
methods.
