Effective local search methods for finding satisfying assignments of CNF formulae exhibit several systematic characteristics in their search. We identify a series of measurable characteristics of local search behavior that are predictive of problem solving efficiency. These measures are shown to be useful for diagnosing inefficiencies in given search procedures, tuning parameters, and predicting the value of innovations to existing strategies. We then introduce a new local search method, SDF ("smoothed descent and flood"), that builds upon the intuitions gained by our study. SDF works by greedily descending in an informative objective (that considers how strongly clauses are satisfied, in addition to counting the number of unsatisfied clauses) and, once trapped in a local minima, "floods" this minima by re-weighting unsatisfied clauses to create a new descent direction. The resulting procedure exhibits superior local search characteristics under our measures. We show that this method can compete with the state of the art techniques, and significantly reduces the number of search steps relative to many recent methods.

We present a new unsupervised algorithm for training structured predictors that is discriminative, convex, and avoids the use of EM. The idea is to formulate an unsupervised version of structured learning methods, such as maximum margin Markov networks, that can be trained via semidefinite programming. The result is a discriminative training criterion for structured predictors (like hidden Markov models) that remains unsupervised and does not create local minima. To reduce training cost, we reformulate the training procedure to mitigate the dependence on semidefinite programming, and finally propose a heuristic procedure that avoids semidefinite programming entirely. Experimental results show that the convex discriminative procedure can produce better conditional models than conventional Baum-Welch (EM) training.

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Uncertainty in poker stems from two key sources, the shuffled deck and an adversary whose strategy is unknown. One approach to playing poker is to find a pessimistic game-theoretic solution (i.e., a Nash equilibrium), but human players have idiosyncratic weaknesses that can be exploited if some model or counterstrategy can be learned by observing their play. However, games against humans last for at most a few hundred hands, so learning must be very fast to be useful. We explore two approaches to opponent modelling in the context of Kuhn poker, a small game for which game-theoretic solutions are known. Parameter estimation and expert algorithms are both studied. Experiments demonstrate that, even in this small game, convergence to maximally exploitive solutions in a small number of hands is impractical, but that good (e.g., better than Nash) performance can be achieved in as few as 50 hands. Finally, we show that amongst a set of strategies with equal game-theoretic value, in particular the set of Nash equilibrium strategies, some are preferable because they speed learning of the opponent's strategy by exploring it more effectively.

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