Recently, there has been growing interest in systematic search-based and importance sampling-based lifted inference algorithms for statistical relational models (SRMs). These lifted algorithms achieve significant complexity reductions over their propositional counterparts by using lifting rules that leverage symmetries in the relational representation. One drawback of these algorithms is that they use an inference-blind representation of the search space, which makes it difficult to efficiently pre-compute tight upper bounds on the exact cost of inference without running the algorithm to completion. In this paper, we present a principled approach to address this problem. We introduce a lifted analogue of the propositional And/Or search space framework, which we call a lifted And/Or schematic. Given a schematic-based representation of an SRM, we show how to efficiently compute a tight upper bound on the time and space cost of exact inference from a current assignment and the remaining schematic. We show how our bounding method can be used within a lifted importance sampling algorithm, in order to perform effective Rao-Blackwellisation, and demonstrate experimentally that the Rao-Blackwellised version of the algorithm yields more accurate estimates on several real-world datasets.

The paper presents and evaluates the power of parallel search for exact MAP inference in graphical models. We introduce a new parallel shared-memory recursive best-first AND/OR search algorithm, called SPRBFAOO, that explores the search space in a best-first manner while operating with restricted memory. Our experiments show that SPRBFAOO is often superior to the current state-of-the-art sequential AND/OR search approaches, leading to considerable speed-ups (up to 7-fold with 12 threads), especially on hard problem instances.

The greedy algorithm is extensively studied in the field of combinatorial optimization for decades. In this paper, we address the online learning problem when the input to the greedy algorithm is stochastic with unknown parameters that have to be learned over time. We first propose the greedy regret and $\epsilon$-quasi greedy regret as learning metrics comparing with the performance of offline greedy algorithm. We then propose two online greedy learning algorithms with semi-bandit feedbacks, which use multi-armed bandit and pure exploration bandit policies at each level of greedy learning, one for each of the regret metrics respectively. Both algorithms achieve $O(\log T)$ problem-dependent regret bound ($T$ being the time horizon) for a general class of combinatorial structures and reward functions that allow greedy solutions. We further show that the bound is tight in $T$ and other problem instance parameters.

We propose a new integer-linear programming model for the delete relaxation in cost-optimal planning. While a straightforward IP for the delete relaxation is impractical, our enhanced model incorporates variable reduction techniques based on landmarks, relevance-based constraints, dominated action elimination, immediate action application, and inverse action constraints, resulting in an IP that can be used to directly solve delete-free planning problems. We show that our IP model is competitive with previous state-of-the-art solvers for delete-free problems. The LP-relaxation of the IP model is often a very good approximation to the IP, providing an approach to approximating the optimal value of the delete-free task that is complementary to the well-known LM-cut heuristic. We also show that constraints that partially consider delete effects can be added to our IP/LP models. We embed the new IP/LP models into a forward-search based planner, and show that the performance of the resulting planner on standard IPC benchmarks is comparable with the state-of-the-art for cost-optimal planning.

We introduce a novel approach to Compressed Path Databases, space efficient oracles used to very quickly identify the first edge on a shortest path. Our algorithm achieves query running times on the 100 nanosecond scale, being significantly faster than state-of-the-art first-move oracles from the literature. Space consumption is competitive, due to a compression approach that rearranges rows and columns in a first-move matrix and then performs run length encoding (RLE) on the contents of the matrix. One variant of our implemented system was, by a convincing margin, the fastest entry in the 2014 Grid-Based Path Planning Competition. We give a first tractability analysis for the compression scheme used by our algorithm. We study the complexity of computing a database of minimum size for general directed and undirected graphs. We find that in both cases the problem is NP-complete. We also show that, for graphs which can be decomposed along articulation points, the problem can be decomposed into independent parts, with a corresponding reduction in its level of difficulty. In particular, this leads to simple and tractable algorithms with linear running time which yield optimal compression results for trees.

