Custom-Design of FDR Encodings: The Case of Red-Black Planning

Classical planning tasks are commonly described in PDDL, while most planning systems operate on a grounded finite-domain representation (FDR). The translation of PDDL into FDR is complex and has a lot of choice points---it involves identifying so called mutex groups---but most systems rely on the translator that comes with Fast Downward. Yet the translation choice points can strongly impact performance. Prior work has considered optimizing FDR encodings in terms of the number of variables produced. Here we go one step further by proposing to custom-design FDR encodings, optimizing the encoding to suit particular planning techniques. We develop such a custom design here for red-black planning, a partial delete relaxation technique. The FDR encoding affects the causal graph and the domain transition graph structures, which govern the tractable fragment of red-black planning and hence affects the respective heuristic function. We develop integer linear programming techniques optimizing the scope of that fragment in the resulting FDR encoding. We empirically show that the performance of red-black planning can be improved through such FDR custom design.

Design of a recommendation system based on the transition graph

A recommendation system has been built for a web resource’s users that applies statistics about user activities to provide recommendations. The purpose of the system operation is to provide recommendations in the form of an orderly sequence of HTML pages of the resource suggested for the user. The ranking procedure uses statistical information about user transitions between web resource pages. The web resource model is represented in the form of a web graph; the user behavior model is shown as a graph of transitions between resource pages. The web graph is represented by an adjacency matrix; for the transition graph, a weighted matrix of probabilities of transitions between the vertices of the graph has been constructed. It was taken into consideration that user transitions between pages of a web resource may involve entering a URL in the address bar of a browser or by clicking on a link in the current page. The user’s transition between vertices in a finite graph according to probabilities determined by the weight of the graph’s edges is represented by a homogeneous Markov chain and is considered a process of random walk on the graph with the possibility of moving to a random vertex. Random Walk with Restarts was used to rank web resource pages for a particular user. Numerical analysis has been performed for an actual online store website. The initial data on user sessions are divided into training and test samples. According to the training sample, a weighted matrix of the probability of user transitions between web resource pages was constructed. To assess the quality of the built recommendation system, the accuracy, completeness, and Half-life Utility metrics were used. On the elements of the test sample, the accuracy value of 65‒68 % was obtained, the optimal number of elements in the recommendation list was determined. The influence of model parameters on the quality of recommendation systems was investigated.

Companions and an Essential Motion of a Reaction System

For a family of sets we consider elements that belong to the same sets within the family as companions. The global dynamics of a reactions system (as introduced by Ehrenfeucht and Rozenberg) can be represented by a directed graph, called a transition graph, which is uniquely determined by a one-out subgraph, called the 0-context graph. We consider the companion classes of the outsets of a transition graph and introduce a directed multigraph, called an essential motion, whose vertices are such companion classes. We show that all one-out graphs obtained from an essential motion represent 0-context graphs of reactions systems with isomorphic transition graphs. All such 0-context graphs are obtained from one another by swapping the outgoing edges of companion vertices.

Complete transition diagrams of generic Hamiltonian flows with a few heteroclinic orbits

We study the transition graph of generic Hamiltonian surface flows, whose vertices are the topological equivalence classes of generic Hamiltonian surface flows and whose edges are the generic transitions. Using the transition graph, we can describe time evaluations of generic Hamiltonian surface flows (e.g., fluid phenomena) as walks on the graph. We propose a method for constructing the complete transition graph of all generic Hamiltonian flows. In fact, we construct two complete transition graphs of Hamiltonian surface flows having three and four genus elements. Moreover, we demonstrate that a lower bound on the transition distance between two Hamiltonian surface flows with any number of genus elements can be calculated by solving an integer programming problem using vector representations of Hamiltonian surface flows.

Companions and an Essential Motion of a Reaction System

For a family of sets we consider elements that belong to the same sets within the family as companions. The global dynamics of a reactions system (as introduced by Ehrenfeucht and Rozenberg) can be represented by a directed graph, called a transition graph, which is uniquely determined by a one-out subgraph, called the 0-context graph. We consider the companion classes of the outsets of a transition graph and introduce a directed multigraph, called an essential motion, whose vertices are such companion classes. We show that all one-out graphs obtained from an essential motion represent 0-context graphs of reactions systems with isomorphic transition graphs. All such 0-context graphs are obtained from one another by swapping the outgoing edges of companion vertices.

Search Tree Pruning for Progressive Neural Architecture Search (Student Abstract)

Our neural architecture search algorithm progressively searches a tree of neural network architectures. Child nodes are created by inserting new layers determined by a transition graph into a parent network up to a maximum depth and pruned when performance is worse than its parent. This increases efficiency but makes the algorithm greedy. Simpler networks are successfully found before more complex ones that can achieve benchmark performance similar to other top-performing networks.