Understanding the Search Behaviour of Greedy Best-First Search

A classical result in optimal search shows that A* with an admissible and consistent heuristic expands every state whose f-value is below the optimal solution cost and no state whose f-value is above the optimal solution cost. For satisficing search algorithms, a similarly clear understanding is currently lacking. We examine the search behaviour of greedy best-first search (gbfs) in order to make progress towards such an understanding. We introduce the concept of high-water mark benches, which separate the search space into areas that are searched by a gbfs algorithm in sequence. High-water mark benches allow us to exactly determine the set of states that are not expanded under any gbfs tie-breaking strategy. For the remaining states, we show that some are expanded by all gbfs searches, while others are expanded only if certain conditions are met

Machine learning stochastic design models.

Due to the fluid nature of the early stages of the design process, it is difficult to obtain deterministic product design evaluations. This is primarily due to the flexibility of the design at this stage, namely that there can be multiple interpretations of a single design concept. However, it is important for designers to understand how these design concepts are likely to fulfil the original specification, thus enabling the designer to select or bias towards solutions with favourable outcomes. One approach is to create a stochastic model of the design domain. This paper tackles the issues of using a product database to induce a Bayesian model that represents the relationships between the design parameters and characteristics. A greedy learning algorithm is presented and illustrated using a simple case study

A fine grained heuristic to capture web navigation patterns

In previous work we have proposed a statistical model to capture the user behaviour when browsing the web. The user navigation information obtained from web logs is modelled as a hypertext probabilistic grammar (HPG) which is within the class of regular probabilistic grammars. The set of highest probability strings generated by the grammar corresponds to the user preferred navigation trails. We have previously conducted experiments with a Breadth-First Search algorithm (BFS) to perform the exhaustive computation of all the strings with probability above a specified cut-point, which we call the rules. Although the algorithm’s running time varies linearly with the number of grammar states, it has the drawbacks of returning a large number of rules when the cut-point is small and a small set of very short rules when the cut-point is high. In this work, we present a new heuristic that implements an iterative deepening search wherein the set of rules is incrementally augmented by first exploring trails with high probability. A stopping parameter is provided which measures the distance between the current rule-set and its corresponding maximal set obtained by the BFS algorithm. When the stopping parameter takes the value zero the heuristic corresponds to the BFS algorithm and as the parameter takes values closer to one the number of rules obtained decreases accordingly. Experiments were conducted with both real and synthetic data and the results show that for a given cut-point the number of rules induced increases smoothly with the decrease of the stopping criterion. Therefore, by setting the value of the stopping criterion the analyst can determine the number and quality of rules to be induced; the quality of a rule is measured by both its length and probability

Focused Local Search for Random 3-Satisfiability

A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the heuristic of focusing the local moves on the presently unsatisfiedclauses is known to be very effective: the time to solution has been observed to grow only linearly in the number of variables, for a given clauses-to-variables ratio $\alpha$ sufficiently far below the critical satisfiability threshold $\alpha_c \approx 4.27$. We present numerical results on the behaviour of three focused local search algorithms for this problem, considering in particular the characteristics of a focused variant of the simple Metropolis dynamics. We estimate the optimal value for the ``temperature'' parameter $\eta$ for this algorithm, such that its linear-time regime extends as close to $\alpha_c$ as possible. Similar parameter optimisation is performed also for the well-known WalkSAT algorithm and for the less studied, but very well performing Focused Record-to-Record Travel method. We observe that with an appropriate choice of parameters, the linear time regime for each of these algorithms seems to extend well into ratios $\alpha > 4.2$ -- much further than has so far been generally assumed. We discuss the statistics of solution times for the algorithms, relate their performance to the process of ``whitening'', and present some conjectures on the shape of their computational phase diagrams.Comment: 20 pages, lots of figure

Exact ICL maximization in a non-stationary temporal extension of the stochastic block model for dynamic networks

The stochastic block model (SBM) is a flexible probabilistic tool that can be used to model interactions between clusters of nodes in a network. However, it does not account for interactions of time varying intensity between clusters. The extension of the SBM developed in this paper addresses this shortcoming through a temporal partition: assuming interactions between nodes are recorded on fixed-length time intervals, the inference procedure associated with the model we propose allows to cluster simultaneously the nodes of the network and the time intervals. The number of clusters of nodes and of time intervals, as well as the memberships to clusters, are obtained by maximizing an exact integrated complete-data likelihood, relying on a greedy search approach. Experiments on simulated and real data are carried out in order to assess the proposed methodology

Monte Carlo algorithms are very effective in finding the largest independent set in sparse random graphs

The effectiveness of stochastic algorithms based on Monte Carlo dynamics in solving hard optimization problems is mostly unknown. Beyond the basic statement that at a dynamical phase transition the ergodicity breaks and a Monte Carlo dynamics cannot sample correctly the probability distribution in times linear in the system size, there are almost no predictions nor intuitions on the behavior of this class of stochastic dynamics. The situation is particularly intricate because, when using a Monte Carlo based algorithm as an optimization algorithm, one is usually interested in the out of equilibrium behavior which is very hard to analyse. Here we focus on the use of Parallel Tempering in the search for the largest independent set in a sparse random graph, showing that it can find solutions well beyond the dynamical threshold. Comparison with state-of-the-art message passing algorithms reveals that parallel tempering is definitely the algorithm performing best, although a theory explaining its behavior is still lacking.Comment: 14 pages, 12 figure

Monte Carlo Planning method estimates planning horizons during interactive social exchange

Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as a repeated trust task. Behaviour in such exchanges involves complexities related to each agent's preference for equity with their partner, beliefs about the partner's appetite for equity, beliefs about the partner's model of their partner, and so on. Agents may also plan different numbers of steps into the future. Providing a computationally precise account of the behaviour is an essential step towards understanding what underlies choices. A natural framework for this is that of an interactive partially observable Markov decision process (IPOMDP). However, the various complexities make IPOMDPs inordinately computationally challenging. Here, we show how to approximate the solution for the multi-round trust task using a variant of the Monte-Carlo tree search algorithm. We demonstrate that the algorithm is efficient and effective, and therefore can be used to invert observations of behavioural choices. We use generated behaviour to elucidate the richness and sophistication of interactive inference

Monte Carlo Planning method estimates planning horizons during interactive social exchange

Reciprocating interactions represent a central feature of all human exchanges. They have been the target of various recent experiments, with healthy participants and psychiatric populations engaging as dyads in multi-round exchanges such as a repeated trust task. Behaviour in such exchanges involves complexities related to each agent's preference for equity with their partner, beliefs about the partner's appetite for equity, beliefs about the partner's model of their partner, and so on. Agents may also plan different numbers of steps into the future. Providing a computationally precise account of the behaviour is an essential step towards understanding what underlies choices. A natural framework for this is that of an interactive partially observable Markov decision process (IPOMDP). However, the various complexities make IPOMDPs inordinately computationally challenging. Here, we show how to approximate the solution for the multi-round trust task using a variant of the Monte-Carlo tree search algorithm. We demonstrate that the algorithm is efficient and effective, and therefore can be used to invert observations of behavioural choices. We use generated behaviour to elucidate the richness and sophistication of interactive inference