Qualitative reasoning is an important subfield of artificial intelligence where one describes relationships with qualitative, rather than numerical, relations. Many such reasoning tasks, e.g., Allen's interval algebra, can be solved in $2^{O(n \cdot \log n)}$ time, but single-exponential running times $2^{O(n)}$ are currently far out of reach. In this paper we consider single-exponential algorithms via a multivariate analysis consisting of a fine-grained parameter $n$ (e.g., the number of variables) and a coarse-grained parameter $k$ expected to be relatively small. We introduce the classes FPE and XE of problems solvable in $f(k) \cdot 2^{O(n)}$, respectively $f(k)^n$, time, and prove several fundamental properties of these classes. We proceed by studying temporal reasoning problems and (1) show that the Partially Ordered Time problem of effective width $k$ is solvable in $16^{kn}$ time and is thus included in XE, and (2) that the network consistency problem for Allen's interval algebra with no interval overlapping with more than $k$ others is solvable in $(2nk)^{2k} \cdot 2^{n}$ time and is included in FPE. Our multivariate approach is in no way limited to these to specific problems and may be a generally useful approach for obtaining single-exponential algorithms.

Dynamic movement primitives are widely used for learning skills which can be demonstrated to a robot by a skilled human or controller. While their generalization capabilities and simple formulation make them very appealing to use, they possess no strong guarantees to satisfy operational safety constraints for a task. In this paper, we present constrained dynamic movement primitives (CDMP) which can allow for constraint satisfaction in the robot workspace. We present a formulation of a non-linear optimization to perturb the DMP forcing weights regressed by locally-weighted regression to admit a Zeroing Barrier Function (ZBF), which certifies workspace constraint satisfaction. We demonstrate the proposed CDMP under different constraints on the end-effector movement such as obstacle avoidance and workspace constraints on a physical robot. A video showing the implementation of the proposed algorithm using different manipulators in different environments could be found here https://youtu.be/hJegJJkJfys.

Graphical structures estimated by causal learning algorithms from time series data can provide highly misleading causal information if the causal timescale of the generating process fails to match the measurement timescale of the data. Although this problem has been recently recognized, practitioners have limited resources to respond to it, and so must continue using models that they know are likely misleading. Existing methods either (a) require that the difference between causal and measurement timescales is known; or (b) can handle only very small number of random variables when the timescale difference is unknown; or (c) apply to only pairs of variables, though with fewer assumptions about prior knowledge; or (d) return impractically too many solutions. This paper addresses all four challenges. We combine constraint programming with both theoretical insights into the problem structure and prior information about admissible causal interactions. The resulting system provides a practical approach that scales to significantly larger sets (>100) of random variables, does not require precise knowledge of the timescale difference, supports edge misidentification and parametric connection strengths, and can provide the optimum choice among many possible solutions. The cumulative impact of these improvements is gain of multiple orders of magnitude in speed and informativeness.

This paper studies a framework, projected fixed-point method, for graph matching. The framework contains a class of popular graph matching algorithms, including graduated assignment (GA), integer projected fixed-point method (IPFP) and doubly stochastic projected fixed-point method (DSPFP). We propose an adaptive strategy to tune the step size parameter in this framework. Such a strategy improves these algorithms in efficiency and accuracy. Further, it guarantees the convergence of the underlying algorithms. Some preliminary analysis based on distance geometry seems to support that the optimal step size parameter has a high probability of 1 when graphs are fully connected. Secondly, it is observed that a popular projection method, softassign, is sensitive to graphs' cardinality(size). We proposed a dynamical softassign algorithm that is robust to graphs' cardinality. Combining the adaptive step size and the dynamical softassign, we propose a novel graph matching algorithm: the adaptive projected fixed-point method with dynamical softassign. Various experiments demonstrate that the proposed algorithm is significantly faster than several other state-of-art algorithms with no loss of accuracy.

