A Residual-Based Message Passing Algorithm for Constraint Satisfaction Problems

Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in tackling hard computational tasks in optimization, inference, and learning problems. In the context of constraint satisfaction problems (CSPs), when a control parameter (such as constraint density) is tuned, multiple threshold phenomena emerge, signaling fundamental structural transitions in their solution space. Finding solutions around these transition points is exceedingly challenging for algorithm design, where message passing algorithms suffer from a large message fluctuation far from convergence. Here we introduce a residual-based updating step into message passing algorithms, in which messages varying large between consecutive steps are given a high priority in updating process. For the specific example of model RB, a typical prototype of random CSPs with growing domains, we show that our algorithm improves the convergence of message updating and increases the success probability in finding solutions around the satisfiability threshold with a low computational cost. Our approach to message passing algorithms should be of value for exploring their power in developing algorithms to find ground-state solutions and understand the detailed structure of solution space of hard optimization problems.

Mediating Between Contact Feasibility and Robustness of Trajectory Optimization Through Chance Complementarity Constraints

As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as failure to successfully make and maintain contact can be catastrophic. Here, we model uncertainty in terrain geometry and friction characteristics, and combine a risk-sensitive objective with chance constraints to provide a trade-off between robustness to uncertainty and constraint satisfaction with an arbitrarily high feasibility guarantee. We evaluate our approach in two simple examples: a push-block system for benchmarking and a single-legged hopper. We demonstrate that chance constraints alone produce trajectories similar to those produced using strict complementarity constraints; however, when equipped with a robust objective, we show the chance constraints can mediate a trade-off between robustness to uncertainty and strict constraint satisfaction. Thus, our study may represent an important step towards reasoning about contact uncertainty in motion planning.

The Complexity of Promise SAT on Non-Boolean Domains

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin et al. [SICOMP’17] proved a result known as “(2+ɛ)-SAT is NP-hard.” They showed that the problem of distinguishing k -CNF formulas that are g -satisfiable (i.e., some assignment satisfies at least g literals in every clause) from those that are not even 1-satisfiable is NP-hard if g/k < 1/2 and is in P otherwise. We study a generalisation of SAT on arbitrary finite domains, with clauses that are disjunctions of unary constraints, and establish analogous behaviour. Thus, we give a dichotomy for a natural fragment of promise constraint satisfaction problems ( PCSPs ) on arbitrary finite domains. The hardness side is proved using the algebraic approach via a new general NP-hardness criterion on polymorphisms, which is based on a gap version of the Layered Label Cover problem. We show that previously used criteria are insufficient—the problem hence gives an interesting benchmark of algebraic techniques for proving hardness of approximation in problems such as PCSPs.

Теория определимости в контексте информационно-коммуникационных систем

В работе обсуждается проблематика определимости и пространств отношений в исторической перспективе, обрисована роль Альфреда Тарского и Ларса Свенониуса, рассматриваются последние результаты, расширяющие полученные ранее для однородных структур, в частности на случай пополнимых вверх. Приложения включают языки описания баз данных, анализ CSP - Constraint Satisfaction Problem (обобщенной выполнимости).

An approach to finding a global optimum in constrained clustering tasks involving the assessments of several experts

An approach to solving the constrained clustering problem has been developed, based on the aggregation of data obtained as a result of evaluating the characteristics of clustered objects by several independent experts, and the analysis of alternative variants of clustering by constraint programming methods using original heuristics. Objects clusterized are represented as multisets, which makes it possible to use appropriate methods of aggregation of expert opinions. It is proposed to solve the constrained clustering problem as a constraint satisfaction problem. The main attention is paid to the issue of reducing the number and simplifying the constraints of the constraint satisfaction problem at the stage of its formalization. Within the framework of the approach, we have created: a) a method for estimating the optimal value of the objective function by hierarchical clustering of multisets, taking into account a priori constraints of the subject domain, and b) a method for generating additional constraints on the desired solution in the form of “smart tables”, based on the obtained estimate. The approach allows us to find the best partition in the problems of the class under consideration, which are characterized by a high dimension.

Control of Thruster-Assisted, Bipedal Legged Locomotion of the Harpy Robot

Fast constraint satisfaction, frontal dynamics stabilization, and avoiding fallovers in dynamic, bipedal walkers can be pretty challenging. The challenges include underactuation, vulnerability to external perturbations, and high computational complexity that arise when accounting for the system full-dynamics and environmental interactions. In this work, we study the potential roles of thrusters in addressing some of these locomotion challenges in bipedal robotics. We will introduce a thruster-assisted bipedal robot called Harpy. We will capitalize on Harpy’s unique design to propose an optimization-free approach to satisfy gait feasibility conditions. In this thruster-assisted legged locomotion, the reference trajectories can be manipulated to fulfill constraints brought on by ground contact and those prescribed for states and inputs. Unintended changes to the trajectories, especially those optimized to produce periodic orbits, can adversely affect gait stability and hybrid invariance. We will show our approach can still guarantee stability and hybrid invariance of the gaits by employing the thrusters in Harpy. We will also show that the thrusters can be leveraged to robustify the gaits by dodging fallovers or jumping over large obstacles.