Clustering is a well-known unsupervised machine learning approach capable of automatically grouping discrete sets of instances with similar characteristics. Constrained clustering is a semi-supervised extension to this process that can be used when expert knowledge is available to indicate constraints that can be exploited. Well-known examples of such constraints are must-link (indicating that two instances belong to the same group) and cannot-link (two instances definitely do not belong together). The research area of constrained clustering has grown significantly over the years with a large variety of new algorithms and more advanced types of constraints being proposed. However, no unifying overview is available to easily understand the wide variety of available methods, constraints and benchmarks. To remedy this, this study presents in-detail the background of constrained clustering and provides a novel ranked taxonomy of the types of constraints that can be used in constrained clustering. In addition, it focuses on the instance-level pairwise constraints, and gives an overview of its applications and its historical context. Finally, it presents a statistical analysis covering 307 constrained clustering methods, categorizes them according to their features, and provides a ranking score indicating which methods have the most potential based on their popularity and validation quality. Finally, based upon this analysis, potential pitfalls and future research directions are provided.

In this paper, we present a new multibody physics simulation framework that utilizes the subsystem-based structure and the Alternating Direction Method of Multiplier (ADMM). The major challenge in simulating complex high degree of freedom systems is a large number of coupled constraints and large-sized matrices. To address this challenge, we first split the multibody into several subsystems and reformulate the dynamics equation into a subsystem perspective based on the structure of their interconnection. Then we utilize ADMM with our novel subsystem-based variable splitting scheme to solve the equation, which allows parallelizable and modular architecture. The resulting algorithm is fast, scalable, versatile, and converges well while maintaining solution consistency. Several illustrative examples are implemented with performance evaluation results showing advantages over other state-of-the-art algorithms.

We propose a logic of east and west (LEW ) for points in 1D Euclidean space. It formalises primitive direction relations: east (E), west (W) and indeterminate east/west (Iew). It has a parameter τ ∈ N>1, which is referred to as the level of indeterminacy in directions. For every τ ∈ N>1, we provide a sound and complete axiomatisation of LEW , and prove that its satisfiability problem is NP-complete. In addition, we show that the finite axiomatisability of LEW depends on τ : if τ = 2 or τ = 3, then there exists a finite sound and complete axiomatisation; if τ > 3, then the logic is not finitely axiomatisable. LEW can be easily extended to higher-dimensional Euclidean spaces. Extending LEW to 2D Euclidean space makes it suitable for reasoning about not perfectly aligned representations of the same spatial objects in different datasets, for example, in crowd-sourced digital maps.

Autonomous vehicles face the problem of optimizing the expected performance of subsequent maneuvers while bounding the risk of collision with surrounding dynamic obstacles. These obstacles, such as agent vehicles, often exhibit stochastic transitions that should be accounted for in a timely and safe manner. The Constrained Stochastic Shortest Path problem (C-SSP) is a formalism for planning in stochastic environments under certain types of operating constraints. While C-SSP allows specifying constraints in the planning problem, it does not allow for bounding the probability of constraint violation, which is desired in safety-critical applications. This work's first contribution is an exact integer linear programming formulation for Chance-constrained SSP (CC-SSP) that attains deterministic policies. Second, a randomized rounding procedure is presented for stochastic policies. Third, we show that the CC-SSP formalism can be generalized to account for constraints that span through multiple time steps. Evaluation results show the usefulness of our approach in benchmark problems compared to existing approaches.

In real-world decision-making, uncertainty is important yet difficult to handle. Stochastic dominance provides a theoretically sound approach for comparing uncertain quantities, but optimization with stochastic dominance constraints is often computationally expensive, which limits practical applicability. In this paper, we develop a simple yet efficient approach for the problem, the Light Stochastic Dominance Solver (light-SD), that leverages useful properties of the Lagrangian. We recast the inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability and leads to tractable updates or even closed-form solutions for gradient calculations. We prove convergence of the algorithm and test it empirically. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.

Model Predictive Path Integral (MPPI) control is a type of sampling-based model predictive control that simulates thousands of trajectories and uses these trajectories to synthesize optimal controls on-the-fly. In practice, however, MPPI encounters problems limiting its application. For instance, it has been observed that MPPI tends to make poor decisions if unmodeled dynamics or environmental disturbances exist, preventing its use in safety-critical applications. Moreover, the multi-threaded simulations used by MPPI require significant onboard computational resources, making the algorithm inaccessible to robots without modern GPUs. To alleviate these issues, we propose a novel (Shield-MPPI) algorithm that provides robustness against unpredicted disturbances and achieves real-time planning using a much smaller number of parallel simulations on regular CPUs. The novel Shield-MPPI algorithm is tested on an aggressive autonomous racing platform both in simulation and using experiments. The results show that the proposed controller greatly reduces the number of constraint violations compared to state-of-the-art robust MPPI variants and stochastic MPC methods.

