Evaluating an agent's performance in a stochastic setting is necessary for agent development, scientific evaluation, and competitions. Traditionally, evaluation is done using Monte Carlo estimation; the magnitude of the stochasticity in the domain or the high cost of sampling, however, can often prevent the approach from resulting in statistically significant conclusions. Recently, an advantage sum technique has been proposed for constructing unbiased, low variance estimates of agent performance. The technique requires an expert to define a value function over states of the system, essentially a guess of the state's unknown value. In this work, we propose learning this value function from past interactions between agents in some target population. Our learned value functions have two key advantages: they can be applied in domains where no expert value function is available and they can result in tuned evaluation for a specific population of agents (e.g., novice versus advanced agents). We demonstrate these two advantages in the domain of poker. We show that we can reduce variance over state-of-the-art estimators for a specific population of limit poker players as well as construct the first variance reducing estimators for no-limit poker and multi-player limit poker.

Martha White, Michael Bowling