Learning to solve sequential physical reasoning problems from a scene image

In this article, we propose deep visual reasoning, which is a convolutional recurrent neural network that predicts discrete action sequences from an initial scene image for sequential manipulation problems that arise, for example, in task and motion planning (TAMP). Typical TAMP problems are formalized by combining reasoning on a symbolic, discrete level (e.g., first-order logic) with continuous motion planning such as nonlinear trajectory optimization. The action sequences represent the discrete decisions on a symbolic level, which, in turn, parameterize a nonlinear trajectory optimization problem. Owing to the great combinatorial complexity of possible discrete action sequences, a large number of optimization/motion planning problems have to be solved to find a solution, which limits the scalability of these approaches. To circumvent this combinatorial complexity, we introduce deep visual reasoning: based on a segmented initial image of the scene, a neural network directly predicts promising discrete action sequences such that ideally only one motion planning problem has to be solved to find a solution to the overall TAMP problem. Our method generalizes to scenes with many and varying numbers of objects, although being trained on only two objects at a time. This is possible by encoding the objects of the scene and the goal in (segmented) images as input to the neural network, instead of a fixed feature vector. We show that the framework can not only handle kinematic problems such as pick-and-place (as typical in TAMP), but also tool-use scenarios for planar pushing under quasi-static dynamic models. Here, the image-based representation enables generalization to other shapes than during training. Results show runtime improvements of several orders of magnitudes by, in many cases, removing the need to search over the discrete action sequences.

The Game Is Not over Yet—Go in the Post-AlphaGo Era

The game of Go was the last great challenge for artificial intelligence in abstract board games. AlphaGo was the first system to reach supremacy, and subsequent implementations further improved the state of the art. As in chess, the fall of the human world champion did not lead to the end of the game. Now, we have renewed interest in the game due to new questions that emerged in this development. How far are we from perfect play? Can humans catch up? How compressible is Go knowledge? What is the computational complexity of a perfect player? How much energy is really needed to play the game optimally? Here, we investigate these and related questions with respect to the special properties of Go (meaningful draws and extreme combinatorial complexity). Since traditional board games have an important role in human culture, our analysis is relevant in a broader context. What happens in the game world could forecast our relationship with AI entities, their explainability, and usefulness.

Neural Approximate Dynamic Programming for On-Demand Ride-Pooling

On-demand ride-pooling (e.g., UberPool, LyftLine, GrabShare) has recently become popular because of its ability to lower costs for passengers while simultaneously increasing revenue for drivers and aggregation companies (e.g., Uber). Unlike in Taxi on Demand (ToD) services – where a vehicle is assigned one passenger at a time – in on-demand ride-pooling, each vehicle must simultaneously serve multiple passengers with heterogeneous origin and destination pairs without violating any quality constraints. To ensure near real-time response, existing solutions to the real-time ride-pooling problem are myopic in that they optimise the objective (e.g., maximise the number of passengers served) for the current time step without considering the effect such an assignment could have on assignments in future time steps. However, considering the future effects of an assignment that also has to consider what combinations of passenger requests can be assigned to vehicles adds a layer of combinatorial complexity to the already challenging problem of considering future effects in the ToD case.A popular approach that addresses the limitations of myopic assignments in ToD problems is Approximate Dynamic Programming (ADP). Existing ADP methods for ToD can only handle Linear Program (LP) based assignments, however, as the value update relies on dual values from the LP. The assignment problem in ride pooling requires an Integer Linear Program (ILP) that has bad LP relaxations. Therefore, our key technical contribution is in providing a general ADP method that can learn from the ILP based assignment found in ride-pooling. Additionally, we handle the extra combinatorial complexity from combinations of passenger requests by using a Neural Network based approximate value function and show a connection to Deep Reinforcement Learning that allows us to learn this value-function with increased stability and sample-efficiency. We show that our approach easily outperforms leading approaches for on-demand ride-pooling on a real-world dataset by up to 16%, a significant improvement in city-scale transportation problems.

Identities on algebras and combinatorial properties of binary words

We consider polynomial identities and codimension growth of nonassociative algebras over a field of characte-ristics zero. We offer new approach which allows to construct nonassociative algebras starting from a given infinite binary word. The sequence of codimensions of such an algebra is closeely connected with combinatorial complexity of the defining word. These constructions give new examples of algebras with abnormal codimension growth. The first important achievement is that our algebras are finitely generated. The second one is that asymptotic behavior of codimension sequences is quite different unlike all previous examples.

The Combination of Morphological and Evolutionary Algorithms for Graph-based Pathfinding on Maps with Complex Topologies

One of the difficult problems to solve has always been and still remains the problem of finding a path either in a graphic chart or a graphic maze of large size. The main problem is that traditional algorithms require a lot of time due to combinatorial complexity. At the same time, both classical algorithms based on the search of variants (such as Dijkstra's algorithm, A*, ARA*, D* lite), and stochastic algorithms (ant algorithm, genetic), alongside with algorithms based on morphology (wave) are not always able to achieve the goal. The article proposes a new modification of the path-finding algorithm, which is a hybrid of the following: the morphological operations on graphic chart approach and genetic algorithm having a useful property of elasticity in time. The experiments (both synthetic and real data) have shown the feasibility of the proposed idea and its comparison with the most commonly used algorithms of contemporaneity.

Role of Combinatorial Complexity in Genetic Networks

A common motif found in genetic networks is the formation of large complexes. One difficulty in modeling this motif is the large number of possible intermediate complexes that can form. For instance, if a complex could contain up to 10 different proteins, 210 possible intermediate complexes can form. Keeping track of all complexes is difficult and often ignored in mathematical models. Here we present an algorithm to code ordinary differential equations (ODEs) to model genetic networks with combinatorial complexity. In these routines, the general binding rules, which counts for the majority of the reactions, are implemented automatically, thus the users only need to code a few specific reaction rules. Using this algorithm, we find that the behavior of these models depends greatly on the specific rules of complex formation. Through simulating three generic models for complex formation, we find that these models show widely different timescales, distribution of intermediate states, and ability to promote oscillations within feedback loops. These results provide tools for the incorporation of combinatorial complexity of genetic networks and show how this incorporation may be vital to accurately predict the network dynamics.

On Combinatorial Depth Measures

Given a set [Formula: see text] of points and a point [Formula: see text] in the plane, we define a function [Formula: see text] that provides a combinatorial characterization of the multiset of values [Formula: see text], where for each [Formula: see text], [Formula: see text] is the open half-plane determined by [Formula: see text] and [Formula: see text]. We introduce two new natural measures of depth, perihedral depth and eutomic depth, and we show how to express these and the well-known simplicial and Tukey depths concisely in terms of [Formula: see text]. The perihedral and eutomic depths of [Formula: see text] with respect to [Formula: see text] correspond respectively to the number of subsets of [Formula: see text] whose convex hull contains [Formula: see text], and the number of combinatorially distinct bisections of [Formula: see text] determined by a line through [Formula: see text]. We present algorithms to compute the depth of an arbitrary query point in [Formula: see text] time and medians (deepest points) with respect to these depth measures in [Formula: see text] and [Formula: see text] time respectively. For comparison, these results match or slightly improve on the corresponding best-known running times for simplicial depth, whose definition involves similar combinatorial complexity.