It is crucial for robots to be aware of the presence of constraints in order to acquire safe policies. However, explicitly specifying all constraints in an environment can be a challenging task. State-of-the-art constraint inference algorithms learn constraints from demonstrations, but tend to be computationally expensive and prone to instability issues. In this paper, we propose a novel Bayesian method that infers constraints based on preferences over demonstrations. The main advantages of our proposed approach are that it 1) infers constraints without calculating a new policy at each iteration, 2) uses a simple and more realistic ranking of groups of demonstrations, without requiring pairwise comparisons over all demonstrations, and 3) adapts to cases where there are varying levels of constraint violation. Our empirical results demonstrate that our proposed Bayesian approach infers constraints of varying severity, more accurately than state-of-the-art constraint inference methods.

The further possibilities in data management (Wang et al., 2022; uncertain nature of knowledge is widely observed Ren et al., 2023). in the real world, but does not align seamlessly with the first-order logic underpinning existing Uncertain knowledge is widely observed from the daily studies. To bridge this gap, we study the setting events (Zhang et al., 2020) to the interaction of biological of soft queries on uncertain knowledge, which systems (Szklarczyk et al., 2023). Besides, uncertainty is is motivated by the establishment of soft constraint also particularly pervasive in KGs because KGs are constructed programming. We further propose an MLbased by information extraction models that could introduce approach with both forward inference and errors (Angeli et al., 2015; Ponte & Croft, 2017) backward calibration to answer soft queries on and from large corpses that could be noisy (Carlson et al., large-scale, incomplete, and uncertain knowledge 2010). To represent the uncertain knowledge, confidence graphs. Theoretical discussions present that our values p are associated with triples in many well-established methods share the same complexity as state-ofthe-art KGs (Carlson et al., 2010; Speer et al., 2017; Szklarczyk inference algorithms for first-order queries.

Recent studies in neuro-symbolic learning have explored the integration of logical knowledge into deep learning via encoding logical constraints as an additional loss function. However, existing approaches tend to vacuously satisfy logical constraints through shortcuts, failing to fully exploit the knowledge. In this paper, we present a new framework for learning with logical constraints. Specifically, we address the shortcut satisfaction issue by introducing dual variables for logical connectives, encoding how the constraint is satisfied. We further propose a variational framework where the encoded logical constraint is expressed as a distributional loss that is compatible with the model's original training loss. The theoretical analysis shows that the proposed approach bears salient properties, and the experimental evaluations demonstrate its superior performance in both model generalizability and constraint satisfaction.

Neuro-symbolic learning generally consists of two separated worlds, i.e., neural network training and symbolic constraint solving, whose success hinges on symbol grounding, a fundamental problem in AI. This paper presents a novel, softened symbol grounding process, bridging the gap between the two worlds, and resulting in an effective and efficient neuro-symbolic learning framework. Technically, the framework features (1) modeling of symbol solution states as a Boltzmann distribution, which avoids expensive state searching and facilitates mutually beneficial interactions between network training and symbolic reasoning;(2) a new MCMC technique leveraging projection and SMT solvers, which efficiently samples from disconnected symbol solution spaces; (3) an annealing mechanism that can escape from %being trapped into sub-optimal symbol groundings. Experiments with three representative neuro symbolic learning tasks demonstrate that, owining to its superior symbol grounding capability, our framework successfully solves problems well beyond the frontier of the existing proposals.

Motivated by the cost heterogeneity in experimentation across different alternatives, we study the Best Arm Identification with Resource Constraints (BAIwRC) problem. The agent aims to identify the best arm under resource constraints, where resources are consumed for each arm pull. We make two novel contributions. We design and analyze the Successive Halving with Resource Rationing algorithm (SH-RR). The SH-RR achieves a near-optimal non-asymptotic rate of convergence in terms of the probability of successively identifying an optimal arm. Interestingly, we identify a difference in convergence rates between the cases of deterministic and stochastic resource consumption.

