The application of the computational analysis and learning techniques described in previous research, manifest themselves in the form of artificial intelligence (AI). AI represents the ambition to create machines that can think, learn and create solutions to problems with the same range to which the human mind can be applied. AI is absolutely nothing new – all of us are using it every day. Every time we send an email, use a credit card or travel, or search the Internet, AI systems are the bedrock on which we perform these activities. Intelligent algorithms are constantly checking and detecting credit-card fraud, flying and landing airplanes, keeping track of inventories and even manufacturing products in robotic factories.

Non-convex optimization with local search heuristics has been widely used in machine learning, achieving many state-of-art results. It becomes increasingly important to understand why they can work for these NP-hard problems on typical data. The landscape of many objective functions in learning has been conjectured to have the geometric property that "all local optima are (approximately) global optima", and thus they can be solved efficiently by local search algorithms. However, establishing such property can be very difficult. In this paper, we analyze the optimization landscape of the random over-complete tensor decomposition problem, which has many applications in unsupervised learning, especially in learning latent variable models. In practice, it can be efficiently solved by gradient ascent on a non-convex objective. We show that for any small constant $\epsilon > 0$, among the set of points with function values $(1+\epsilon)$-factor larger than the expectation of the function, all the local maxima are approximate global maxima. Previously, the best-known result only characterizes the geometry in small neighborhoods around the true components. Our result implies that even with an initialization that is barely better than the random guess, the gradient ascent algorithm is guaranteed to solve this problem. Our main technique uses Kac-Rice formula and random matrix theory. To our best knowledge, this is the first time when Kac-Rice formula is successfully applied to counting the number of local minima of a highly-structured random polynomial with dependent coefficients.

The goal of the paper is to design sequential strategies which lead to efficient optimization of an unknown function under the only assumption that it has a finite Lipschitz constant. We first identify sufficient conditions for the consistency of generic sequential algorithms and formulate the expected minimax rate for their performance. We introduce and analyze a first algorithm called LIPO which assumes the Lipschitz constant to be known. Consistency, minimax rates for LIPO are proved, as well as fast rates under an additional H\"older like condition. An adaptive version of LIPO is also introduced for the more realistic setup where the Lipschitz constant is unknown and has to be estimated along with the optimization. Similar theoretical guarantees are shown to hold for the adaptive LIPO algorithm and a numerical assessment is provided at the end of the paper to illustrate the potential of this strategy with respect to state-of-the-art methods over typical benchmark problems for global optimization.

In many robot motion planning problems such as manipulation planning for a personal robot in a kitchen or an industrial manipulator in a warehouse, all motion planning queries are in an environment that is largely static. Consequently, one should be able to improve the performance of a planning algorithm by training on this static environment ahead of operation time. In this work, we propose a method to improve the performance of heuristic search-based motion planners in such environments. The first, learning, phase of our proposed method analyzes search performance on multiple planning episodes to infer local minima zones, that is, regions where the existing heuristic(s) are weakly correlated with the true cost-to-go. Then, in the planning phase of the method, the learnt local minima are used to modify the original search graph in a way that improves search performance. We prove that our method preserves guarantees on completeness and bounded suboptimality with respect to the original search graph. Experimentally, we observe significant improvements in success rate and planning time for challenging 11 degree-of-freedom mobile manipulation problems.

We consider the motion-planning problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We suggest a natural cost function that balances path length and risk-exposure time. Specifically, we consider the discrete setting where we are given a graph, or a roadmap, and we wish to compute the minimal-cost path under this cost function. Interestingly, paths defined using our cost function do not have an optimal substructure. Namely, subpaths of an optimal path are not necessarily optimal. Thus, the Bellman condition is not satisfied and standard graph-search algorithms such as Dijkstra cannot be used. We present a path-finding algorithm, which can be seen as a natural generalization of Dijkstra’s algorithm. Our algorithm runs in O ((n B · n) log(n B · n) + n B · m) time, where n and m are the number of vertices and edges of the graph, respectively, and n B is the number of intersections between edges and the boundary of the risk zone. We present simulations on robotic platforms demonstrating both the natural paths produced by our cost function and the computational efficiency of our algorithm.

