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We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT…
Solving combinatorial optimization problems involve satisfying a set of hard constraints while optimizing some objectives. In this context, exact or approximate methods can be used. While exact methods guarantee the optimal solution, they…
We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
We present an standard constraints generation algorithm to find an explicit set whose robustness is equal to the robustness of the feasible solution set of a combinatorial optimization problem with cost uncertainty. Computational experience…
Optical computing often employs tailor-made hardware to implement specific algorithms, trading generality for improved performance in key aspects like speed and power efficiency. An important computing approach that is still missing its…
This paper proposes a multi-step probabilistic forecasting framework using a single neural-network based model to generate simultaneous point and interval forecasts. Our approach ensures non-crossing prediction intervals (PIs) through a…
Conceptual process design is a crucial aspect of chemical engineering that involves process synthesis. Mixed-integer nonlinear programming is a powerful framework for modeling such design problems by combining discrete and continuous…
Quantum annealing is a heuristic algorithm for searching the ground state of an Ising model. Heuristic algorithms aim to obtain near-optimal solutions with a reasonable computation time. Accordingly, many algorithms have so far been…
Hyperbolic polynomials is a class of real-roots polynomials that has wide range of applications in theoretical computer science. Each hyperbolic polynomial also induces a hyperbolic cone that is of particular interest in optimization due to…
Decades of exponential scaling in high performance computing (HPC) efficiency is coming to an end. Transistor based logic in complementary metal-oxide semiconductor (CMOS) technology is approaching physical limits beyond which further…
Ou et al. (2022) introduce the problem of learning set functions from data generated by a so-called optimal subset oracle. Their approach approximates the underlying utility function with an energy-based model, whose parameters are…
For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models…
Domain-specific heuristics are a crucial technique for the efficient solving of problems that are large or computationally hard. Answer Set Programming (ASP) systems support declarative specifications of domain-specific heuristics to…
We discuss efficient methods to optimize the metrological performance over local Hamiltonians in a bipartite quantum system. For a given quantum state, our methods find the best local Hamiltonian for which the state outperforms separable…
Backpropagation (BP), the standard learning algorithm for artificial neural networks, is often considered biologically implausible. In contrast, the standard learning algorithm for predictive coding (PC) models in neuroscience, known as the…
In this paper we propose for the first time the hyperparameter optimization (HPO) algorithm POCAII. POCAII differs from the Hyperband and Successive Halving literature by explicitly separating the search and evaluation phases and utilizing…
Sparse decision tree optimization has been one of the most fundamental problems in AI since its inception and is a challenge at the core of interpretable machine learning. Sparse decision tree optimization is computationally hard, and…
In discrete-variable black-box optimization, the number of candidate solutions grows combinatorially, while each evaluation is often expensive. Therefore, it is important to identify promising solutions efficiently within a limited number…
In optimization routines used for on-line Model Predictive Control (MPC), linear systems of equations are usually solved in each iteration. This is true both for Active Set (AS) methods as well as for Interior Point (IP) methods, and for…