Related papers: Learning-augmented smooth integer programs with PA…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented…
We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneous linear…
Monotone learning describes learning processes in which expected performance consistently improves as the amount of training data increases. However, recent studies challenge this conventional wisdom, revealing significant gaps in the…
We consider integer and linear programming problems for which the linear constraints exhibit a (recursive) block-structure: The problem decomposes into independent and efficiently solvable sub-problems if a small number of constraints is…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
The present paper is about estimation and prediction in high-dimensional additive models under a sparsity assumption ($p\gg n$ paradigm). A PAC-Bayesian strategy is investigated, delivering oracle inequalities in probability. The…
Solving non-linear Diophantine systems lies at the mathematical core of integer optimization and cryptography. While the general unbounded problem is undecidable, even over bounded integer domains it remains classically intractable in the…
Network adaptation is essential for the efficient operation of Cloud-RANs. Unfortunately, it leads to highly intractable mixed-integer nonlinear programming problems. Existing solutions typically rely on convex relaxation, which yield…
Data-driven algorithms can adapt their internal structure or parameters to inputs from unknown application-specific distributions, by learning from a training sample of inputs. Several recent works have applied this approach to problems in…
A large body of the literature on automated program repair develops approaches where patches are automatically generated to be validated against an oracle (e.g., a test suite). Because such an oracle can be imperfect, the generated patches,…
We apply the PAC-Bayes theory to the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-bounds) and explicit trade-off…
We consider solving a combinatorial optimization problem with unknown knapsack constraints using a membership oracle for each unknown constraint such that, given a solution, the oracle determines whether the constraint is satisfied or not…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
A large body of the literature of automated program repair develops approaches where patches are generated to be validated against an oracle (e.g., a test suite). Because such an oracle can be imperfect, the generated patches, although…
We study reinforcement learning (RL) with linear function approximation. Existing algorithms for this problem only have high-probability regret and/or Probably Approximately Correct (PAC) sample complexity guarantees, which cannot guarantee…
This paper describes a simple, but effective sampling method for optimizing and learning a discrete approximation (or surrogate) of a multi-dimensional function along a one-dimensional line segment of interest. The method does not rely on…
We initiate the study of smoothed analysis for the sequential probability assignment problem with contexts. We study information-theoretically optimal minmax rates as well as a framework for algorithmic reduction involving the maximum…