We address the problem of finding shortest paths in graphs where some edges have a prior probability of existence, and their existence can be verified during planning with time- consuming operations. Our work is motivated by real-world robot motion planning, where edge existence is often expensive to verify (typically involves time-consuming collision-checking between the robot and world models), but edge existence probabilities are readily available. The goal then, is to develop an anytime algorithm that can return good solutions quickly by somehow leveraging the existence probabilities, and continue to return better-quality solutions or provide tighter suboptimality bounds with more time. While our motivation is fast and high-quality motion planning for robots, this work presents two fundamental contributions applicable to generic graphs with probabilistic edges. They are: a) an algorithm for efficiently computing all relevant shortest paths in a graph with probabilistic edges, and as a by-product the expected shortest path cost, and b) an anytime algorithm for evaluating (verifying existence of) edges in a collection of paths, which is optimal in expectation under a chosen distribution of the algorithm interruption time. Finally, we provide a practical approach to integrate a) and b) in the context of robot motion planning and demonstrate significant improvements in success rate and planning time for a 11 degree-of-freedom mobile manipulation planning problem. We also conduct additional evaluations on a 2D grid navigation domain to study our algorithm’s behavior.

This paper develops an effective, cooperative, and probabilistically-complete multi-robot motion planner. The approach takes into account geometric and differential constraints imposed by the obstacles and the robot dynamics by using sampling to expand a motion tree in the composite state space of all the robots. Scalability and efficiency is achieved by using solutions to a simplified problem representation that does not take dynamics into account to guide the motion-tree expansion. The heuristic solutions are obtained by constructing roadmaps over low-dimensional configuration spaces and relying on cooperative multi-agent graph search to effectively find graph routes. Experimental results with second-order vehicle models operating in complex environments, where cooperation among the robots is required to find solutions, demonstrate significant improvements over related work.

Querying graph structured data is a fundamental operation that enables important applications including knowledge graph search, social network analysis, and cyber-network security. However, the growing size of real-world data graphs poses severe challenges for graph databases to meet the response-time requirements of the applications. Planning the computational steps of query processing — Query Planning — is central to address these challenges. In this paper, we study the problem of learning to speedup query planning in graph databases towards the goal of improving the computational-efficiency of query processing via training queries. We present a Learning to Plan (L2P) framework that is applicable to a large class of query reasoners that follow the Threshold Algorithm (TA) approach. First, we define a generic search space over candidate query plans, and identify target search trajectories (query plans) corresponding to the training queries by performing an expensive search. Subsequently, we learn greedy search control knowledge to imitate the search behavior of the target query plans. We provide a concrete instantiation of our L2P framework for STAR, a state-of-the-art graph query reasoner. Our experiments on benchmark knowledge graphs including dbpedia, yago, and freebase show that using the query plans generated by the learned search control knowledge, we can significantly improve the speed of STAR with negligible loss in accuracy.

Pruning techniques based on strong stubborn sets have recently shown their potential for SAS+ planning as heuristic search. Strong stubborn sets exploit operator independency to safely prune the search space. Like SAS+ planning, fully observable nondeterministic (FOND) planning faces the state explosion problem. However, it is unclear how stubborn set techniques carry over to the nondeterministics setting. In this paper, we introduce stubborn set pruning to FOND planning. We lift the notion of strong stubborn sets and introduce the conceptually more powerful notion of weak stubborn sets to FOND planning. Our experimental analysis shows that weak stubborn sets are beneficial to an LAO* search, and in particular show favorable performance when combined with symmetries and active operator pruning.

For the past 25 years, heuristic search has been used to solve domain-independent probabilistic planning problems, but with heuristics that determinise the problem and ignore precious probabilistic information. To remedy this situation, we explore the use of occupation measures, which represent the expected number of times a given action will be executed in a given state of a policy. By relaxing the well-known linear program that computes them, we derive occupation measure heuristics -- the first admissible heuristics for stochastic shortest path problems (SSPs) taking probabilities into account. We show that these heuristics can also be obtained by extending recent operator-counting heuristic formulations used in deterministic planning. Since the heuristics are formulated as linear programs over occupation measures, they can easily be extended to more complex probabilistic planning models, such as constrained SSPs (C-SSPs). Moreover, their formulation can be tightly integrated into i-dual, a recent LP-based heuristic search algorithm for (constrained) SSPs, resulting in a novel probabilistic planning approach in which policy update and heuristic computation work in unison. Our experiments in several domains demonstrate the benefits of these new heuristics and approach.