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Bound propagation is an important Artificial Intelligence technique used in Constraint Programming tools to deal with numerical constraints. It is typically embedded within a search procedure ("branch and prune") and used at every node of…
The celebrated result of Kabanets and Impagliazzo (Computational Complexity, 2004) showed that PIT algorithms imply circuit lower bounds, and vice versa. Since then it has been a major challenge to understand the precise connections between…
Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…
Algorithm selection is typically based on models of algorithm performance, learned during a separate offline training sequence, which can be prohibitively expensive. In recent work, we adopted an online approach, in which a performance…
In machine learning, the selection of a promising model from a potentially large number of competing models and the assessment of its generalization performance are critical tasks that need careful consideration. Typically, model selection…
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
Optimal Transport (OT) is a fundamental tool for comparing probability distributions, but its exact computation remains prohibitive for large datasets. In this work, we introduce novel families of upper and lower bounds for the OT problem…
We introduce lower-bound certificates for classical planning tasks, which can be used to prove the unsolvability of a task or the optimality of a plan in a way that can be verified by an independent third party. We describe a general…
We consider the problem of tracking a target whose dynamics is modeled by a continuous It\=o semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds…
Different techniques have been used to prove several transference theorems of the form "nontrivial algorithms for a circuit class C yield circuit lower bounds against C". In this survey we revisit many of these results. We discuss how…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
In this paper, we evaluate the capability of transformer-based language models in making inferences over uncertain text that includes uncertain rules of reasoning. We cover both Pre-trained Language Models (PLMs) and generative Large…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of…
We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel sound and complete witnesses for LTL verification over imperative programs. Our…
In automated planning, the need for explanations arises when there is a mismatch between a proposed plan and the user's expectation. We frame Explainable AI Planning in the context of the plan negotiation problem, in which a succession of…
We study how to utilize (possibly machine-learned) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. The goal is to minimize the number of queries needed to solve the problem. We consider…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is…