Recent advances in constrained reinforcement learning (RL) have endowed reinforcement learning with certain safety guarantees. However, deploying existing constrained RL algorithms in continuous control tasks with general hard constraints remains challenging, particularly in those situations with non-convex hard constraints. Inspired by the generalized reduced gradient (GRG) algorithm, a classical constrained optimization technique, we propose a reduced policy optimization (RPO) algorithm that combines RL with GRG to address general hard constraints. RPO partitions actions into basic actions and nonbasic actions following the GRG method and outputs the basic actions via a policy network. Subsequently, RPO calculates the nonbasic actions by solving equations based on equality constraints using the obtained basic actions. The policy network is then updated by implicitly differentiating nonbasic actions with respect to basic actions. Additionally, we introduce an action projection procedure based on the reduced gradient and apply a modified Lagrangian relaxation technique to ensure inequality constraints are satisfied. To the best of our knowledge, RPO is the first attempt that introduces GRG to RL as a way of efficiently handling both equality and inequality hard constraints. It is worth noting that there is currently a lack of RL environments with complex hard constraints, which motivates us to develop three new benchmarks: two robotics manipulation tasks and a smart grid operation control task. With these benchmarks, RPO achieves better performance than previous constrained RL algorithms in terms of both cumulative reward and constraint violation. We believe RPO, along with the new benchmarks, will open up new opportunities for applying RL to real-world problems with complex constraints.

Generative models can produce synthetic patient records for analytical tasks when real data is unavailable or limited. However, current methods struggle with adhering to domain-specific knowledge and removing invalid data. We present ConSequence, an effective approach to integrating domain knowledge into sequential generative neural network outputs. Our rule-based formulation includes temporal aggregation and antecedent evaluation modules, ensured by an efficient matrix multiplication formulation, to satisfy hard and soft logical constraints across time steps. Existing constraint methods often fail to guarantee constraint satisfaction, lack the ability to handle temporal constraints, and hinder the learning and computational efficiency of the model. In contrast, our approach efficiently handles all types of constraints with guaranteed logical coherence. We demonstrate ConSequence's effectiveness in generating electronic health records, outperforming competitors in achieving complete temporal and spatial constraint satisfaction without compromising runtime performance or generative quality. Specifically, ConSequence successfully prevents all rule violations while improving the model quality in reducing its test perplexity by 5% and incurring less than a 13% slowdown in generation speed compared to an unconstrained model.

While semidefinite programming (SDP) has traditionally been limited to moderate-sized problems, recent algorithms augmented with matrix sketching techniques have enabled solving larger SDPs. However, these methods achieve scalability at the cost of an increase in the number of necessary iterations, resulting in slower convergence as the problem size grows. Furthermore, they require iteration-dependent parameter schedules that prohibit effective utilization of warm-start initializations important in practical applications with incrementally-arriving data or mixed-integer programming. We present SpecBM, a provably correct, fast and scalable algorithm for solving massive SDPs that can leverage a warm-start initialization to further accelerate convergence. Our proposed algorithm is a spectral bundle method for solving general SDPs containing both equality and inequality constraints. Moveover, when augmented with an optional matrix sketching technique, our algorithm achieves the dramatically improved scalability of previous work while sustaining convergence speed. We empirically demonstrate the effectiveness of our method, both with and without warm-starting, across multiple applications with large instances. For example, on a problem with 600 million decision variables, SpecBM achieved a solution of standard accuracy in less than 7 minutes, where the previous state-of-the-art scalable SDP solver requires more than 16 hours. Our method solves an SDP with more than 10^13 decision variables on a single machine with 16 cores and no more than 128GB RAM; the previous state-of-the-art method had not achieved an accurate solution after 72 hours on the same instance. We make our implementation in pure JAX publicly available.

Causal Structure Learning (CSL), amounting to extracting causal relations among the variables in a dataset, is widely perceived as an important step towards robust and transparent models. Constraint-based CSL leverages conditional independence tests to perform causal discovery. We propose Shapley-PC, a novel method to improve constraint-based CSL algorithms by using Shapley values over the possible conditioning sets to decide which variables are responsible for the observed conditional (in)dependences. We prove soundness and asymptotic consistency and demonstrate that it can outperform state-of-the-art constraint-based, search-based and functional causal model-based methods, according to standard metrics in CSL.

Temporal facts, which are used to describe events that occur during specific time periods, have become a topic of increased interest in the field of knowledge graph (KG) research. In terms of quality management, the introduction of time restrictions brings new challenges to maintaining the temporal consistency of KGs. Previous studies rely on manually enumerated temporal constraints to detect conflicts, which are labor-intensive and may have granularity issues. To address this problem, we start from the common pattern of temporal facts and propose a pattern-based temporal constraint mining method, PaTeCon. Unlike previous studies, PaTeCon uses graph patterns and statistical information relevant to the given KG to automatically generate temporal constraints, without the need for human experts. In this paper, we illustrate how this method can be optimized to achieve significant speed improvement. We also annotate Wikidata and Freebase to build two new benchmarks for conflict detection. Extensive experiments demonstrate that our pattern-based automatic constraint mining approach is highly effective in generating valuable temporal constraints.

