Related papers: Generalized Multi-Constraint Extremum Seeking
We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the…
The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…
Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world…
In this paper, we propose a generalized conditional gradient method for multiobjective optimization, which can be viewed as an improved extension of the classical Frank-Wolfe (conditional gradient) method for single-objective optimization.…
We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control.…
Existing error-bound-based analyses for stochastic algorithms that exhibit certain descent properties, such as randomized coordinate descent and randomized projection methods, are often limited in scope and typically lead to overly…
In this work, we propose a novel optimization model termed "sum-of-minimum" optimization. This model seeks to minimize the sum or average of $N$ objective functions over $k$ parameters, where each objective takes the minimum value of a…
In this work, we introduce the Equivariance Seeker Model (ESM), a data-driven method for discovering the underlying finite equivariant symmetry group of an arbitrary function. ESM achieves this by optimizing a loss function that balances…
In this paper, we investigate the problem of source seeking with a unicycle in the presence of local extrema. Our study is motivated by the fact that most of the existing source seeking methods follow the gradient direction of the signal…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Safe learning and optimization deals with learning and optimization problems that avoid, as much as possible, the evaluation of non-safe input points, which are solutions, policies, or strategies that cause an irrecoverable loss (e.g.,…
We present a first-order method for solving constrained optimization problems. The method is derived from our previous work, a modified search direction method inspired by singular value decomposition. In this work, we simplify its…
We consider the problem of sequentially maximizing an unknown function $f$ over a set of actions of the form $(s,\mathbf{x})$, where the selected actions must satisfy a safety constraint with respect to an unknown safety function $g$. We…
In high dimensional regression settings, sparsity enforcing penalties have proved useful to regularize the data-fitting term. A recently introduced technique called screening rules propose to ignore some variables in the optimization…
Predictive algorithms are now used to help distribute a large share of our society's resources and sanctions, such as healthcare, loans, criminal detentions, and tax audits. Under the right circumstances, these algorithms can improve the…
The widespread use of AI and ML models in sensitive areas raises significant concerns about fairness. While the research community has introduced various methods for bias mitigation in binary classification tasks, the issue remains…
Extreme Learning Machine (ELM) is an emerging learning paradigm for nonlinear regression problems and has shown its effectiveness in the machine learning community. An important feature of ELM is that the learning speed is extremely fast…
Recent research has shown that seemingly fair machine learning models, when used to inform decisions that have an impact on peoples' lives or well-being (e.g., applications involving education, employment, and lending), can inadvertently…
We present a new framework for analysing the Expectation Maximization (EM) algorithm. Drawing on recent advances in the theory of gradient flows over Euclidean-Wasserstein spaces, we extend techniques from alternating minimization in…