Related papers: How hard is learning to cut? Trade-offs and sample…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from…
Cutting-plane methods have enabled remarkable successes in integer programming over the last few decades. State-of-the-art solvers integrate a myriad of cutting-plane techniques to speed up the underlying tree-search algorithm used to find…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
Data-driven algorithm design is a paradigm that uses statistical and machine learning techniques to select from a class of algorithms for a computational problem an algorithm that has the best expected performance with respect to some…
Learning with few samples is a major challenge for parameter-rich models like deep networks. In contrast, people learn complex new concepts even from very few examples, suggesting that the sample complexity of learning can often be reduced.…
The branch-and-cut algorithm is the method of choice to solve large scale integer programming problems in practice. A key ingredient of branch-and-cut is the use of cutting planes which are derived constraints that reduce the search space…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
Structured prediction can be considered as a generalization of many standard supervised learning tasks, and is usually thought as a simultaneous prediction of multiple labels. One standard approach is to maximize a score function on the…
In modern deep learning, algorithmic choices (such as width, depth, and learning rate) are known to modulate nuanced resource tradeoffs. This work investigates how these complexities necessarily arise for feature learning in the presence of…
Efficient sampling from constraint manifolds, and thereby generating a diverse set of solutions for feasibility problems, is a fundamental challenge. We consider the case where a problem is factored, that is, the underlying nonlinear…
Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs…
While much of the work in the design of convolutional networks over the last five years has revolved around the empirical investigation of the importance of depth, filter sizes, and number of feature channels, recent studies have shown that…
Social and real-world considerations such as robustness, fairness, social welfare and multi-agent tradeoffs have given rise to multi-distribution learning paradigms, such as collaborative learning, group distributionally robust…
Cutting planes are essential for solving mixed-integer linear problems (MILPs), because they facilitate bound improvements on the optimal solution value. For selecting cuts, modern solvers rely on manually designed heuristics that are tuned…
There has long been debates on how we could interpret neural networks and understand the decisions our models make. Specifically, why deep neural networks tend to be error-prone when dealing with samples that output low softmax scores. We…
Top-down induction of decision trees has been observed to suffer from the inadequate functioning of the pruning phase. In particular, it is known that the size of the resulting tree grows linearly with the sample size, even though the…
Domain knowledge can often be encoded in the structure of a network, such as convolutional layers for vision, which has been shown to increase generalization and decrease sample complexity, or the number of samples required for successful…
The problem of learning the structure of a high dimensional graphical model from data has received considerable attention in recent years. In many applications such as sensor networks and proteomics it is often expensive to obtain samples…
Strategic classification, i.e. classification under possible strategic manipulations of features, has received a lot of attention from both the machine learning and the game theory community. Most works focus on analysing properties of the…