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Stochastic Multi-Objective Optimization (SMOO) is critical for decision-making trading off multiple potentially conflicting objectives in uncertain environments. SMOO aims at identifying the Pareto frontier, which contains all mutually…
In this paper, we propose a fast method for exactly enumerating a very large number of all lower cost solutions for various combinatorial problems. Our method is based on backtracking for a given decision diagram which represents all the…
Graph search planning algorithms for navigation typically rely heavily on heuristics to efficiently plan paths. As a result, while such approaches require no training phase and can directly plan long horizon paths, they often require…
It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper,…
In supervised learning, decision trees are valued for their interpretability and performance. While greedy decision tree algorithms like CART remain widely used due to their computational efficiency, they often produce sub-optimal solutions…
Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
The Maximally Diverse Grouping Problem (MDGP) is the problem of assigning a set of elements to mutually disjoint groups in order to maximise the overall diversity between the elements. Because the MDGP is NP-complete, most studies have…
We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding…
Optimal decision tree (\odt) is a fundamental problem arising in applications such as active learning, entity identification, and medical diagnosis. An instance of \odt is given by $m$ hypotheses, out of which an unknown ``true'' hypothesis…
Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the…
In addition to the best model architecture and hyperparameters, a full AutoML solution requires selecting appropriate hardware automatically. This can be framed as a multi-objective optimization problem: there is not a single best hardware…
We tackle the problem of goal-directed graph construction: given a starting graph, a budget of modifications, and a global objective function, the aim is to find a set of edges whose addition to the graph achieves the maximum improvement in…
Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…
Gradient Boosted Decision Trees (GBDTs) are dominant machine learning algorithms for modeling discrete or tabular data. Unlike neural networks with millions of trainable parameters, GBDTs optimize loss function in an additive manner and…
We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions…
Although many real-world stochastic planning problems are more naturally formulated by hybrid models with both discrete and continuous variables, current state-of-the-art methods cannot adequately address these problems. We present the…
In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…
It is desirable in many multi-objective machine learning applications, such as multi-task learning with conflicting objectives and multi-objective reinforcement learning, to find a Pareto solution that can match a given preference of a…