Learning Team Strategies with Multiple Policy-sharing Agents: a Soccer Case Study

We use simulated soccer to study multiagent learning. Each team's players (agents) share action set and policy but may behave diierently due to position-dependent inputs. All agents making up a team are rewarded or punished collectively in case of goals. We conduct simulations with varying team sizes, and compare two learning algorithms: TD-Q learning with linear neural networks (TD-Q) and Probabilistic Incremental Program Evolution (PIPE). TD-Q is based on evaluation functions (EFs) mapping input/action pairs to expected reward, while PIPE searches policy space directly. PIPE uses adaptive \probabilistic prototype trees" to synthesize programs that calculate action probabilities from current inputs. Our results show that TD-Q encounters several diiculties in learning appropriate shared EFs. PIPE, however, does not depend on EFs and can nd good policies faster and more reliably. This suggests that in multiagent learning scenarios direct search through policy space can ooer advantages over EF-based approaches.