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In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
Policy tree search is a family of tree search algorithms that use a policy to guide the search. These algorithms provide guarantees on the number of expansions required to solve a given problem that are based on the quality of the policy.…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
We study the problem of set discovery where given a few example tuples of a desired set, we want to find the set in a collection of sets. A challenge is that the example tuples may not uniquely identify a set, and a large number of…
Cutting plane methods, particularly outer approximation, are a well-established approach for solving nonlinear discrete optimization problems without relaxing the integrality of decision variables. While powerful in theory, their…
We consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-cuts) that defines the convex hull of the integer…
Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational…
We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical…
Fast, autonomous flight in unstructured, cluttered environments such as forests is challenging because it requires the robot to compute new plans in realtime on a computationally-constrained platform. In this paper, we enable this…
Decision trees are popular classification models, providing high accuracy and intuitive explanations. However, as the tree size grows the model interpretability deteriorates. Traditional tree-induction algorithms, such as C4.5 and CART,…
When using sampling-based motion planners, such as PRMs, in configuration spaces, it is difficult to determine how many samples are required for the PRM to find a solution consistently. This is relevant in Task and Motion Planning (TAMP),…
Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of…
In line with the growing trend of using machine learning to help solve combinatorial optimisation problems, one promising idea is to improve node selection within a mixed integer programming (MIP) branch-and-bound tree by using a learned…
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…
We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…
We present a study of several generic tree search techniques applied to the Sequential Ordering Problem. This study enables us to propose a simple and competitive tree search algorithm. It consists of an iterative Beam Search algorithm that…
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…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
Policy-gradient methods are widely used for learning control policies. They can be easily distributed to multiple workers and reach state-of-the-art results in many domains. Unfortunately, they exhibit large variance and subsequently suffer…
It is common to encounter situations where one must solve a sequence of similar computational problems. Running a standard algorithm with worst-case runtime guarantees on each instance will fail to take advantage of valuable structure…