Improving Search with Supervised Learning in Trick-Based Card Games

In trick-taking card games, a two-step process of state sampling and evaluation is widely used to approximate move values. While the evaluation component is vital, the accuracy of move value estimates is also fundamentally linked to how well the sampling distribution corresponds the true distribution. Despite this, recent work in trick-taking card game AI has mainly focused on improving evaluation algorithms with limited work on improving sampling. In this paper, we focus on the effect of sampling on the strength of a player and propose a novel method of sampling more realistic states given move history. In particular, we use predictions about locations of individual cards made by a deep neural network --- trained on data from human gameplay - in order to sample likely worlds for evaluation. This technique, used in conjunction with Perfect Information Monte Carlo (PIMC) search, provides a substantial increase in cardplay strength in the popular trick-taking card game of Skat.Comment: Accepted for publication at AAAI-1

A Survey of Monte Carlo Tree Search Methods

Monte Carlo tree search (MCTS) is a recently proposed search method that combines the precision of tree search with the generality of random sampling. It has received considerable interest due to its spectacular success in the difficult problem of computer Go, but has also proved beneficial in a range of other domains. This paper is a survey of the literature to date, intended to provide a snapshot of the state of the art after the first five years of MCTS research. We outline the core algorithm's derivation, impart some structure on the many variations and enhancements that have been proposed, and summarize the results from the key game and nongame domains to which MCTS methods have been applied. A number of open research questions indicate that the field is ripe for future work

Variance Reduction in Monte Carlo Counterfactual Regret Minimization (VR-MCCFR) for Extensive Form Games using Baselines

Learning strategies for imperfect information games from samples of interaction is a challenging problem. A common method for this setting, Monte Carlo Counterfactual Regret Minimization (MCCFR), can have slow long-term convergence rates due to high variance. In this paper, we introduce a variance reduction technique (VR-MCCFR) that applies to any sampling variant of MCCFR. Using this technique, per-iteration estimated values and updates are reformulated as a function of sampled values and state-action baselines, similar to their use in policy gradient reinforcement learning. The new formulation allows estimates to be bootstrapped from other estimates within the same episode, propagating the benefits of baselines along the sampled trajectory; the estimates remain unbiased even when bootstrapping from other estimates. Finally, we show that given a perfect baseline, the variance of the value estimates can be reduced to zero. Experimental evaluation shows that VR-MCCFR brings an order of magnitude speedup, while the empirical variance decreases by three orders of magnitude. The decreased variance allows for the first time CFR+ to be used with sampling, increasing the speedup to two orders of magnitude

Monte Carlo Approaches to Parameterized Poker Squares

The paper summarized a variety of Monte Carlo approaches employed in the top three performing entries to the Parameterized Poker Squares NSG Challenge competition. In all cases AI players benefited from real-time machine learning and various Monte Carlo game-tree search techniques

ALTERNATIVE SELECTION FUNCTIONS FOR INFORMATION SET MONTE CARLO TREE SEARCH

We evaluate the performance of various selection methods for the Monte Carlo Tree Search algorithm in two-player zero-sum extensive-form games with imperfect information. We compare the standard Upper Confident Bounds applied to Trees (UCT) along with the less common Exponential Weights for Exploration and Exploitation (Exp3) and novel Regret matching (RM) selection in two distinct imperfect information games: Imperfect Information Goofspiel and Phantom Tic-Tac-Toe. We show that UCT after initial fast convergence towards a Nash equilibrium computes increasingly worse strategies after some point in time. This is not the case with Exp3 and RM, which also show superior performance in head-to-head matches

Bayesian inference in time series

Time Series