Nguyen, Truong-Huy Dinh (National University of Singapore) | Hsu, David (National University of Singapore) | Lee, Wee-Sun (National University of Singapore) | Leong, Tze-Yun (National University of Singapore) | Kaelbling, Leslie Pack (Massachusetts Institute of Technology) | Lozano-Perez, Tomas (Massachusetts Institute of Technology) | Grant, Andrew Haydn (Singapore-MIT GAMBIT Game Lab)
We apply decision theoretic techniques to construct non-player characters that are able to assist a human player in collaborative games. The method is based on solving Markov decision processes, which can be difficult when the game state is described by many variables. To scale to more complex games, the method allows decomposition of a game task into subtasks, each of which can be modelled by a Markov decision process. Intention recognition is used to infer the subtask that the human is currently performing, allowing the helper to assist the human in performing the correct task. Experiments show that the method can be effective, giving near-human level performance in helping a human in a collaborative game.
Procedural content generation via machine learning (PCGML) has been growing in recent years. However, many PCGML approaches are only explored in the context of linear platforming games, and focused on modeling structural level information. Previously, we developed a multi-layer level representation, where each layer is designed to capture specific level information. In this paper, we apply our multi-layer approach to Lode Runner, a game with non-linear paths and complex actions. We test our approach by generating levels for Lode Runner with a constrained multi-dimensional Markov chain (MdMC) approach that ensures playability and a standard MdMC sampling approach. We compare the levels sampled when using multi-layer representation against those sampled using the single-layer representation; we compare using both the constrained sampling algorithm and the standard sampling algorithm.
One of the topics in data science or statistics I found interesting, but having difficulty understanding is Bayesian analysis. During the course of my General Assembly's Data Science Immersive boot camp, I have had a chance to explore Bayesian statistics, but I really think I need some review and reinforcement. This is my personal endeavour to have a better understanding of Bayesian thinking, and how it can be applied to real-life cases. For this post, I am mainly inspired by a Youtube series by Rasmus Bååth, "Introduction to Bayesian data analysis". He is really good at giving you an intuitive understanding of Bayesian analysis, not by bombarding you with all the complicated formulas, but by providing you with a thought-process of Bayesian statistics. The topic I chose for this post is baseball.
In designing Markov Decision Processes (MDP), one must define the world, its dynamics, a set of actions, and a reward function. MDPs are often applied in situations where there is a clear choice of reward functions and in these cases significant care must be taken to construct a reward function that induces the desired behavior. In this paper, we consider an analogous design problem: crafting a target distribution in Targeted Trajectory Distribution MDPs (TTD-MDPs). TTD-MDPs produce probabilistic policies that minimize divergence from a target distribution of trajectories from an underlying MDP. They are an extension of MDPs that provide variety of experience during repeated execution. Here, we present a brief overview of TTD-MDPs with approaches for constructing target distributions. Then we present a novel authorial idiom for creating target distributions using prototype trajectories. We evaluate these approaches on a drama manager for an interactive game.
The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess ranking and multiclass classification. Numerous extensions of the basic model have also been proposed in the literature including models with ties, multiple comparisons, group comparisons and random graphs. From a computational point of view, Hunter (2004) has proposed efficient iterative MM (minorization-maximization) algorithms to perform maximum likelihood estimation for these generalized Bradley-Terry models whereas Bayesian inference is typically performed using MCMC (Markov chain Monte Carlo) algorithms based on tailored Metropolis-Hastings (M-H) proposals. We show here that these MM\ algorithms can be reinterpreted as special instances of Expectation-Maximization (EM) algorithms associated to suitable sets of latent variables and propose some original extensions. These latent variables allow us to derive simple Gibbs samplers for Bayesian inference. We demonstrate experimentally the efficiency of these algorithms on a variety of applications.