Recent research has shown that integrating domain knowledge into deep learning architectures is effective -- it helps reduce the amount of required data, improves the accuracy of the models' decisions, and improves the interpretability of models. However, the research community is missing a convened benchmark for systematically evaluating knowledge integration methods. In this work, we create a benchmark that is a collection of nine tasks in the domains of natural language processing and computer vision. In all cases, we model external knowledge as constraints, specify the sources of the constraints for each task, and implement various models that use these constraints. We report the results of these models using a new set of extended evaluation criteria in addition to the task performances for a more in-depth analysis. This effort provides a framework for a more comprehensive and systematic comparison of constraint integration techniques and for identifying related research challenges. It will facilitate further research for alleviating some problems of state-of-the-art neural models.

The safe linear bandit problem (SLB) is an online approach to linear programming with unknown objective and unknown round-wise constraints, under stochastic bandit feedback of rewards and safety risks of actions. We study aggressive \emph{doubly-optimistic play} in SLBs, and their role in avoiding the strong assumptions and poor efficacy associated with extant pessimistic-optimistic solutions. We first elucidate an inherent hardness in SLBs due the lack of knowledge of constraints: there exist `easy' instances, for which suboptimal extreme points have large `gaps', but on which SLB methods must still incur $\Omega(\sqrt{T})$ regret and safety violations due to an inability to refine the location of optimal actions to arbitrary precision. In a positive direction, we propose and analyse a doubly-optimistic confidence-bound based strategy for the safe linear bandit problem, DOSLB, which exploits supreme optimism by using optimistic estimates of both reward and safety risks to select actions. Using a novel dual analysis, we show that despite the lack of knowledge of constraints, DOSLB rarely takes overly risky actions, and obtains tight instance-dependent $O(\log^2 T)$ bounds on both efficacy regret and net safety violations up to any finite precision, thus yielding large efficacy gains at a small safety cost and without strong assumptions. Concretely, we argue that algorithm activates noisy versions of an `optimal' set of constraints at each round, and activation of suboptimal sets of constraints is limited by the larger of a safety and efficacy gap we define.

Determining the role of event arguments is a crucial subtask of event extraction. Most previous supervised models leverage costly annotations, which is not practical for open-domain applications. In this work, we propose to use global constraints with prompting to effectively tackles event argument classification without any annotation and task-specific training. Specifically, given an event and its associated passage, the model first creates several new passages by prefix prompts and cloze prompts, where prefix prompts indicate event type and trigger span, and cloze prompts connect each candidate role with the target argument span. Then, a pre-trained language model scores the new passages, making the initial prediction. Our novel prompt templates can easily adapt to all events and argument types without manual effort. Next, the model regularizes the prediction by global constraints exploiting cross-task, cross-argument, and cross-event relations. Extensive experiments demonstrate our model's effectiveness: it outperforms the best zero-shot baselines by 12.5% and 10.9% F1 on ACE and ERE with given argument spans and by 4.3% and 3.3% F1, respectively, without given argument spans. We have made our code publicly available.

In many applications of Reinforcement Learning (RL), it is critically important that the algorithm performs safely, such that instantaneous hard constraints are satisfied at each step, and unsafe states and actions are avoided. However, existing algorithms for ''safe'' RL are often designed under constraints that either require expected cumulative costs to be bounded or assume all states are safe. Thus, such algorithms could violate instantaneous hard constraints and traverse unsafe states (and actions) in practice. Therefore, in this paper, we develop the first near-optimal safe RL algorithm for episodic Markov Decision Processes with unsafe states and actions under instantaneous hard constraints and the linear mixture model. It not only achieves a regret $\tilde{O}(\frac{d H^3 \sqrt{dK}}{\Delta_c})$ that tightly matches the state-of-the-art regret in the setting with only unsafe actions and nearly matches that in the unconstrained setting, but is also safe at each step, where $d$ is the feature-mapping dimension, $K$ is the number of episodes, $H$ is the number of steps in each episode, and $\Delta_c$ is a safety-related parameter. We also provide a lower bound $\tilde{\Omega}(\max\{dH \sqrt{K}, \frac{H}{\Delta_c^2}\})$, which indicates that the dependency on $\Delta_c$ is necessary. Further, both our algorithm design and regret analysis involve several novel ideas, which may be of independent interest.