Bounded rationality, that is, decision-making and planning under resource limitations, is widely regarded as an important open problem in artificial intelligence, reinforcement learning, computational neuroscience and economics. This paper offers a consolidated presentation of a theory of bounded rationality based on information-theoretic ideas. We provide a conceptual justification for using the free energy functional as the objective function for characterizing bounded-rational decisions. This functional possesses three crucial properties: it controls the size of the solution space; it has Monte Carlo planners that are exact, yet bypass the need for exhaustive search; and it captures model uncertainty arising from lack of evidence or from interacting with other agents having unknown intentions. We discuss the single-step decision-making case, and show how to extend it to sequential decisions using equivalence transformations. This extension yields a very general class of decision problems that encompass classical decision rules (e.g.

We study the problem of computing possible and necessary winners for partially specified weighted and unweighted tournaments. This problem arises naturally in elections with incompletely specified votes, partially completed sports competitions, and more generally in any scenario where the outcome of some pairwise comparisons is not yet fully known. We specifically consider a number of well-known solution concepts---including the uncovered set, Borda, ranked pairs, and maximin---and show that for most of them, possible and necessary winners can be identified in polynomial time. These positive algorithmic results stand in sharp contrast to earlier results concerning possible and necessary winners given partially specified preference profiles.

Blind Source Separation (BSS) has proven to be a powerful tool for the analysis of composite patterns in engineering and science. We introduce Convex Analysis of Mixtures (CAM) for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the convex data scatter plot. We prove a sufficient and necessary condition for identifying the mixing matrix through edge detection, which also serves as the foundation for CAM to be applied not only to the exact-determined and over-determined cases, but also to the under-determined case. We show the optimality of the edge detection strategy, even for cases where source well-groundedness is not strictly satisfied. The CAM algorithm integrates plug-in noise filtering using sector-based clustering, an efficient geometric convex analysis scheme, and stability-based model order selection. We demonstrate the principle of CAM on simulated data and numerically mixed natural images. The superior performance of CAM against a panel of benchmark BSS techniques is demonstrated on numerically mixed gene expression data. We then apply CAM to dissect dynamic contrast-enhanced magnetic resonance imaging data taken from breast tumors and time-course microarray gene expression data derived from in-vivo muscle regeneration in mice, both producing biologically plausible decomposition results.

To identify the location of objects of a particular class, a passive computer vision system generally processes all the regions in an image to finally output few regions. However, we can use structure in the scene to search for objects without processing the entire image. We propose a search technique that sequentially processes image regions such that the regions that are more likely to correspond to the query class object are explored earlier. We frame the problem as a Markov decision process and use an imitation learning algorithm to learn a search strategy. Since structure in the scene is essential for search, we work with indoor scene images as they contain both unary scene context information and object-object context in the scene. We perform experiments on the NYU-depth v2 dataset and show that the unary scene context features alone can achieve a significantly high average precision while processing only 20-25\% of the regions for classes like bed and sofa. By considering object-object context along with the scene context features, the performance is further improved for classes like counter, lamp, pillow and sofa.

Finding high quality plans for large planning problems is hard. Although some current anytime planners are often able to improve plans quickly, they tend to reach a limit at which the plans produced are still very far from the best possible, but these planners fail to find any further improvement, even when given several hours of runtime. We present an approach to continuing plan quality optimisation at larger time scales, and its implementation in a system called BDPO2. Key to this approach is a decomposition into subproblems of improving parts of the current best plan. The decomposition is based on block deordering, a form of plan deordering which identifies hierarchical plan structure. BDPO2 can be seen as an application of the large neighbourhood search (LNS) local search strategy to planning, where the neighbourhood of a plan is defined by replacing one or more subplans with improved subplans. On-line learning is also used to adapt the strategy for selecting subplans and subplanners over the course of plan optimisation. Even starting from the best plans found by other means, BDPO2 is able to continue improving plan quality, often producing better plans than other anytime planners when all are given enough runtime. The best results, however, are achieved by a combination of different techniques working together.