Related papers: Contextual Strongly Convex Simulation Optimization…
We consider a smoothed online convex optimization (SOCO) problem with predictions, where the learner has access to a finite lookahead window of time-varying stage costs, but suffers a switching cost for changing its actions at each stage.…
This paper is devoted to first-order algorithms for smooth convex optimization with inexact gradients. Unlike the majority of the literature on this topic, we consider the setting of relative rather than absolute inexactness. More…
Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…
The worst-case robust adaptive beamforming problem for general-rank signal model is considered. Its formulation is to maximize the worst-case signal-to-interference-plus-noise ratio (SINR), incorporating a positive semidefinite constraint…
In many situations, simulation models are developed to handle complex real-world business optimisation problems. For example, a discrete-event simulation model is used to simulate the trailer management process in a big Fast-Moving Consumer…
Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
This paper focuses on the online saddle point problem, which involves a sequence of two-player time-varying convex-concave games. Considering the nonstationarity of the environment, we adopt the duality gap and the dynamic Nash equilibrium…
We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence…
Large-scale nonconvex optimization problems are ubiquitous in modern machine learning, and among practitioners interested in solving them, Stochastic Gradient Descent (SGD) reigns supreme. We revisit the analysis of SGD in the nonconvex…
How can we plan efficiently in a large and complex environment when the time budget is limited? Given the original simulator of the environment, which may be computationally very demanding, we propose to learn online an approximate but much…
In this short note, we establish, for the first time, the convergence rate of SOAP, an efficient and popular matrix-based optimizer for training deep neural networks. Our analysis extends to a more general variant of SOAP that admits…
We study problem-dependent rates, i.e., generalization errors that scale near-optimally with the variance, the effective loss, or the gradient norms evaluated at the "best hypothesis." We introduce a principled framework dubbed "uniform…
We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…
The paradigm of decision-making has been revolutionised by reinforcement learning and deep learning. Although this has led to significant progress in domains such as robotics, healthcare, and finance, the use of RL in practice is…
The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…
Model Predictive Control (MPC) has shown the great performance of target optimization and constraint satisfaction. However, the heavy computation of the Optimal Control Problem (OCP) at each triggering instant brings the serious delay from…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…