We consider the problem of belief tracking in a planning setting where states are valuations over a set of variables that are partially observable, and beliefs stand for the sets of states that are possible. While the problem is intractable in the worst case, it has been recently shown that in deterministic conformant and contingent problems, belief tracking is exponential in a width parameter that is often bounded and small. In this work, we extend these results in two ways. First, we introduce a width notion that applies to non-deterministic problems as well, develop a factored belief tracking algorithm that is exponential in the problem width, and show how it applies to existing benchmarks. Second, we introduce a meaningful, powerful, and sound approximation scheme, beam tracking, that is exponential in a smaller parameter, the problem causal width, and has much broader applicability. We illustrate the value of this algorithm over large instances of problems such as Battleship, Minesweeper, and Wumpus, where it yields state-of-the-art performance in real-time.

We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at every step. We empirically and theoretically show that the per-iteration cost of our algorithms is much less than [30], and our algorithms can be used to efficiently minimize a dierence between submodular functions under various combinatorial constraints, a problem not previously addressed. We provide computational bounds and a hardness result on the multiplicative inapproximability of minimizing the dierence between submodular functions. We show, however, that it is possible to give worst-case additive bounds by providing a polynomial time computable lower-bound on the minima. Finally we show how a number of machine learning problems can be modeled as minimizing the dierence between submodular functions. We experimentally show the validity of our algorithms by testing them on the problem of feature selection with submodular cost features.

Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables. Recently, it was shown that use of non-Gaussianity identifies a causal ordering of variables in a linear acyclic model without using any prior knowledge on the network structure, which is not the case with conventional methods. However, existing estimation methods are based on iterative search algorithms and may not converge to a correct solution in a finite number of steps. In this paper, we propose a new direct method to estimate a causal ordering based on non-Gaussianity. In contrast to the previous methods, our algorithm requires no algorithmic parameters and is guaranteed to converge to the right solution within a small fixed number of steps if the data strictly follows the model.

Sequential decision problems are often approximately solvable by simulating possible future action sequences. Metalevel decision procedures have been developed for selecting which action sequences to simulate, based on estimating the expected improvement in decision quality that would result from any particular simulation; an example is the recent work on using bandit algorithms to control Monte Carlo tree search in the game of Go. In this paper we develop a theoretical basis for metalevel decisions in the statistical framework of Bayesian selection problems, arguing (as others have done) that this is more appropriate than the bandit framework. We derive a number of basic results applicable to Monte Carlo selection problems, including the first finite sampling bounds for optimal policies in certain cases; we also provide a simple counterexample to the intuitive conjecture that an optimal policy will necessarily reach a decision in all cases. We then derive heuristic approximations in both Bayesian and distribution-free settings and demonstrate their superiority to bandit-based heuristics in one-shot decision problems and in Go.

Bandit based methods for tree search have recently gained popularity when applied to huge trees, e.g. in the game of go [6]. Their efficient exploration of the tree enables to re- turn rapidly a good value, and improve preci- sion if more time is provided. The UCT algo- rithm [8], a tree search method based on Up- per Confidence Bounds (UCB) [2], is believed to adapt locally to the effective smoothness of the tree. However, we show that UCT is "over-optimistic" in some sense, leading to a worst-case regret that may be very poor. We propose alternative bandit algorithms for tree search. First, a modification of UCT us- ing a confidence sequence that scales expo- nentially in the horizon depth is analyzed. We then consider Flat-UCB performed on the leaves and provide a finite regret bound with high probability. Then, we introduce and analyze a Bandit Algorithm for Smooth Trees (BAST) which takes into account ac- tual smoothness of the rewards for perform- ing efficient "cuts" of sub-optimal branches with high confidence. Finally, we present an incremental tree expansion which applies when the full tree is too big (possibly in- finite) to be entirely represented and show that with high probability, only the optimal branches are indefinitely developed. We illus- trate these methods on a global optimization problem of a continuous function, given noisy values.

We present a heuristic search algorithm for solving first-order MDPs (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, we apply state abstraction directly on the FOMDP avoiding propositionalization. Such kind of abstraction is referred to as firstorder state abstraction. Secondly, guided by an admissible heuristic, the search is restricted only to those states that are reachable from the initial state. We demonstrate the usefullness of the above techniques for solving FOMDPs on a system, referred to as FCPlanner, that entered the probabilistic track of the International Planning Competition (IPC'2004).

We study propagation for the Sequence constraint in the context of constraint programming based on limited-width MDDs. Our first contribution is proving that establishing MDD-consistency for Sequence is NP-hard. Yet, we also show that this task is fixed parameter tractable with respect to the length of the sub-sequences. In addition, we propose a partial filtering algorithm that relies on a specific decomposition of the constraint and a novel extension of MDD filtering to node domains. We experimentally evaluate the performance of our proposed filtering algorithm, and demonstrate that the strength of the MDD propagation increases as the maximum width is increased. In particular, MDD propagation can outperform conventional domain propagation for Sequence by reducing the search tree size and solving time by several orders of magnitude. Similar improvements are observed with respect to the current best MDD approach that applies the decomposition of Sequence into Among constraints.

In the field of domain-independent planning, several powerful planners implementing different techniques have been developed. However, no one of these systems outperforms all others in every known benchmark domain. In this work, we propose a multi-planner approach that automatically configures a portfolio of planning techniques for each given domain. The configuration process for a given domain uses a set of training instances to: (i) compute and analyze some alternative sets of macro-actions for each planner in the portfolio identifying a (possibly empty) useful set, (ii) select a cluster of planners, each one with the identified useful set of macro-actions, that is expected to perform best, and (iii) derive some additional information for configuring the execution scheduling of the selected planners at planning time. The resulting planning system, called PbP (Portfolio- based Planner), has two variants focusing on speed and plan quality. Different versions of PbP entered and won the learning track of the sixth and seventh International Planning Competitions. In this paper, we experimentally analyze PbP considering planning speed and plan quality in depth. We provide a collection of results that help to understand PbPs behavior, and demonstrate the effectiveness of our approach to configuring a portfolio of planners with macro-actions.

In this paper we introduce an evolutionary algorithm for the solution of linear integer programs. The strategy is based on the separation of the variables into the integer subset and the continuous subset; the integer variables are fixed by the evolutionary system, and the continuous ones are determined in function of them, by a linear program solver. We report results obtained for some standard benchmark problems, and compare them with those obtained by branch-and-bound. The performance of the evolutionary algorithm is promising. Good feasible solutions were generally obtained, and in some of the difficult benchmark tests it outperformed branch-and-bound.

We present new algorithms for detecting the emergence of a community in large networks from sequential observations. The networks are modeled using Erdos-Renyi random graphs with edges forming between nodes in the community with higher probability. Based on statistical changepoint detection methodology, we develop three algorithms: the Exhaustive Search (ES), the mixture, and the Hierarchical Mixture (H-Mix) methods. Performance of these methods is evaluated by the average run length (ARL), which captures the frequency of false alarms, and the detection delay. Numerical comparisons show that the ES method performs the best; however, it is exponentially complex. The mixture method is polynomially complex by exploiting the fact that the size of the community is typically small in a large network. However, it may react to a group of active edges that do not form a community. This issue is resolved by the H-Mix method, which is based on a dendrogram decomposition of the network. We present an asymptotic analytical expression for ARL of the mixture method when the threshold is large. Numerical simulation verifies that our approximation is accurate even in the non-asymptotic regime. Hence, it can be used to determine a desired threshold efficiently. Finally, numerical examples show that the mixture and the H-Mix methods can both detect a community quickly with a lower complexity than the ES method.