Solving Imperfect Information Games Using Decomposition

Decomposition, i.e. independently analyzing possible subgames, has proven to be an essential principle for effective decision-making in perfect information games. However, in imperfect information games, decomposition has proven to be problematic. To date, all proposed techniques for decomposition in imperfect information games have abandoned theoretical guarantees. This work presents the first technique for decomposing an imperfect information game into subgames that can be solved independently, while retaining optimality guarantees on the full-game solution. We can use this technique to construct theoretically justified algorithms that make better use of information available at run-time, overcome memory or disk limitations at run-time, or make a time/space trade-off to overcome memory or disk limitations while solving a game. In particular, we present an algorithm for subgame solving which guarantees performance in the whole game, in contrast to existing methods which may have unbounded error. In addition, we present an offline game solving algorithm, CFR-D, which can produce a Nash equilibrium for a game that is larger than available storage.Comment: 7 pages by 2 columns, 5 figures; April 21 2014 - expand explanations and theor

Heart Rate Response to Sound and Light

Heart rate response to varying sound and light intensitie

No-Regret Learning in Extensive-Form Games with Imperfect Recall

Counterfactual Regret Minimization (CFR) is an efficient no-regret learning algorithm for decision problems modeled as extensive games. CFR's regret bounds depend on the requirement of perfect recall: players always remember information that was revealed to them and the order in which it was revealed. In games without perfect recall, however, CFR's guarantees do not apply. In this paper, we present the first regret bound for CFR when applied to a general class of games with imperfect recall. In addition, we show that CFR applied to any abstraction belonging to our general class results in a regret bound not just for the abstract game, but for the full game as well. We verify our theory and show how imperfect recall can be used to trade a small increase in regret for a significant reduction in memory in three domains: die-roll poker, phantom tic-tac-toe, and Bluff.Comment: 21 pages, 4 figures, expanded version of article to appear in Proceedings of the Twenty-Ninth International Conference on Machine Learnin

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

Small business owner persistence: Do personal characteristics matter?

Recent research suggests that (1) business failure rates are lower than previously thought and (2) business owners exit businesses for myriad reasons besides performance. Despite these findings, relatively little is known about whether personal characteristics (i.e. expectations, competencies, education) of small firm owners influence their likelihood to persist with business ownership. Given this gap, the present study investigates the relationship between owner characteristics and persistence intentions. Framed by threshold theory, we theorize and test whether owner growth expectations, satisfaction, education, competencies, and financial investment influence their persistence intentions. Results indicate that owner future growth expectations for the business, their opportunity recognition abilities, and their satisfaction with the business significantly impact persistence intentions. Implications of study findings are discussed.&nbsp

An Examination of How Personal Characteristics Moderate the Relationship between Startup Intent and Entrepreneurship Education

Purpose - While research has identified a consistent link between startup intent and entrepreneurship education (EE) intentions, studies also indicate that many entrepreneurs lack the EE they need. However, research examining factors that explain why certain individuals with high startup intent pursue EE while others do not is rare.Given this, the purpose of this paper is to examine how individual characteristics moderate the startup intent EE intentions relationship. Design/methodology/approach - Survey data were gathered on 199 US adults. Moderators examined include attitudes toward education, perceived entrepreneurial efficacy, propensity for risk taking and the Big Five personality traits. Linear regression models were used to test each of the moderation relationships predicted. Findings - Notable findings suggest that extroversion, openness to experience, agreeableness, perceived entrepreneurial efficacy and risk propensity reduce the chances that individuals with high startup intent will pursue EE, while viewing education as instrumental enhances the relationship. Research limitations/implications - Study findings imply that EE programs might not be reaching critical target markets, suggest that EE programs might need to be modified to attract individuals with high startup intent and indicate that individual characteristics are key factors that determine why certain individuals with high startup intent pursue EE while others with the same desires do not pursue EE. Originality/value - This study builds on previous work that looks at the relationship between startup intent and EE intentions by investigating how individual characteristics either amplify or diminish the relationship, increasing scholarly knowledge about why certain individuals with highstartup intent pursue EE while others do not