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A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as…
Constraint Optimization Problems (COP) are often considered without sufficient knowledge on the boundaries of the objective variable to optimize. When available, tight boundaries are helpful to prune the search space or estimate problem…
When gradient-based methods are impractical, black-box optimization (BBO) provides a valuable alternative. However, BBO often struggles with high-dimensional problems and limited trial budgets. In this work, we propose a novel approach…
Recently, bi-level optimization (BLO) has taken center stage in some very exciting developments in the area of signal processing (SP) and machine learning (ML). Roughly speaking, BLO is a classical optimization problem that involves two…
Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however,…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
Modular composition is the problem of computing the composition of two univariate polynomials modulo a third one. For a long time, the fastest algebraic algorithm for this problem was that of Brent and Kung (1978). Recently, we improved…
Many real-world functions are defined over both categorical and category-specific continuous variables and thus cannot be optimized by traditional Bayesian optimization (BO) methods. To optimize such functions, we propose a new method that…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Byte-Pair Encoding (BPE) is a widely used method for subword tokenization, with origins in grammar-based text compression. It is employed in a variety of language processing tasks such as machine translation or large language model (LLM)…
In real-world services such as ChatGPT, aligning models based on user feedback is crucial for improving model performance. However, due to the simplicity and convenience of providing feedback, users typically offer only basic binary…
We propose an algorithm for a family of optimization problems where the objective can be decomposed as a sum of functions with monotonicity properties. The motivating problem is optimization of hyperparameters of machine learning…
In this paper, we study the computational complexity of the quadratic unconstrained binary optimization (QUBO) problem under the functional problem FP^NP categorization. We focus on four sub-classes: (1) When all coefficients are integers…
Quadratic unconstrained binary optimization (QUBO) has become the standard format for optimization using quantum computers, i.e., for both the quantum approximate optimization algorithm (QAOA) and quantum annealing (QA). We present a…
Deep Optimisation (DO) combines evolutionary search with Deep Neural Networks (DNNs) in a novel way - not for optimising a learning algorithm, but for finding a solution to an optimisation problem. Deep learning has been successfully…
Probabilistic programming systems enable users to encode model structure and naturally reason about uncertainties, which can be leveraged towards improved Bayesian optimization (BO) methods. Here we present a probabilistic program embedding…
Bayesian Optimization (BO) is an effective method for optimizing expensive-to-evaluate black-box functions with a wide range of applications for example in robotics, system design and parameter optimization. However, scaling BO to problems…
A novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the proposed method through the employment of multiple interacting…
Macro placement is the problem of placing memory blocks on a chip canvas. It can be formulated as a combinatorial optimization problem over sequence pairs, a representation which describes the relative positions of macros. Solving this…
While Bayesian Optimization (BO) is a very popular method for optimizing expensive black-box functions, it fails to leverage the experience of domain experts. This causes BO to waste function evaluations on bad design choices (e.g., machine…