Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost function in terms of expected values and higher moments of the states, and chance constraints that ensure probabilistic constraint satisfaction. The generalized polynomial chaos framework is used to propagate the time-invariant stochastic uncertainties through the nonlinear system dynamics, and to efficiently sample from the probability densities of the states to approximate the satisfaction probability of the chance constraints. To increase computational efficiency by avoiding excessive sampling, a statistical analysis is proposed to systematically determine a-priori the least conservative constraint tightening required at a given sample size to guarantee a desired feasibility probability of the sample-approximated chance constraint optimization problem. In addition, a method is presented for sample-based approximation of the analytic gradients of the chance constraints, which increases the optimization efficiency significantly. The proposed stochastic nonlinear model predictive control approach is applicable to a broad class of nonlinear systems with the sufficient condition that each term is analytic with respect to the states, and separable with respect to the inputs, states and parameters. The closed-loop performance of the proposed approach is evaluated using the Williams-Otto reactor with seven states, and ten uncertain parameters and initial conditions. The results demonstrate the efficiency of the approach for real-time stochastic model predictive control and its capability to systematically account for probabilistic uncertainties in contrast to a nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro

A Mining-Based Compression Approach for Constraint Satisfaction Problems

In this paper, we propose an extension of our Mining for SAT framework to Constraint satisfaction Problem (CSP). We consider n-ary extensional constraints (table constraints). Our approach aims to reduce the size of the CSP by exploiting the structure of the constraints graph and of its associated microstructure. More precisely, we apply itemset mining techniques to search for closed frequent itemsets on these two representation. Using Tseitin extension, we rewrite the whole CSP to another compressed CSP equivalent with respect to satisfiability. Our approach contrast with previous proposed approach by Katsirelos and Walsh, as we do not change the structure of the constraints.Comment: arXiv admin note: substantial text overlap with arXiv:1304.441

Constrained Policy Optimization for Controlled Self-Learning in Conversational AI Systems

Recently, self-learning methods based on user satisfaction metrics and contextual bandits have shown promising results to enable consistent improvements in conversational AI systems. However, directly targeting such metrics by off-policy bandit learning objectives often increases the risk of making abrupt policy changes that break the current user experience. In this study, we introduce a scalable framework for supporting fine-grained exploration targets for individual domains via user-defined constraints. For example, we may want to ensure fewer policy deviations in business-critical domains such as shopping, while allocating more exploration budget to domains such as music. Furthermore, we present a novel meta-gradient learning approach that is scalable and practical to address this problem. The proposed method adjusts constraint violation penalty terms adaptively through a meta objective that encourages balanced constraint satisfaction across domains. We conduct extensive experiments using data from a real-world conversational AI on a set of realistic constraint benchmarks. Based on the experimental results, we demonstrate that the proposed approach is capable of achieving the best balance between the policy value and constraint satisfaction rate

A Parallel and Distributed Framework for Constraint Solving

With the increased availability of affordable parallel and distributed hardware, programming models for these architectures has become the focus of significant attention. Constraint programming, which can be seen as the encoding of processes as a Constraint Satisfaction Problem, because of its data-driven and control-insensitive approach is a prime candidate to serve as the basis for a framework which effectively exploits parallel architectures. To effectually apply the power of distributed computational systems, there must be an effective sharing of the work involved in the search for a solution to a Constraint Satisfaction Problem (CSP) between all the participating agents, and it must happen dynamically, as it is hard to predict the effort associated with the exploration of some part of the search space. We describe and provide an initial experimental assessment of an implementation of a work stealing-based approach to distributed CSP solving, which relies on multiple back-ends for the distributed computing mechanisms -- from the multicore CPU to supercomputer clusters running MPI or other interprocess communication platforms

Confidence-based Reasoning in Stochastic Constraint Programming

In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the original problem being analysed; by solving this reduced problem, with a given confidence probability, we obtain assignments that satisfy the chance constraints in the original model within prescribed error tolerance thresholds. To achieve this, we blend concepts from stochastic constraint programming and statistics. We discuss both exact and approximate variants of our method. The framework we introduce can be immediately employed in concert with existing approaches for solving stochastic constraint programs. A thorough computational study on a number of stochastic combinatorial optimisation problems demonstrates the effectiveness of our approach.Comment: 53 pages, working draf

Humanoid Motion Description Language

In this paper we propose a description language for specifying motions for humanoid robots and for allowing humanoid robots to acquire motor skills. Locomotion greatly increases our ability to interact with our environments, which in turn increases our mental abilities. This principle also applies to humanoid robots. However, there are great difficulties to specify humanoid motions and to represent motor skills, which in most cases require four-dimensional space representations. We propose a representation framework that includes the following attributes: motion description layers, egocentric reference system, progressive quantized refinement, and automatic constraint satisfaction. We also outline strategies for acquiring new motor skills by learning from trial and error, macro approach, and programming. Then, we outline the development of a new humanoid motion description language called Cybele

Margin allocation and trade-off in complex systems design and optimization

Presented is an approach for interactive margin management. Existing methods enable a fixed set of allowable margin combinations to be identified, but these have limitations with regard to supporting interactive exploration of the effects of: 1) margins on other margins, 2) margins on performance and 3) margins on the probabilities of constraint satisfaction. To this purpose, the concept of a margin space is introduced. It is bi-directionally linked to the design space, to enable the designer to understand how assigning margins on certain parameters limits the allowable margins that can be assigned to other parameters. Also, a novel framework has been developed. It incorporates the margin space concept as well as enablers, including interactive visualization techniques, which can aide the designer to explore the margin and design spaces dynamically, as well as the effects of margins on the probability of constraint satisfaction and on performance. The framework was implemented into a prototype software tool, AirCADia, which was used for a qualitative evaluation by practicing designers. The evaluation, conducted as part of the EU TOICA project, demonstrated the usefulness of the approach