Belief Propagation (BP) is an important message-passing algorithm for various reasoning tasks over graphical models, including solving the Constraint Optimization Problems (COPs). It has been shown that BP can achieve state-of-the-art performance on various benchmarks by mixing old and new messages before sending the new one, i.e., damping. However, existing methods of tuning a static damping factor for BP not only are laborious but also harm their performance. Moreover, existing BP algorithms treat each variable node's neighbors equally when composing a new message, which also limits their exploration ability. To address these issues, we seamlessly integrate BP, Gated Recurrent Units (GRUs), and Graph Attention Networks (GATs) within the message-passing framework to reason about dynamic weights and damping factors for composing new BP messages. Our model, Deep Attentive Belief Propagation (DABP), takes the factor graph and the BP messages in each iteration as the input and infers the optimal weights and damping factors through GRUs and GATs, followed by a multi-head attention layer. Furthermore, unlike existing neural-based BP variants, we propose a novel self-supervised learning algorithm for DABP with a smoothed solution cost, which does not require expensive training labels and also avoids the common out-of-distribution issue through efficient online learning. Extensive experiments show that our model significantly outperforms state-of-the-art baselines.

Dynamic Movement Primitives (DMPs) offer great versatility for encoding, generating and adapting complex end-effector trajectories. DMPs are also very well suited to learning manipulation skills from human demonstration. However, the reactive nature of DMPs restricts their applicability for tool use and object manipulation tasks involving non-holonomic constraints, such as scalpel cutting or catheter steering. In this work, we extend the Cartesian space DMP formulation by adding a coupling term that enforces a pre-defined set of non-holonomic constraints. We obtain the closed-form expression for the constraint forcing term using the Udwadia-Kalaba method. This approach offers a clean and practical solution for guaranteed constraint satisfaction at run-time. Further, the proposed analytical form of the constraint forcing term enables efficient trajectory optimization subject to constraints. We demonstrate the usefulness of this approach by showing how we can learn robotic cutting skills from human demonstration.

Bandits with knapsacks (BwK) is an influential model of sequential decision-making under uncertainty that incorporates resource consumption constraints. In each round, the decision-maker observes an outcome consisting of a reward and a vector of nonnegative resource consumptions, and the budget of each resource is decremented by its consumption. In this paper we introduce a natural generalization of the stochastic BwK problem that allows non-monotonic resource utilization. In each round, the decision-maker observes an outcome consisting of a reward and a vector of resource drifts that can be positive, negative or zero, and the budget of each resource is incremented by its drift. Our main result is a Markov decision process (MDP) policy that has constant regret against a linear programming (LP) relaxation when the decision-maker knows the true outcome distributions. We build upon this to develop a learning algorithm that has logarithmic regret against the same LP relaxation when the decision-maker does not know the true outcome distributions. We also present a reduction from BwK to our model that shows our regret bound matches existing results.

We study the problem of online dynamic pricing with two types of fairness constraints: a "procedural fairness" which requires the proposed prices to be equal in expectation among different groups, and a "substantive fairness" which requires the accepted prices to be equal in expectation among different groups. A policy that is simultaneously procedural and substantive fair is referred to as "doubly fair". We show that a doubly fair policy must be random to have higher revenue than the best trivial policy that assigns the same price to different groups. In a two-group setting, we propose an online learning algorithm for the 2-group pricing problems that achieves $\tilde{O}(\sqrt{T})$ regret, zero procedural unfairness and $\tilde{O}(\sqrt{T})$ substantive unfairness over $T$ rounds of learning. We also prove two lower bounds showing that these results on regret and unfairness are both information-theoretically optimal up to iterated logarithmic factors. To the best of our knowledge, this is the first dynamic pricing algorithm that learns to price while satisfying two fairness constraints at the same time.

Structural decomposition methods, such as generalized hypertree decompositions, have been successfully used for solving constraint satisfaction problems (CSPs). As decompositions can be reused to solve CSPs with the same constraint scopes, investing resources in computing good decompositions is beneficial, even though the computation itself is hard. Unfortunately, current methods need to compute a completely new decomposition even if the scopes change only slightly. In this paper, we make the first steps toward solving the problem of updating the decomposition of a CSP $P$ so that it becomes a valid decomposition of a new CSP $P'$ produced by some modification of $P$. Even though the problem is hard in theory, we propose and implement a framework for effectively updating GHDs. The experimental evaluation of our algorithm strongly suggests practical applicability.

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.