In robotics, ergodic control extends the tracking principle by specifying a probability distribution over an area to cover instead of a trajectory to track. The original problem is formulated as a spectral multiscale coverage problem, typically requiring the spatial distribution to be decomposed as Fourier series. This approach does not scale well to control problems requiring exploration in search space of more than 2 dimensions. To address this issue, we propose the use of tensor trains, a recent low-rank tensor decomposition technique from the field of multilinear algebra. The proposed solution is efficient, both computationally and storage-wise, hence making it suitable for its online implementation in robotic systems. The approach is applied to a peg-in-hole insertion task requiring full 6D end-effector poses, implemented with a 7-axis Franka Emika Panda robot. In this experiment, ergodic exploration allows the task to be achieved without requiring the use of force/torque sensors.

In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search methods can find the ground truth with a small error. By analyzing the landscape of the non-convex problem, we first propose a global guarantee on the maximum distance between an arbitrary local minimizer and the ground truth under the assumption that the RIP constant is smaller than 1/2. We show that this distance shrinks to zero as the intensity of the noise reduces. Our new guarantee is sharp in terms of the RIP constant and is much stronger than the existing results. We then present a local guarantee for problems with an arbitrary RIP constant, which states that any local minimizer is either considerably close to the ground truth or far away from it. The developed results demonstrate how the noise intensity and the RIP constant of the problem affect the locations of the local minima relative to the true solution.

Width-based search algorithms seek plans by prioritizing states according to a suitably defined measure of novelty, that maps states into a set of novelty categories. Space and time complexity to evaluate state novelty is known to be exponential on the cardinality of the set. We present novel methods to obtain polynomial approximations of novelty and width-based search. First, we approximate novelty computation via random sampling and Bloom filters, reducing the runtime and memory footprint. Second, we approximate the best-first search using an adaptive policy that decides whether to forgo the expansion of nodes in the open list. These two techniques are integrated into existing width-based algorithms, resulting in new planners that perform significantly better than other state-of-the-art planners over benchmarks from the International Planning Competitions.

Multi working-machines pathfinding solution enables more mobile machines simultaneously to work inside of a working site so that the productivity can be expected to increase evolutionary. To date, the potential cooperation conflicts among construction machinery limit the amount of construction machinery investment in a concrete working site. To solve the cooperation problem, civil engineers optimize the working site from a logistic perspective while computer scientists improve pathfinding algorithms' performance on the given benchmark maps. In the practical implementation of a construction site, it is sensible to solve the problem with a hybrid solution; therefore, in our study, we proposed an algorithm based on a cutting-edge multi-pathfinding algorithm to enable the massive number of machines cooperation and offer the advice to modify the unreasonable part of the working site in the meantime. Using the logistic information from BIM, such as unloading and loading point, we added a pathfinding solution for multi machines to improve the whole construction fleet's productivity. In the previous study, the experiments were limited to no more than ten participants, and the computational time to gather the solution was not given; thus, we publish our pseudo-code, our tested map, and benchmark our results. Our algorithm's most extensive feature is that it can quickly replan the path to overcome the emergency on a construction site.

In Kauffman-s NK model, myopic local search involves flipping one randomly-chosen bit of an N-bit decision string in every time step and accepting the new configuration if that has higher fitness. One issue is that, this algorithm consumes the full extent of computational resources allocated - given by the number of alternative configurations inspected - even though search is expected to terminate the moment there are no neighbors having higher fitness. Otherwise, the algorithm must compute the fitness of all N neighbors in every time step, consuming a high amount of resources. In order to get around this problem, I describe an algorithm that allows search to logically terminate relatively early, without having to evaluate fitness of all N neighbors at every time step. I further suggest that when the efficacy of two algorithms need to be compared head to head, imposing a common limit on the number of alternatives evaluated - metering - provides the necessary level field.

Polly is the LLVM project's polyhedral loop nest optimizer. Recently, user-directed loop transformation pragmas were proposed based on LLVM/Clang and Polly. The search space exposed by the transformation pragmas is a tree, wherein each node represents a specific combination of loop transformations that can be applied to the code resulting from the parent node's loop transformations. We have developed a search algorithm based on Monte Carlo tree search (MCTS) to find the best combination of loop transformations. Our algorithm consists of two phases: exploring loop transformations at different depths of the tree to identify promising regions in the tree search space and exploiting those regions by performing a local search. Moreover, a restart mechanism is used to avoid the MCTS getting trapped in a local solution. The best and worst solutions are transferred from the previous phases of the restarts to leverage the search history. We compare our approach with random, greedy, and breadth-first search methods on PolyBench kernels and ECP proxy applications. Experimental results show that our MCTS algorithm finds pragma combinations with a speedup of 2.3x over Polly's heuristic optimizations on average.

