DatalogMTL is an extension of Datalog with metric temporal operators that has found applications in temporal ontology-based data access and query answering, as well as in stream reasoning. Practical algorithms for DatalogMTL are reliant on materialisation-based reasoning, where temporal facts are derived in a forward chaining manner in successive rounds of rule applications. Current materialisation-based procedures are, however, based on a naive evaluation strategy, where the main source of inefficiency stems from redundant computations. In this paper, we propose a materialisation-based procedure which, analogously to the classical seminaive algorithm in Datalog, aims at minimising redundant computation by ensuring that each temporal rule instance is considered at most once during the execution of the algorithm. Our experiments show that our optimised seminaive strategy for DatalogMTL is able to significantly reduce materialisation times.

This paper studies the robustness aspect of reinforcement learning algorithms in the presence of errors. Specifically, we revisit the benchmark problem of discrete-time linear quadratic regulation (LQR) and study the long-standing open question: Under what conditions is the policy iteration method robustly stable for dynamical systems with unbounded, continuous state and action spaces? Using advanced stability results in control theory, it is shown that policy iteration for LQR is inherently robust to small errors and enjoys local input-to-state stability: whenever the error in each iteration is bounded and small, the solutions of the policy iteration algorithm are also bounded, and, moreover, enter and stay in a small neighborhood of the optimal LQR solution. As an application, a novel off-policy optimistic least-squares policy iteration for the LQR problem is proposed, when the system dynamics are subjected to additive stochastic disturbances. The proposed new results in robust reinforcement learning are validated by a numerical example.

This paper presents a new approach of automatic text summarization which combines domain oriented text analysis (DoTA) and rhetorical structure theory (RST) in a grammar form: the attributed rhetorical structure grammar (ARSG), where the non-terminal symbols are domain keywords, called domain relations, while the rhetorical relations serve as attributes. We developed machine learning algorithms for learning such a grammar from a corpus of sample domain texts, as well as parsing algorithms for the learned grammar, together with adjustable text summarization algorithms for generating domain specific summaries. Our practical experiments have shown that with support of domain knowledge the drawback of missing very large training data set can be effectively compensated. We have also shown that the knowledge based approach may be made more powerful by introducing grammar parsing and RST as inference engine. For checking the feasibility of model transfer, we introduced a technique for mapping a grammar from one domain to others with acceptable cost. We have also made a comprehensive comparison of our approach with some others.

We consider the asymmetric orthogonal tensor decomposition problem, and present an orthogonalized alternating least square algorithm that converges to rank-$r$ of the true tensor factors simultaneously in $O(\log(\log(\frac{1}{\epsilon})))$ steps under our proposed Trace Based Initialization procedure. Trace Based Initialization requires $O(1/{\log (\frac{\lambda_{r}}{\lambda_{r+1}})})$ number of matrix subspace iterations to guarantee a "good" initialization for the simultaneous orthogonalized ALS method, where $\lambda_r$ is the $r$-th largest singular value of the tensor. We are the first to give a theoretical guarantee on orthogonal asymmetric tensor decomposition using Trace Based Initialization procedure and the orthogonalized alternating least squares. Our Trace Based Initialization also improves convergence for symmetric orthogonal tensor decomposition.

We introduce a new notion of systematicity for satisfiability algorithms with restarts, saying that an algorithm is strongly systematic if it is systematic independent of restart policy but weakly systematic if it is systematic for some restart policies but not others. We show that existing satisfiability engines are generally only weakly systematic, and describe flex, a strongly systematic algorithm that uses an amount of memory polynomial in the size of the problem. On large number factoring problems, flex appears to outperform weakly systematic approaches.

Recent advances in Symbolic Dynamic Programming (SDP) combined withthe extended algebraic decision diagram (XADD) have provided exactsolutions for expressive subclasses of finite-horizon Hybrid MarkovDecision Processes (HMDPs) with mixed continuous and discrete stateand action parameters. Unfortunately, SDP suffers from two majordrawbacks: (1) it solves for all states and can be intractable formany problems that inherently have large optimal XADD value functionrepresentations; and (2) it cannot maintain compact (pruned) XADDrepresentations for domains with nonlinear dynamics and reward due tothe need for nonlinear constraint checking. In this work, wesimultaneously address both of these problems by introducing real-timeSDP (RTSDP). RTSDP addresses (1) by focusing the solution and valuerepresentation only on regions reachable from a set of initial statesand RTSDP addresses (2) by using visited states as witnesses ofreachable regions to assist in pruning irrelevant or unreachable(nonlinear) regions of the value function. To this end, RTSDP enjoysprovable convergence over the set of initial states and substantialspace and time savings over SDP as we demonstrate in a variety of hybrid domains ranging from inventory to reservoir to traffic control.