Unmanned Aerial Vehicle (UAVs) have become very popular in the last decade due to some advantages such as strong terrain adaptation, low cost, zero casualties, and so on. One of the most interesting advances in this field is the automation of mission planning (task allocation) and real-time replanning, which are highly useful to increase the autonomy of the vehicle and reduce the operator workload. These automated mission planning and replanning systems require a Human Computer Interface (HCI) that facilitates the visualization and selection of plans that will be executed by the vehicles. In addition, most missions should be assessed before their real-life execution. This paper extends QGroundControl, an open-source simulation environment for flight control of multiple vehicles, by adding a mission designer that permits the operator to build complex missions with tasks and other scenario items; an interface for automated mission planning and replanning, which works as a test bed for different algorithms, and a Decision Support System (DSS) that helps the operator in the selection of the plan. In this work, a complete guide of these systems and some practical use cases are provided.

Designing molecules with desirable properties, such as drug-likeliness and high binding affinities towards protein targets, is a challenging problem. In this paper, we propose the Dual-Space Optimization (DSO) method that integrates latent space sampling and data space selection to solve this problem. DSO iteratively updates a latent space generative model and a synthetic dataset in an optimization process that gradually shifts the generative model and the synthetic data towards regions of desired property values. Our generative model takes the form of a Latent Prompt Transformer (LPT) where the latent vector serves as the prompt of a causal transformer. Our extensive experiments demonstrate effectiveness of the proposed method, which sets new performance benchmarks across single-objective, multi-objective and constrained molecule design tasks.

Constrained Markov decision processes (CMDPs) are a common way to model safety constraints in reinforcement learning. State-of-the-art methods for efficiently solving CMDPs are based on primal-dual algorithms. For these algorithms, all currently known regret bounds allow for error cancellations -- one can compensate for a constraint violation in one round with a strict constraint satisfaction in another. This makes the online learning process unsafe since it only guarantees safety for the final (mixture) policy but not during learning. As Efroni et al. (2020) pointed out, it is an open question whether primal-dual algorithms can provably achieve sublinear regret if we do not allow error cancellations. In this paper, we give the first affirmative answer. We first generalize a result on last-iterate convergence of regularized primal-dual schemes to CMDPs with multiple constraints. Building upon this insight, we propose a model-based primal-dual algorithm to learn in an unknown CMDP. We prove that our algorithm achieves sublinear regret without error cancellations.

In the recent literature on machine learning and decision making, calibration has emerged as a desirable and widely-studied statistical property of the outputs of binary prediction models. However, the algorithmic aspects of measuring model calibration have remained relatively less well-explored. Motivated by [BGHN23], which proposed a rigorous framework for measuring distances to calibration, we initiate the algorithmic study of calibration through the lens of property testing. We define the problem of calibration testing from samples where given $n$ draws from a distribution $\mathcal{D}$ on (predictions, binary outcomes), our goal is to distinguish between the case where $\mathcal{D}$ is perfectly calibrated, and the case where $\mathcal{D}$ is $\varepsilon$-far from calibration. We design an algorithm based on approximate linear programming, which solves calibration testing information-theoretically optimally (up to constant factors) in time $O(n^{1.5} \log(n))$. This improves upon state-of-the-art black-box linear program solvers requiring $\Omega(n^\omega)$ time, where $\omega > 2$ is the exponent of matrix multiplication. We also develop algorithms for tolerant variants of our testing problem, and give sample complexity lower bounds for alternative calibration distances to the one considered in this work. Finally, we present preliminary experiments showing that the testing problem we define faithfully captures standard notions of calibration, and that our algorithms scale to accommodate moderate sample sizes.

Finding Minimal Unsatisfiable Subsets (MUSes) of binary constraints is a common problem in infeasibility analysis of over-constrained systems. However, because of the exponential search space of the problem, enumerating MUSes is extremely time-consuming in real applications. In this work, we propose to prune formulas using a learned model to speed up MUS enumeration. We represent formulas as graphs and then develop a graph-based learning model to predict which part of the formula should be pruned. Importantly, our algorithm does not require data labeling by only checking the satisfiability of pruned formulas. It does not even require training data from the target application because it extrapolates to data with different distributions. In our experiments we combine our algorithm with existing MUS enumerators and validate its effectiveness in multiple benchmarks including a set of real-world problems outside our training distribution. The experiment results show that our method significantly accelerates MUS enumeration on average on these benchmark problems.