Boolean Satisfiability (SAT) is a well-known NP-complete problem. Despite this theoretical hardness, SAT solvers based on Conflict Driven Clause Learning (CDCL) can solve large SAT instances from many important domains. CDCL learns clauses from conflicts, a technique that allows a solver to prune its search space. The selection heuristics in CDCL prioritize variables that are involved in recent conflicts. While only a fraction of decisions generate any conflicts, many generate multiple conflicts. In this paper, we study conflict-generating decisions in CDCL in detail. We investigate the impact of single conflict (sc) decisions, which generate only one conflict, and multi-conflict (mc) decisions which generate two or more. We empirically characterize these two types of decisions based on the quality of the learned clauses produced by each type of decision. We also show an important connection between consecutive clauses learned within the same mc decision, where one learned clause triggers the learning of the next one forming a chain of clauses. This leads to the consideration of similarity between conflicts, for which we formulate the notion of conflictsproximity as a similarity measure. We show that conflicts in mc decisions are more closely related than consecutive conflicts generated from sc decisions. Finally, we develop Common Reason Variable Reduction (CRVR) as a new decision strategy that reduces the selection priority of some variables from the learned clauses of mc decisions. Our empirical evaluation of CRVR implemented in three leading solvers demonstrates performance gains in benchmarks from the main track of SAT Competition-2020.

Width-based planning methods exploit the use of conjunctive goals for decomposing problems into subproblems of low width. However, algorithms like SIW fail when the goal is not serializable. In this work, we address this limitation of SIW by using a simple but powerful language for expressing problem decompositions introduced recently by Bonet and Geffner, called policy sketches. A policy sketch R consists of a set of Boolean and numerical features and a set of sketch rules that express how the values of these features are supposed to change. Like general policies, policy sketches are domain general, but unlike policies, the changes captured by sketch rules do not need to be achieved in a single step. We show that many planning domains that cannot be solved by SIW are provably solvable in low polynomial time with the SIW_R algorithm, the version of SIW that employs user-provided policy sketches. Policy sketches are thus shown to be a powerful language for expressing domain-specific knowledge in a simple and compact way and a convenient alternative to languages such as HTNs or temporal logics. Furthermore, policy sketches make it easy to express general problem decompositions and prove key properties like their complexity and width.

We present PSEUDo, an adaptive feature learning technique for exploring visual patterns in multi-track sequential data. Our approach is designed with the primary focus to overcome the uneconomic retraining requirements and inflexible representation learning in current deep learning-based systems. Multi-track time series data are generated on an unprecedented scale due to increased sensors and data storage. These datasets hold valuable patterns, like in neuromarketing, where researchers try to link patterns in multivariate sequential data from physiological sensors to the purchase behavior of products and services. But a lack of ground truth and high variance make automatic pattern detection unreliable. Our advancements are based on a novel query-aware locality-sensitive hashing technique to create a feature-based representation of multivariate time series windows. Most importantly, our algorithm features sub-linear training and inference time. We can even accomplish both the modeling and comparison of 10,000 different 64-track time series, each with 100 time steps (a typical EEG dataset) under 0.8 seconds. This performance gain allows for a rapid relevance feedback-driven adaption of the underlying pattern similarity model and enables the user to modify the speed-vs-accuracy trade-off gradually. We demonstrate superiority of PSEUDo in terms of efficiency, accuracy, and steerability through a quantitative performance comparison and a qualitative visual quality comparison to the state-of-the-art algorithms in the field. Moreover, we showcase the usability of PSEUDo through a case study demonstrating our visual pattern retrieval concepts in a large meteorological dataset. We find that our adaptive models can accurately capture the user's notion of similarity and allow for an understandable exploratory visual pattern retrieval in large multivariate time series datasets.

This paper studies early-stopped mirror descent applied to noisy sparse phase retrieval, which is the problem of recovering a $k$-sparse signal $\mathbf{x}^\star\in\mathbb{R}^n$ from a set of quadratic Gaussian measurements corrupted by sub-exponential noise. We consider the (non-convex) unregularized empirical risk minimization problem and show that early-stopped mirror descent, when equipped with the hyperbolic entropy mirror map and proper initialization, achieves a nearly minimax-optimal rate of convergence, provided the sample size is at least of order $k^2$ (modulo logarithmic term) and the minimum (in modulus) non-zero entry of the signal is on the order of $\|\mathbf{x}^\star\|_2/\sqrt{k}$. Our theory leads to a simple algorithm that does not rely on explicit regularization or thresholding steps to promote sparsity. More generally, our results establish a connection between mirror descent and sparsity in the non-convex problem of noisy sparse phase retrieval, adding to the literature on early stopping that has mostly focused on non-sparse, Euclidean, and convex settings via gradient descent. Our proof combines a potential-based analysis of mirror descent with a quantitative control on a variational coherence property that we establish along the path of mirror descent, up to a prescribed stopping time.