This work develops a first Model Predictive Control for European Space Agencies 3-dof free-floating platform. The challenges of the platform are the on/off thrusters, which cannot be actuated continuously and which are subject to certain timing constraints. This work compares penalty-term, Linear Complementarity Constraints, and classical Mixed Integer formulations in order to develop a controller that natively handles binary inputs. Furthermore, linear constraints are proposed which enforce the timing constraints. Only the Mixed Integer formulation turns out to work sufficiently. Hence, this work develops a new Mixed Integer MPC on the decoupled model of the platform. Feasibility analysis and simulation results show that for a short enough prediction horizon, this controller can (sub)optimally stabilize and control the system under consideration of the constraints in real-time.

Constraint Programming (CP) has been successfully used to model and solve complex combinatorial problems. However, modeling is often not trivial and requires expertise, which is a bottleneck to wider adoption. In Constraint Acquisition (CA), the goal is to assist the user by automatically learning the model. In (inter)active CA, this is done by interactively posting queries to the user, e.g., asking whether a partial solution satisfies their (unspecified) constraints or not. While interac tive CA methods learn the constraints, the learning is related to symbolic concept learning, as the goal is to learn an exact representation. However, a large number of queries is still required to learn the model, which is a major limitation. In this paper, we aim to alleviate this limitation by tightening the connection of CA and Machine Learning (ML), by, for the first time in interactive CA, exploiting statistical ML methods. We propose to use probabilistic classification models to guide interactive CA to generate more promising queries. We discuss how to train classifiers to predict whether a candidate expression from the bias is a constraint of the problem or not, using both relation-based and scope-based features. We then show how the predictions can be used in all layers of interactive CA: the query generation, the scope finding, and the lowest-level constraint finding. We experimentally evaluate our proposed methods using different classifiers and show that our methods greatly outperform the state of the art, decreasing the number of queries needed to converge by up to 72%.

In the article, within the framework of the Boolean Satisfiability problem (SAT), the problem of estimating the hardness of specific Boolean formulas w.r.t. a specific complete SAT solving algorithm is considered. Based on the well-known Strong Backdoor Set (SBS) concept, we introduce the notion of decomposition hardness (d-hardness). If $B$ is an arbitrary subset of the set of variables occurring in a SAT formula $C$, and $A$ is an arbitrary complete SAT solver , then the d-hardness expresses an estimate of the hardness of $C$ w.r.t. $A$ and $B$. We show that the d-hardness of $C$ w.r.t. a particular $B$ can be expressed in terms of the expected value of a special random variable associated with $A$, $B$, and $C$. For its computational evaluation, algorithms based on the Monte Carlo method can be used. The problem of finding $B$ with the minimum value of d-hardness is formulated as an optimization problem for a pseudo-Boolean function whose values are calculated as a result of a probabilistic experiment. To minimize this function, we use evolutionary algorithms. In the experimental part, we demonstrate the applicability of the concept of d-hardness and the methods of its estimation to solving hard unsatisfiable SAT instances.

Graph matching is a fundamental problem in pattern recognition, with many applications such as software analysis and computational biology. One well-known type of graph matching problem is graph isomorphism, which consists of deciding if two graphs are identical. Despite its usefulness, the properties that one may check using graph isomorphism are rather limited, since it only allows strict equality checks between two graphs. For example, it does not allow one to check complex structural properties such as if the target graph is an arbitrary length sequence followed by an arbitrary size loop. We propose a generalization of graph isomorphism that allows one to check such properties through a declarative specification. This specification is given in the form of a Regular Graph Pattern (ReGaP), a special type of graph, inspired by regular expressions, that may contain wildcard nodes that represent arbitrary structures such as variable-sized sequences or subgraphs. We propose a SAT-based algorithm for checking if a target graph matches a given ReGaP. We also propose a preprocessing technique for improving the performance of the algorithm and evaluate it through an extensive experimental evaluation on benchmarks from the CodeSearchNet dataset.

This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating preferences over so-called \emph{swaps}, for which optimal solutions in general are already known to be of exponential size. We first analyze a trivial 2-approximation algorithm that simply outputs the best of the given input preferences, and establish a structural condition under which the approximation ratio of this algorithm is improved to $4/3$. We then propose a polynomial-time approximation algorithm whose outputs are provably no worse than those of the trivial algorithm, but often substantially better. A family of problem instances is presented for which our improved algorithm produces optimal solutions, while, for any $\varepsilon$, the trivial algorithm can\emph{not}\/ attain a $(2-\varepsilon)$-approximation. These results may lead to the first polynomial-time approximation algorithm that solves the CP-net aggregation problem for swaps with an approximation ratio substantially better than $2$.